Journal of Intelligent & Fuzzy Systems - Volume 30, issue 2

Authors: Zhang, Haidong | He, Yanping | Xiong, Lianglin

Article Type: Research Article

Abstract: In this paper, a single-granulation dual hesitant fuzzy rough set model based on dual hesitant fuzzy tolerance relations is first introduced. By the combination of multi-granulation rough sets and the single-granulation dual hesitant fuzzy rough sets, we then develop a new multi-granulation rough set model, called a multi-granulation dual hesitant fuzzy rough set. In the multi-granulation framework, two types of multi-granulation dual hesitant fuzzy rough sets are proposed, which are named the optimistic multi-granulation dual hesitant fuzzy rough sets and pessimistic multi-granulation dual hesitant fuzzy rough sets. Finally, the relationships among the single-granulation dual hesitant fuzzy rough sets, optimistic multi-granulation …dual hesitant fuzzy rough sets and pessimistic multi-granulation dual hesitant fuzzy rough sets are investigated. Show more

Keywords: Dual hesitant fuzzy tolerance relation, Single-granulation dual hesitant fuzzy rough set, Multi-granulation dual hesitant fuzzy rough set

DOI: 10.3233/IFS-151851

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 623-637, 2016

Authors: Baghmisheh, Mahdi | Ezzati, Reza

Article Type: Research Article

Abstract: In this paper we present an efficient iterative procedure based on the triangular functions (TFs) to obtain the numerical solution of the specific nonlinear fuzzy Fredholm integral equations of the second kind. The error estimation of the proposed method is given in terms of uniform modulus of continuity. Also, we prove the stability of the method with respect to the choice of the first iteration. Finally, in order to demonstrate the accuracy and the convergence of the method, some numerical examples are included.

Keywords: Nonlinear fuzzy Fredholm integral equation, iterative procedure, triangular functions, numerical stability

DOI: 10.3233/IFS-151783

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 639-649, 2016

Authors: Tahmasbpour, A. | Borzooei, R.A. | Rashmanlou, Hossein

Article Type: Research Article

Abstract: The main purpose of this paper is to introduce the notion of bipolar f -morphism on bipolar fuzzy graphs and regular bipolar fuzzy graphs. We study the action of bipolar f -morphism on bipolar fuzzy graphs and derive some elegant results on weak and co-weak isomorphism. Also, we define d 2 -degree and total d 2 -degree of a vertex in bipolar fuzzy graphs and study (2, k )-regularity and totally (2, k )-regularity of bipolar fuzzy graphs. d 2 -degree and total d 2 -degree of a vertex in bipolar fuzzy graphs are highly utilized by computer science, geometry, …algebra, number theory and operation research. In addition these properties will also be helpful to study large bipolar fuzzy graph as a combination of small, bipolar fuzzy graphs and to derive its properties from those of the smaller ones. Show more

Keywords: Total degree, totally regular bipolar fuzzy graph, bipolar f-morphism

DOI: 10.3233/IFS-151784

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 651-658, 2016

Authors: Pan, Xianli | Xu, Yitian

Article Type: Research Article

Abstract: The support vector machine (SVM) has gained prominence in classification problems. One characteristic of it is that the optimal decision hyperplane is only determined by support vectors (SVs). Inspired by this, we propose two novel sample selection methods based on the idea of potential SVs. One is the distance-based sample selection method (DSSM), it calculates the distance between each pair of samples from different classes, and then selects those nearer to the other class as potential SVs. The other is the K-nearest neighbors (Knn)-based sample selection method (KSSM), which is presented on account of the boundary nearest SVM (BNSVM). The …BNSVM regards the nearest neighbors between two classes as potential SVs. While our KSSM extends the neighbor number from one in BNSVM to k . In addition, we present a method to choose an appropriate k . Afterwards, we do classification with these potential SVs. These selected samples contain useful information for classification which ensures the accuracy of classifiers. Moreover, the DSSM and KSSM work fast since they are only related to the distance and do not need to do iterations. Experiments conducted on small datasets and large-scaled ones show the validity of our DSSM and KSSM. Show more

Keywords: SVM, Sample selection, DSSM, KSSM

DOI: 10.3233/IFS-151785

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 659-670, 2016

Authors: Karunambigai, M.G. | Akram, Muhammad | Buvaneswari, R.

Article Type: Research Article

Abstract: In this paper, the concept of strong and superstrong vertices in intuitionistic fuzzy graphs (IFGs) are introduced. Necessary and sufficient conditions for the existence of strong and superstrong vertices in intuitionistic fuzzy graphs are discussed. Necessary and sufficient conditions for an edge to be strong in intuitionistic fuzzy graphs are also dealt and the existence of strong and superstrong vertices in strong IFGs are studied. An algorithm is defined to identify an intuitionistic fuzzy steady path between two vertices of IFGs which finds application in decision making problems.

Keywords: Strong vertex, superstrong vertex, cycle IFG, strong IFG

DOI: 10.3233/IFS-151786

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 671-678, 2016

Authors: Li, Erqiang | Shi, Fugui

Article Type: Research Article

Abstract: In this paper, motivated by the free product of crisp matroids, the free product of M -fuzzifying matroids is defined when M is a finite Boolean algebra and a number of fundamental properties of the operation are derived. Parallel to crisp matroids, the minors of M -fuzzifying matroids are described in terms of the M -fuzzifying truncation operator and its dual, the M -fuzzifying Higgs lift operator.

