Journal of Intelligent & Fuzzy Systems - Volume 34, issue 1

Authors: Gong, Yanbing | Yang, Shuxin | Ma, Hailiang | Ge, Min

Article Type: Research Article

Abstract: In order to increase the explanatory performance of fuzzy regression model, the least square method usually is applied to determine the numeric coefficients based on the concept of distance. In this paper, we consider the fuzzy linear regression model with fuzzy input, fuzzy output and crisp parameters and combine centroid point and radius of gyration point for defuzzification from the viewpoint of geometric quality. A new distance is introduced based on the geometric coordinate points (GCP) of triangular fuzzy number. In order to estimate of regression coefficients, we merge least square method with the new GCP distance and propose least …square GCP distance method. Finally, an example of employee job performance is given to illustrate the effective and feasibility of the method. Comparisons with existing methods show that total estimation error using the same distance criterion, the explanatory performance of the GCP method is satisfactory, and the calculation is relatively simple. Show more

Keywords: Fuzzy regression model, geometric coordinate points, least square method, performance evaluation

DOI: 10.3233/JIFS-171433

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 395-404, 2018

Authors: Bandyopadhyay, Abhirup | Kar, Samarjit

Article Type: Research Article

Abstract: Type-2 fuzzy sets are generally used to describe those membership values of fuzzy sets that are imprecise. This paper attempts to develop the theory of type-2 fuzzy partial differential equations (T2FPDE) using type-2 fuzzy initial condition. The theory of type-2 FPDEs could be used with type-2 fuzzy initial values, type-2 fuzzy boundary values and type-2 fuzzy parameters. Some natural phenomena can be modelled as dynamical systems whose initial conditions and/or parameters might be imprecise in nature. This imprecision of initial values and/or parameters are generally modelled by fuzzy sets. In this paper the concept of generalized H 2 -differentiability is …applied. This concept is based on the enlargement of the class of differentiable type-2 fuzzy mappings which are commonly known as Hukuhara derivatives. Some theorem is presented to show the solution of a fuzzy type-1 and type-2 PDE could be obtained by solving the corresponding embedded systems based on fuzzy differential inclusions. An algorithm is also developed to simulate of type-2 fuzzy partial differential equations and obtain its solution numerically. Some illustrative examples have also been provided for different type-2 FPDE models. Show more

Keywords: Type-2 FPDE, Type-2 Hukuhara partial derivatives, Type-2 fuzzy differential inclusion, numerical solutions, Type-2 fuzzy heat equation, Type-2 fuzzy wave equation, Type-2 fuzzy advection equation

DOI: 10.3233/JIFS-17175

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 405-422, 2018

Authors: Dai, Jianhua | Yan, Yuejun | Li, Zhaowen | Liao, Beishui

Article Type: Research Article

Abstract: Interval-valued information systems are general models of single-valued information systems. Interval-values appear to a way to describe the uncertainty that affects the observed objects. However, there are relatively few studies on incomplete interval-valued data. The aim of this paper is to present a dominance-based fuzzy rough set approach to incomplete interval-valued information systems. A fuzzy dominance relation which aims to describe the degree of dominance in terms of pairs of objects is proposed. Based on the proposed relation, we extend the definitions of fuzzy approximation operators and investigate the uncertainty measurement issue. A new form of fuzzy conditional entropy to …measure attribute importance is presented. Meanwhile, a corresponding heuristic attribute reduction algorithm is constructed for incomplete interval-valued decision systems. Experiments show that the presented fuzzy conditional entropy and the proposed algorithm are effective. Show more

Keywords: Dominance-based fuzzy rough set approach, incomplete interval-valued data, uncertainty measurement, conditional entropy, attribute reduction

DOI: 10.3233/JIFS-17178

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 423-436, 2018

Authors: Chen, Liang-Hsuan | Chang, Chia-Jung

Article Type: Research Article

Abstract: Fuzzy regression models (FRMs) are used to describe the contribution of the corresponding fuzzy explanatory variables in explaining the fuzzy response variable. The selection of explanatory variables greatly affects the cost of establishing an FRM and its performance in applications. This paper investigates the quality of fit and suitable variable selection for building up FRMs. Based on the existing formulation of an FRM, a theorem and four related propositions are provided and proven. Then, two fitness measures, namely R 2 and adjusted R 2 , are proposed to evaluate …the fitting performance of potential FRMs for selecting a suitable model from all possible FRMs. In addition, based on the idea of the average marginal contribution, a stepwise selection procedure that includes forward and backward selections is developed to efficiently find a suitable subset of explanatory variables without requiring the fitting of all possible FRMs. Unlike the existing selection procedure that only includes the forward selection, the backward selection in the proposed stepwise procedure can avoid multicollinearity among explanatory variables. In addition, the proposed fitness measures and stepwise selection procedure are generalized to make them applicable to any data type of explanatory variables and response. The applicability and feasibility of the proposed measures and variable selection procedure are demonstrated using numerical examples and comparisons with existing approaches. Show more

Keywords: Fuzzy sets, fuzzy regression, goodness of fit, stepwise variable selection

DOI: 10.3233/JIFS-17206

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 437-457, 2018

Authors: Meng, Xiao-Li | Shi, Fu-Gui | Yao, Jen-Chih

Article Type: Research Article

Abstract: In this paper, a fuzzy evaluation approach is developed to evaluate the efficiency of decision making units (DMUs) with a fuzzy output. In the