Keywords: M-fuzzifying matroid, Free product of M-fuzzifying matroids, M-fuzzifying truncation, M-fuzzifying Higgs lift

DOI: 10.3233/IFS-151788

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 679-690, 2016

Authors: Yao, Dengbao | Liu, Xiaoxing | Zhang, Xu | Wang, Cuicui

Article Type: Research Article

Abstract: The main purpose of the paper is to develop a general analytical framework of uncertainty measures, which provides a fresh new look into the uncertain information of hesitant fuzzy sets (HFSs). We first refine the axiomatic principles of hesitant fuzzy entropy based on the fuzzy factor and hesitant factor, and propose some distance-based entropy formulas of HFSs. Then, a novel hesitant fuzzy cross-entropy is defined to measure the discrimination of uncertain information of different HFSs. Meanwhile, the relationship between cross-entropy and entropy of HFSs is also discussed, and the hesitant fuzzy entropy may be divided into arithmetic average of fuzzy …entropy and hesitant entropy. Moreover, some parameterized uncertainty measures are investigated, and two comparative examples are presented to demonstrate their reasonability. Finally, we apply these proposed measures in multiple attribute decision-making problem to illustrate their efficiency and applicability. Show more

Keywords: Hesitant fuzzy entropy, fuzzy factor, hesitant factor, cross-entropy, parameterized uncertainty measures

DOI: 10.3233/IFS-151790

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 691-703, 2016

Authors: Rafiee, R. | Khalookakaie, R. | Ataei, M. | Jalali, S.M.E. | Sereshki, F. | Azarfar, A.

Article Type: Research Article

Abstract: A fuzzy expert semi-quantitative (FESQ) method is presented to analyze the parameters influencing rock mass cavability in block caving mines. In the proposed method, fuzzy numbers are used to allow the incorporation of uncertainty in coding the interaction matrix. Since in the classic ESQ method a fixed single value is defined as the interaction between two parameters, based on one expert view, it seems necessary to improve the method to be able to cover different views of different experts. To illustrate the application of the proposed method, first the parameters influencing the cavability in the block caving mines are selected, …then a matrix of interaction between parameters are introduced using fuzzy numbers. Every fuzzy number has its own membership function designed based on experts’ views. Finally the dominant and subordinated parameters are determined and interpreted by fuzzy logic. The proposed fuzzy codding method is very useful in humanistic decision making systems with existence of uncertainty, vagueness and imprecision. Show more

Keywords: ESQ codding, fuzzy numbers, cavability, RES

DOI: 10.3233/IFS-151791

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 705-715, 2016

Authors: Zhai, Junhai | Li, Ta | Wang, Xizhao

Article Type: Research Article

Abstract: Motivated by the idea of cross-validation, a novel instance selection algorithm is proposed in this paper. The novelties of the proposed algorithm are that (1) it cross selects the important instances from the original data set with a committee, (2) it can deal with the problem of selecting instance from large data sets. We experimentally compared our algorithm with five state-of-the-art approaches which are CNN, ENN, RNN, MCS, and ICF on 3 artificial data sets and 6 UCI data sets, including 4 large data sets, ranking from 130K to 4898K in size. The experimental results show that the proposed algorithm …is very efficient and effective, especially on large data sets. Show more

Keywords: Instances selection, extreme learning machine, K–L divergence, large data sets

DOI: 10.3233/IFS-151792

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 717-728, 2016

Authors: Atagün, Akın Osman | Aygün, Emin

Article Type: Research Article

Abstract: In this paper, we introduce two new operations on soft sets, called inverse production and characteristic production, by using Molodtsov’s definition of the soft sets. We prove that the set of all soft sets over a universe U is an abelian group under the each operations and called “the inverse group of soft sets” and “the characteristic group of soft sets”. We finally show that these groups are isomorphic.

Keywords: Soft set, group structure, inverse group of soft sets, characteristic group of soft sets

DOI: 10.3233/IFS-151793

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 729-733, 2016

Authors: Salman, Ayed | Omran, Mahamed G.H. | Clerc, Maurice | Alsharhan, Salah

Article Type: Research Article

Abstract: Comprehensive Learning Particle Swarm Optimizer (CLPSO) is a state-of-the-art variant of PSO, which maintains the diversity of its swarm by learning from different exemplars on different dimensions. Preserving the swarm diversity enables CLPSO to address the premature convergence problem associated with the canonical PSO. In this paper, the performance of the recently proposed fuzzy-controlled CLPSO (FC-CLPSO) is investigated on 24 problems; five of them are real-world engineering problems and six high-dimensional problems. In addition, two new CLPSO variants inspired by the Artificial Bee Colony (ABC) algorithm are proposed, CLPSO-ABC and FC-CLSPO-ABC. These two methods are compared with CLPSO and …FC-CLPSO. The results show that FC-CLPSO-ABC outperforms the other three methods. FC-CLSPO-ABC is then compared with three other state-of-the-art swarm intelligence approaches on 24 problems. The results show that FC-CLPSO-ABC generally outperforms the other approaches. Show more

Keywords: Swarm intelligence, particle swarm optimization, comprehensive learning particle swarm optimizer, fuzzy systems, artificial bee colony, metaheuristics, stochastic search

DOI: 10.3233/IFS-151794

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 735-746, 2016

Authors: Zhao, Hua | Xu, Zeshui

Article Type: Research Article

Abstract: In this paper we develop a new measure for calculating the correlation coefficients between intuitionistic fuzzy sets (IFSs), and prove its desirable axiomatic properties. Then we present an algorithm for multi-attribute decision making. The algorithm first defines the intuitionistic fuzzy ideal solution (IFIS) and the intuitionistic fuzzy negative ideal solution (IFNIS). Then based on the IFIS, the IFNIS and the developed correlation coefficient, the algorithm gives a simple and straightforward method to rank and select the given alternatives. Two numerical examples are used to illustrate our algorithm. Finally we extend the correlation coefficient and the algorithm to interval-valued intuitionistic fuzzy …environment. Show more

Keywords: Intuitionistic fuzzy set, interval-valued intuitionistic fuzzy set, correlation coefficient, ideal point

DOI: 10.3233/IFS-151795

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 747-757, 2016

Authors: Liu, Chun-an

Article Type: Research Article

Abstract: Dynamic nonlinear constrained optimization problems (DNCOP) have been arisen in a diverse range of sciences, such as agriculture, economics, airspace engineering, chemistry, mechanics, management etc.. In order to solve DNCOP, we are interested in the designed algorithm not only to find the optimal solutions or the quasi-optimum solutions, but recover and track the trajectory of the optimal solutions changing with the time. In this paper, the considering DNCOP is transformed into a dynamic unconstrained optimization problem by adding the slack variables to the inequations constraint of the original problem firstly. Secondly, an improved imperialist competitive optimization algorithm for solving the …DNCOP is proposed. At last, the computation simulations show that the proposed algorithm is more effective and can find the better optimal solutions or the quasi-optimum solutions in environment-varying than the compared algorithms for dynamic nonlinear constrained optimization problem. Show more

Keywords: Dynamic optimization, nonlinear constrained optimization, imperialist competitive algorithm, optimal solution

DOI: 10.3233/IFS-151797

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 759-772, 2016

Authors: Xia, Meimei | Zhang, Runtong | Badr, Youakim

Article Type: Research Article

Abstract: In this paper, the multi-criteria decision making in which criteria are assumed to be dependent with each other is investigated. Choquet integral is employed to aggregate the criteria evaluations of alternatives to reflect the interactions of the criteria. Objective and subjective information are integrated to derive the interactions of the criteria. The objective information of alternatives is expressed by decision matrix, whereas the subjective information is expressed by utilities or interval preference relations. Models are given to minimize the objective and subjective information. The proposed method can be considered as an extension of the existing methods, and can obtain smaller …deviations and better overall evaluations of alternatives. Show more

Keywords: Multi-criteria decision making, objective information, subjective information, Choquet integral

DOI: 10.3233/IFS-151798

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 773-781, 2016

Authors: Li, Qing | Wang, Fanggui

Article Type: Research Article

Abstract: The generalized inverse is an important result in matrix theory. In this paper, a necessary and sufficient condition for the regularity of a given intuitionistic fuzzy matrix is provided. For regular intuitionistic fuzzy matrices, how to solve the problem of finding all generalized inverses is discussed.

Keywords: Generalized inverse, matrix, regular intuitionistic fuzzy matrix, intuitionistic fuzzy set, MR(2000) Subject Classification: 15A09

DOI: 10.3233/IFS-151800

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 783-789, 2016

Authors: Boroujeni, Marziyeh | Basiri, Abdolali | Rahmany, Sajjad | Valibouze, Annick

Article Type: Research Article

Abstract: Finding solutions for fuzzy polynomial systems has recently received much attention and many efforts have been made to make the available algorithms for solving such problems more and more efficient. In the present paper, Wu’s algorithm is introduced as a solution procedure to obtain fuzzy polynomial systems solutions. In this approach, the parametric form of the problem is first obtained from the computation of r -cuts of fuzzy polynomials. Wu’s algorithm is then applied in order to convert the parametric form of a fuzzy polynomial system into a finite number of characteristic sets. We then have the right relation between …solutions of these sets and those of the polynomial system. The most outstanding advantage of the proposed method lies in the fact that it leads to solve triangular sets amenable to easy solution. Show more

Keywords: Polynomial systems, fuzzy polynomial systems, characteristic sets, Wu’s algorithm

DOI: 10.3233/IFS-151801

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 791-800, 2016

Authors: Atta-ur-Rahman, | Qureshi, Ijaz Mansoor | Malik, Aqdas Naveed | Naseem, Muhammad Tahir

Article Type: Research Article

Abstract: Adaptive Coding and Modulation (ACM) is one of the most promising features in many communication systems like WIFI, WiMAX and DVB-S2, in terms of throughput and link utilization. In this way the transmission parameters like power, code rate and modulation symbol are adapted according to the varying link conditions. In this paper we propose a Fuzzy Rule Based System (FRBS) for an efficient ACM in DVB-S2 standard. We have taken it as a constrained optimization problem in which the link reliability and throughput is maximized, while power constraint is satisfied. To do so we have selected the standard transmission Modulations …and Codes (MODCODs) optimally using FRBS, according to the DVB-S2 downlink channel state information (CSI) at different sites. The FRBS module can easily be embedded in the ACM management module (AMM) which is a software module. Significance of the proposed scheme over other schemes is shown through simulations. Show more

Keywords: DVB-S2, FRBS, ACM, MODCODs, DVB-S

DOI: 10.3233/IFS-151802

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 801-810, 2016

Authors: Huang, Ling | Xie, Xuhuan | Zhao, Yuxin | Hu, Zhongrui

Article Type: Research Article

Abstract: The T-S fuzzy system with disturbance and fault is considered in the paper, and an observer with disturbance attenuation and fault detection is designed. With the linear matrix inequalities method, a sufficient condition on the existence of the observer with disturbance attenuation is provided, and a sufficient condition on the existence of the observer with fault detection is given, the two performance indices are then combined, and an optimization problem is formulated to solve the two problems simultaneously. A numerical example is given to show the effectiveness of the proposed method.

Keywords: T-S fuzzy system, disturbance attenuation, fault detection

DOI: 10.3233/IFS-151803

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 811-819, 2016

Authors: Beg, Ismat | Rashid, Tabasam

Article Type: Research Article

Abstract: First we give notion of integral of intuitionistic fuzzy set and introduce intuitionistic fuzzy implicator and intuitionistic fuzzy inclusion measure. Then we propose a new measure of similarity between two intuitionistic fuzzy sets based on intuitionistic fuzzy inclusion measure. Examples are given to illustrate our notion and the application of this new similarity measure in multi-criteria decision making.

Keywords: Intuitionistic fuzzy sets, intuitionistic fuzzy implication, intuitionistic fuzzy inclusion, intuitionistic fuzzy similarity measure, multi-criteria decision making

DOI: 10.3233/IFS-151805

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 821-829, 2016

Authors: Wang, Hongzhou

Article Type: Research Article

Abstract: This paper provides some existence results about first-order fuzzy differential equation with two-point boundary value condition. Firstly, we study a class of linear fuzzy differential equation and some necessary conditions for the existence of solutions are provided. Based on these conditions and the upper and lower solutions method, we obtain some existence results about first-order nonlinear differential equations with the same boundary value condition.

Keywords: Nonlinear fuzzy differential equations, boundary value problem, monotone iterative technique, upper and lower solutions

DOI: 10.3233/IFS-151806

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 831-843, 2016

Authors: Firouz, Mansour Hosseini | Ghadimi, Noradin

Article Type: Research Article

Abstract: In this paper, a new controller based on combination of Fuzzy Power System Stabilizer (FPSS) and Flexible Ac Transmission Systems (FACTS) proposed in multi machine power system environment. In this model, the power system oscillation damping has been analyzed by considering the wide area control method. A fuzzy controller is a nonlinear controller and it is not so sensitive to system topology, parameter and operating condition changes as the conventional ones. According to wide area power system complexity and variation of the loads and network conditions, FPSS has been considered in this paper. Where, this structure is based on fewer …fuzzy rules and less computational burden. Furthermore, the proposed FACTS controller has been improved by Vector Evaluated Honey Bee Mating Optimization (VEHBMO) as an optimization problem. Effectiveness of the proposed method has been applied over two case studies of single-machine infinite-bus (SMIB) and ten machine 39 bus New England power system. Obtained results demonstrate the superiority of proposed strategy. Show more

Keywords: FACTS, FPSS, VEHBMO, wide area control, multi machine power system

DOI: 10.3233/IFS-151807

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 845-859, 2016

Authors: Tosun, Umut

Article Type: Research Article

Abstract: M-Tree, Slim-Tree, DF-Tree, and Omni-Tree are some of the popular dynamic structures which can grow incrementally by splitting overflowed nodes, and adding new levels to the tree very much like the B-tree variants. Unfortunately, they have been shown to perform very poorly compared to flat structures such as AESA, LAESA, Spaghettis, and Kvp that use a fixed set of global pivots. HKvp index structure is an extension of Kvp allowing the elimination of pivots as well as the database objects. The number of pivots can be easily increased to provide more selectivity and query performance. However, there is an optimum …number of pivots for a given query radius, and using too many pivots increases the costs of queries and index initialization. In this paper, a new set of pivot elimination mechanisms is proposed to determine the right number of pivots for different query radii. The suggested pivot elimination schemes perform significant cost reduction in terms of number of distance computations, and they estimate the drop rate value for HKvp on query time. Show more

Keywords: Kvp, Hkvp, pivot elimination, distance computation

DOI: 10.3233/IFS-151808

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 861-868, 2016

Authors: Guo, Jian

Article Type: Research Article

Abstract: Failure mode and effects analysis (FMEA) is an extensively used engineering technique for defining, identifying and prioritizing the potential failure modes. Traditionally the Risk Priority Number (RPN) is used to rank the potential failure modes. In this paper, a new risk assessment methodology which combines intuitionistic fuzzy sets (IFSs) with evidence theory is proposed to analyze the potential failure modes. The risk factors S, O, and D are evaluated by using linguistic variables and intuitionistic fuzzy numbers, which can be transformed into the basic probability assignment functions. The Jousselme distance is used to compute the weights of decision makers in …order to efficiently combine highly conflicting evidence. The weighted average of evidence is obtained and the classical Dempster’s combination rule is used to combine the mass functions modified. The proposed approach is applied thereafter to the prioritization of failure modes. A numerical example for risk assessment is given to illustrate the effectiveness and rationality of the proposed method finally. Show more

Keywords: Failure mode and effects analysis, intuitionistic fuzzy set, evidence theory, Jousselme distance of evidence, group decision making

DOI: 10.3233/IFS-151809

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 869-881, 2016

Authors: Keshavarz, Esmail

Article Type: Research Article

Abstract: In this paper, a new vertex-coloring problem of a fuzzy graph with crisp vertices and fuzzy edges is studied. Membership degree of a fuzzy edge is interpreted as incompatibility degree of its associated incident vertices. This interpretation can be used to define the concept of total incompatibility . Here, unlike the traditional graph coloring problems, two adjacent vertices can receive same colors; these type of vertices and their associated edge are named incompatible vertices and incompatible edge, respectively. In proposed coloring methodology, the total incompatibility of a vertex-coloring is defined as the sum of incompatibility degrees of all incompatible …edges. Then, based on the minimum possible degree of total incompatibilities, fuzzy chromatic number of a fuzzy graph is introduced. In order to find an optimal k-coloring, with minimum degree of total incompatibly, firstly a binary programming problem is formulated. Then, a hybrid local search genetic algorithm is designed to solve the large-size problems. Practical uses of the proposed algorithm are illustrated and analyzed by different-size problems. Finally, a cell site assignment problem, as a real world application of the presented fuzzy graph vertex-coloring, is formulated and solved. Show more

Keywords: Fuzzy graph, incompatibility degree, fuzzy chromatic number, binary programming, genetic algorithm

DOI: 10.3233/IFS-151810

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 883-893, 2016

Authors: Abadpour, Arash

Article Type: Research Article

Abstract: Data clustering is the generic process of splitting a set of datums into a number of homogenous sets. Nevertheless, although a clustering process inputs datums as a set of separate mathematical objects, these entities are in fact correlated within a spatial context specific to the problem class in hand. For example, when the data acquisition process yields a 2D matrix of regularly sampled measurements, as it is the case with image sensors which utilize different modalities, adjacent datums are highly correlated. Hence, the clustering process must take into consideration the spatial context of the datums. A review of the literature, …however, reveals that a significant majority of the well-established clustering techniques in the literature ignore spatial context. Other approaches, which do consider spatial context, however, either utilize pre- or post-processing operations or engineer into the cost function one or more regularization terms which reward spatial contiguity. We argue that employing cost functions and constraints based on heuristics and intuition is a hazardous approach from an epistemological perspective. This is in addition to the other shortcomings of those approaches. Instead, in this paper, we apply Bayesian inference on the clustering problem and construct a mathematical model for data clustering which is aware of the spatial context of the datums. This model utilizes a robust loss function and is independent of the notion of homogeneity relevant to any particular problem class. We then provide a solution strategy and assess experimental results generated by the proposed method in comparison with the literature and from the perspective of computational complexity and spatial contiguity. Show more

Keywords: Fuzzy clustering, Bayesian modeling, robust clustering, correlated clustering, spatial context, bilateral clustering

DOI: 10.3233/IFS-151811

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 895-919, 2016

Authors: Kocken, Hale Gonce | Ahlatcioglu, Mehmet | Albayrak, Inci

Article Type: Research Article

Abstract: In this paper, a new algorithm is proposed to find the solutions of a general (square or nonsquare) Fully Fuzzy Linear Equation System (FFLS) with arbitrary trapezoidal fuzzy numbers, i.e. there are no sign restrictions on the variables or the parameters of the system. We introduce the “feasible (strong) fuzzy solution” and “approximate fuzzy solution” concepts, then accordingly “no solution” case of a general FFLS is defined. And a model is proposed by means of a mixed integer programming modelling of “min” and “max” concepts in the multiplication of two arbitrary trapezoidal fuzzy numbers. With the logic of goal programming, …the objective function of this model is constructed within the deviation variables. Based on the proposed model, also an algorithm is presented to determine the nature of solutions of a general FFLS. The method is illustrated with some numerical examples. Our numerical results for the examples from the literature are analyzed within some distance functions. Show more

Keywords: General fully fuzzy linear equation system, trapezoidal fuzzy number, fuzzy decision making, mixed integer programming problem, feasible and approximate fuzzy solution

DOI: 10.3233/IFS-151813

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 921-933, 2016

Authors: Al Ghour, Samer | Fora, Ali

Article Type: Research Article

Abstract: We extend the concept of being countable dense homogeneous to include fuzzy topological spaces. Our extension is proved to be a good extension in the sense of Lowen. We study the relation between fuzzy CDH spaces and some ordinary topological spaces generated by these fuzzy spaces.

Keywords: Homogeneity, countable dense homogeneity, fuzzy topological spaces, good extension

DOI: 10.3233/IFS-151815

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 935-941, 2016

Authors: Adam, Fatma | Hassan, Nasruddin

Article Type: Research Article

Abstract: Molodtsov introduced the concept of soft set as a general mathematical tool for dealing with uncertainty. In this work,we first defined a multi Q-fuzzy soft expert set and its basic operations, namely complement, union, intersection, OR and AND. We then construct a decision-making method on multi Q-fuzzy soft expert set. We finally provide an example to show that the method can be successfully applied to problems which contain uncertainties.

Keywords: Multi Q-fuzzy set, soft set, soft expert set

DOI: 10.3233/IFS-151816

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 943-950, 2016

Authors: Akram, Muhammad | Kavikumar, Jacob | Khamis, Azme Bin

Article Type: Research Article

Abstract: This paper aims at introducing the notion of intuitionistic N-fuzzy set (INFS) and its application along with its examples. As the application of this set, its idea has been applied to a newly defined algebraic structure “BiΓ-Ternary Semigroup”. The notions of intuitionistic N-fuzzy biΓ-ternary subsemigroup and intuitionistic N-fuzzy biΓ-left (right, lateral and bi) ideals have been defined and related properties have been investigated here. The characterization of biΓ-ternary semigroup under these ideals has been established.

Keywords: BiΓ-ternary smigroup, intuitionistic N-fuzzy set, intuitionistic N-fuzzy biΓ-ternary subsmigroup, intuitionistic N-fuzzy biΓ-ideal

DOI: 10.3233/IFS-151817

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 951-960, 2016

Authors: Guan, Lihe | Hu, Feng | Han, Fengqing

Article Type: Research Article

Abstract: In data mining, many real-life data sets are not only incomplete, but also encompass various kinds of knowledge and are shared by many users. Different users may prefer different kinds of knowledge. Nowadays how to mine rules meeting users’ requirements from incomplete data sets has become one of the important research issues of data mining. In this paper, we investigate decision rules induction methods in incomplete decision tables by considering attribute order. The users’ requirements are described by an attribute order. Then a hierarchical algorithm of decision rules mining based on the attribute order is proposed, and its properties and …complexity are examined. An example is given to illustrate the algorithm. Simulation experimental results show that compared with the algorithm MLEM2, the proposed algorithm is valid and effective. Show more

Keywords: Data mining, rough set, incomplete decision table, knowledge discovery

DOI: 10.3233/IFS-151818

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 961-969, 2016

Authors: Dey, Samir | Roy, Tapan Kumar

Article Type: Research Article

Abstract: Real world engineering design problems are usually characterized by the presence of many conflicting objectives. In this paper, we will make an approach to solve multi-objective structural model using parameterized t-norms based on fuzzy optimization programming technique. Here, binary t-norms are expressed in extended n-ary t-norms and their basic properties and some special cases have been discussed. In this structural model formulation, the objective functions are the weight of the truss and the deflection of loaded joint; the design variables are the cross-sections of the truss members; the constraints are the stresses in members. A classical truss optimization example is …presented here to demonstrate the efficiency of our proposed optimization approach. The test problem includes a three-bar planar truss subjected to a single load condition. This approximation approach is used to solve this multi-objective structural optimization model. The model is illustrated with numerical examples. Show more

Keywords: Multi-objective optimization, t-norms, fuzzy set, structural optimization

DOI: 10.3233/IFS-151819

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 971-982, 2016

Authors: Senthil, S. | Chandrakumar, R. David

Article Type: Research Article

Abstract: In this paper we introduce a new fuzzy c-means objective function called kernel induced fuzzy c-means based on Gaussian function for the purpose of segmentation of medical images. The originality of this algorithm is based on the fact that the conventional FCM-based algorithm considers no spatial content information, which makes it sensitive to noise. The new algorithm is formulated by incorporating the spatial neighbourhood information into the spatial neighbourhood into the original FCM algorithm by apriori probability and initialized by a kernel function induced histogram based FCM algorithm. The probability in the algorithm that indicates the spatial influence of the …neighbouring pixels on the centre pixel plays a key role in this algorithm and it obtains efficient method for calculating membership and updating prototypes by minimizing the new objective function of Gaussian based fuzzy c-means. The performance of proposed algorithm has been tested with medical images to reduce the inhomogeneities and to allow the labelling of a pixel to be influenced by the labels in its immediate neighbourhood. Also this paper compares the results of proposed method with the results of existing basic fuzzy c-means. Show more

Keywords: Fuzzy c-means, clustering, kernel function, Gaussian function, histogram, probability, segmentation

DOI: 10.3233/IFS-151820

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 983-990, 2016

Authors: Zhang, Jiguo | Liu, Gaofeng | Gong, Yanbing

Article Type: Research Article

Abstract: The paper recalls the definition of intuitionistic fuzzy sets and the principle of information diffusion and analyzes several existent point operators. Giving an axiomatic definition for transforming intuitionistic fuzzy sets into fuzzy sets, we deduce a new conversion operator which seeks to obtain one and only one fuzzy set for each intuitionistic set. A new distance measure is defined for intuitionistic fuzzy sets, and then the corresponding measure formula for the fuzzy entropy of intuitionistic fuzzy sets is proposed. Finally, some examples are illustrated for comparison with some existing formulae.

Keywords: Fuzzy entropy, transformation operator, distances, intuitionistic fuzzy sets, fuzzy sets

DOI: 10.3233/IFS-151821

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 991-998, 2016

Authors: Baban, Calin Florin | Baban, Marius | Suteu, Marius Darius

Article Type: Research Article

Abstract: The state of the textile machines can be evaluated by monitoring different parameters, such as vibration and temperature, so their maintenance can be performed a short time before the failure. However, the evolution of each monitored parameter can conduct to different decisions regarding the maintenance actions. Within this framework, fuzzy logic was proposed for planning the predictive maintenance activities of the textile machines. A fuzzy decision making system was developed and its effectiveness was illustrated for the planning of the predictive maintenance of a sewing machine needle. The results of the case study show fuzzy logic as a proactive approach …to perform when needed maintenance activities of textile machines. Show more

Keywords: Fault detection, parameters monitoring, fuzzy logic, predictive maintenance

DOI: 10.3233/IFS-151822

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 999-1006, 2016

Authors: Abbasi Ganji, Zainab | Sadeghpour Gildeh, Bahram

Article Type: Research Article

Abstract: Process capability indices are numerical measures used to determine whether the process products meet the quality requirement dedicated by the customers and producers or not. When the products’ quality counts on two or more correlated characteristics, multivariate process capability indices are applied. In this paper, we focus on two indices proposed by Shahriari and Abdollahzadeh (2009) and Taam et al. (1993). The traditional multivariate capability indices can’t be applied if the specification limits and target value of each characteristic are presented in a linguistic form. Instead, the fuzzy set theory is used to deal with these circumstances. Here, the fuzzy …formulations of the indices are developed. Furthermore, numerical examples are presented to illustrate the applicability of the proposed methods and we make a comparison between them. Show more

Keywords: Multivariate normal distribuition, multivariate capability index, fuzzy logic, triangular fuzzy number, trapezoidal fuzzy quantity

DOI: 10.3233/IFS-151823

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1007-1017, 2016

Authors: Liu, Bingsheng | Shen, Yinghua | Mu, Lingling | Chen, Xiaohong | Chen, Liwen

Article Type: Research Article

Abstract: In this paper, we regard the membership degree and the non-membership degree of the intuitionistic fuzzy set (IFS) as a whole and propose a new approach to measuring the correlation degree between the IFSs in finite sets. Like the computational process of the correlation coefficient between the real number variables, we first define the deviation of the intuitionistic fuzzy numbers, the variance of the IFS, and the covariance of the IFSs; then propose the formula to get the correlation coefficient between the IFSs. The proposed method not only reflects the symbol attribute of the correlation degree between the IFSs (the …value of the correlation coefficient lies in the interval [–1, 1]), but also makes sure the integrity of the IFS is maintained. Several examples are given to show the feasibility and advantages of the proposed method. Moreover, we extend this approach to the interval-valued intuitionistic fuzzy set (IVIFS) case. Show more

Keywords: Intuitionistic fuzzy set, interval-valued intuitionistic fuzzy set, correlation measurement, correlation coefficient, deviation

DOI: 10.3233/IFS-151824

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1019-1028, 2016

Authors: Zhang, Haidong | Shu, Lan | Liao, Shilong

Article Type: Research Article

Abstract: Interval-valued hesitant fuzzy rough set, defined by Zhang et al. [55], is an extension of hesitant fuzzy rough sets, interval-valued fuzzy rough sets and fuzzy rough sets. For further studying the theories and applications of interval-valued hesitant fuzzy rough sets, in this paper, we mainly investigate the topological structures of interval-valued hesitant fuzzy rough sets. Firstly, the concept of interval-valued hesitant fuzzy topological spaces is introduced by us. Then relationships between interval-valued hesitant fuzzy rough approximation spaces and interval-valued hesitant fuzzy topological spaces are further established. It is proved that the set of all lower approximation sets based on an …interval-valued hesitant fuzzy reflexive and transitive approximation space forms an interval-valued hesitant fuzzy topology; and conversely, for an interval-valued hesitant fuzzy rough topological space, there exists an interval-valued hesitant fuzzy reflexive and transitive approximation space such that the topology in the interval-valued hesitant fuzzy rough topological space is just the set of all lower approximation sets in the interval-valued hesitant fuzzy reflexive and transitive approximation space. That is to say, there exists a one-to-one correspondence between the set of all interval-valued hesitant fuzzy reflexive and transitive approximation spaces and the set of all interval-valued hesitant fuzzy rough topological spaces. Finally, a practical application is provided to illustrate the validity of the interval-valued hesitant fuzzy rough set model. Show more

Keywords: Interval-valued hesitant fuzzy set, Interval-valued hesitant fuzzy rough set, Interval-valued hesitant fuzzy topological space

DOI: 10.3233/IFS-151826

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1029-1043, 2016

Authors: Yang, Hai-Long | Guo, Zhi-Lian | She, Yanhong | Liao, Xiuwu

Article Type: Research Article

Abstract: Smarandache initiated neutrosophic sets (NSs) which can be used as a mathematical tool for dealing with indeterminate and inconsistent information. In order to apply NSs conveniently, single valued neutrosophic sets (SVNSs) were proposed by Wang et al. In this paper, we propose single valued neutrosophic relations (SVNRs) and study their properties. The notions of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a SVNR are introduced, respectively. Their accurate calculate formulas and some properties are explored. Some examples are also given. Finally, single valued neutrosophic relation mappings and inverse single valued neutrosophic relation mappings are introduced, and some …interesting properties are also obtained. Show more

Keywords: Single valued neutrosophic sets, single valued neutrosophic relations, kernels, closures, single valued neutrosophic relation mappings, inverse single valued neutrosophic relation mappings

DOI: 10.3233/IFS-151827

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1045-1056, 2016

Authors: Tiwari, S.P. | Yadav, Vijay K. | Dubey, M.K.

Article Type: Research Article

Abstract: The purpose of present work is to introduce and study two minimal realizations for a given fuzzy behaviour in bicategory-theoretic setup. One such realization is based on Myhill Nerode’s theory, while the other realization is based on derivative of the given fuzzy behaviour. It is shown here that there exists a unique 2-cell in bicategory of crisp deterministic fuzzy machines between both the realizations.

Keywords: Bicategory, crisp deterministic fuzzy automaton, fuzzy behaviour, minimal realization

DOI: 10.3233/IFS-151828

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1057-1065, 2016

Authors: Ghaedi, Amir | Fard, Elaheh Taherian | Fotoohabadi, Hadi | Kavousi-Fard, Farzaneh

Article Type: Research Article

Abstract: The appearance of Plug-in Electric Vehicles (PEVs) in the electric grids is providing new opportunities when some new challenges are also created. Technically, PEVs are movable loads that can benefit to both owners and utilities in case of using Vehicle-to-Grid (V2G) technology. Therefore, this article aims to investigate the Distribution Feeder Reconfiguration (DFR) effect to optimally manage PEV performance in a probabilistic framework. The proposed stochastic framework will capture the uncertainties of location of PEVs as well as driving pattern and battery State-of-Charge (SOC). In addition, a new self-adaptive evolutionary swarm algorithm based on Social Spider Optimization (SSO) algorithm is …proposed that will search the problem space globally. The simulation results on the IEEE standard test system shows the high performance of the proposed method. Show more

Keywords: Plug-in Electric Vehicle (PEV), Vehicle-to-Grid (V2G), feeder reconfiguration, Social Spider Optimization (SSO)

DOI: 10.3233/IFS-151829

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1067-1075, 2016

Authors: Akbari, Kourosh | Rahmani, Ehsan | Abbasi, Alireza | Askari, Mohammad-Reza

Article Type: Research Article

Abstract: In the current paper, the optimal placement merits of distribution generations (DGs) are investigated in the economical version of a grid-parallel mode. The proposed method is constructed based on a probabilistic approach which is called Point Estimate Method (PEM) to consider the uncertainty associated with the load demand prediction error along with the variation of cost of electricity and power production of DGs. The objective functions are the total active power losses, the total emission produced and the total cost related to the grid & DGs and cost of reliability. These functions are set to be optimized that result in …utilizing an interactive fuzzy approach based on improved particle swarm optimization (IPSO) to let the decision maker apply his/her preferences to the system. It is apt to mention that the application of the interactive fuzzy approach is based on the result of conflicting behaviors of the investigated objective functions. Through using the Tai-Power distribution test system the feasibility and the efficiency of the proposed method have been shown. Show more

Keywords: Distributed generation, stochastic modeling, point estimate method, improved particle swarm optimization

DOI: 10.3233/IFS-151883

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1077-1086, 2016

Authors: Alkhazaleh, Shawkat

Article Type: Research Article

Abstract: In 2013 Ayman A. Hazaymeh in his PhD thesis introduced the concept of time-fuzzy soft set as a generalization of fuzzy soft set. In this paper and as a generalization of neutrosophic soft set we introduce the concept of time-neutrosophic soft set and study some of its properties. We also, define its basic operations, complement, union intersection, “AND” and “OR” and study their properties. Also, we give hypothetical application of this concept in decision making problems.

Keywords: Neutrosophic set, soft set, neutrosophic soft set, time-neutrosophic soft set

DOI: 10.3233/IFS-151831

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1087-1098, 2016

Authors: Das, Debaroti | De, P.K.

Article Type: Research Article

Abstract: Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on L p metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.

Keywords: Trapezoidal intuitionistic fuzzy number(TRIFN), Triangular intuitionistic fuzzy number(TIFN), value and ambiguity index, ranking, distance measure

DOI: 10.3233/IFS-151832

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1099-1107, 2016

Authors: Chakraborty, Dipankar | Jana, Dipak Kumar | Roy, Tapan Kumar

Article Type: Research Article

Abstract: The expected value of intuitionistic fuzzy number using credibility measures has been developed here. A new method for solving a multi-objective, multi-item intuitionistic fuzzy solid transportation problems for damageable items are proposed using expected value of intuitionistic fuzzy numbers and several special cases have been derived from the proposed model. The optimal results are obtained by using three different techniques (i) Interactive satisfied method, (ii) Global criteria method and (iii) Goal programming method. A real life problem is presented to illustrate the proposed models and the results are compared in fuzzy and intuitionistic fuzzy environments.

Keywords: Intuitionistic fuzzy numbers, possibility, necessity, creditability, expected value, solid transportation problem

DOI: 10.3233/IFS-151833

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1109-1122, 2016

Authors: Ma, Zhen Ming

Article Type: Research Article

Abstract: In this paper, we shall give answers to show that two open problems, which is proposed by Turunen et al. in (Erratum to:) n -Fold implicative basic logic is Gödel logic [Soft Computing 16 (2012): 177–181,183]. That is, each n -fold positive implicative filter is an n -fold Boolean filter and in an n -fold fantastic BL-algebra, n -fold implicative basic logic and n -fold positive implicative basic logic coincide.

Keywords: Non-classical logics, BL-algebras, n-fold Boolean filters, n-fold positive implicative filters

DOI: 10.3233/IFS-151834

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1123-1126, 2016

Authors: Zhang, Zhiming

Article Type: Research Article

Abstract: Intuitionistic fuzzy rough sets are the generalization of traditional rough sets by combining intuitionistic fuzzy set theory and rough set theory. The existing researches on intuitionistic fuzzy rough sets mainly concentrate on the establishment of lower and upper approximation operators by using constructive and axiomatic approaches. Less effort has been put on the attributes reduction of databases based on intuitionistic fuzzy rough sets. The aim of this paper is to focus on attributes reduction based on intuitionistic fuzzy rough sets. After reviewing attributes reduction with traditional rough sets, some equivalent conditions to describe the relative reduction with intuitionistic fuzzy rough …sets are proposed, and the structure of reduction is completely examined. Based on discernibility matrix, an algorithm to compute all the attributes reductions is also developed. At last we employ an example to illustrate the concepts of attributes reduction. Show more

Keywords: Intuitionistic fuzzy rough set, rough set, intuitionistic fuzzy set, attributes reduction, discernibility matrix

DOI: 10.3233/IFS-151835

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1127-1137, 2016

Authors: Mareay, R.

Article Type: Research Article

Abstract: Rough set theory is an important non-numeric method for dealing with uncertainty and data mining. In this paper, we study rough sets and rough fuzzy sets on two universes via covering models. We introduce a new definition for the lower and upper approximation by taking a covering of the second universe of discourse. Some properties of the new model are revealed. We believe that this model will be more realistic in the sense that rough sets (resp. rough fuzzy sets) are approximated by sets (resp. fuzzy sets) on the same universe. Moreover, some results, examples and counter examples are provided.

Keywords: Rough sets, covering, approximation space, strong covering, rough fuzzy sets

DOI: 10.3233/IFS-151837

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1139-1146, 2016

Authors: Chou, Chien-Chang

Article Type: Research Article

Abstract: Similarity measure is one of essential concepts in fuzzy systems. This study presents a generalized similarity measure for fuzzy numbers. The generalized similarity measure for fuzzy numbers takes account of the membership degree of fuzzy number. Finally, the generalized similarity measure for fuzzy numbers is compared with nine existing methods for similarity measure of fuzzy numbers by using some sets of fuzzy numbers. The comparison result shows that the generalized similarity measure proposed in this paper seems to be generalized and promising.

Keywords: Fuzzymathematics, membership degree, generalized similaritymeasure, fuzzy decision-making, similarity relationship

DOI: 10.3233/IFS-151838

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1147-1155, 2016

Authors: Goudarzi, Sobhan | Khodabakhshi, Mohammad Bagher | Moradi, Mohammad Hassan

Article Type: Research Article

Abstract: Fuzzy functions (FFs) models were introduced as an alternate representation of the fuzzy rule based approaches. This paper presents novel Interactively Recurrent Fuzzy Functions (IRFFs) for nonlinear chaotic time series prediction. Chaotic sequences are strongly dependent on their initial conditions as well as past states, therefore feed forward FFs models cannot perform properly. To overcome this weakness, recurrent structure of FFs is proposed by placing local and global feedbacks in the output parts of multidimensional subspaces. IRFFs’ optimized parameters should minimize the output error and maximize clusters density. To achieve these contradictory goals, Non-dominated Sorting Genetic Algorithm II (NSGAII) is …applied for simultaneously optimizing the objectives. Also, feedback loop parameters are tuned by utilizing gradient descent algorithm with line search strategy based on the strong Wolfe condition. The experimental setup includes comparative studies on prediction of benchmark chaotic sequences and real lung sound data. Further simulations demonstrate that our proposed approach effectively learns complex temporal sequences and outperforms fuzzy rule based approaches and feed forward FFs. Show more

Keywords: Recurrent fuzzy functions, chaotic time series prediction, non-dominated sorting genetic algorithm, unsupervised optimal fuzzy clustering, multivariate adaptive regression spline

DOI: 10.3233/IFS-151839

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1157-1168, 2016

Authors: Senapati, Tapan | Shum, K.P.

Article Type: Research Article

Abstract: In this paper, by using the t -norm T and t -conorm S , we introduce the intuitionistic fuzzy bi-normed KU -ideals of a KU -algebra. Some properties of intuitionistic fuzzy bi-normed KU -ideals of a KU -algebra under the homomorphism are discussed. The direct product and the (T , S )-product of intuitionistic fuzzy bi-normed KU -ideals are particularly investigated. Some results obtained in this paper can be regarded as extended and generalized results recently given by S.M. Mostafa et al. concerning the intuitionistic fuzzy KU -ideals in KU -algebras.

Keywords: KU-algebra, T-norm, T-conorm, intuitionistic fuzzy bi-normed KU-ideal, homomorphism, upper(lower)-level cut

DOI: 10.3233/IFS-151841

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 2, pp. 1169-1180, 2016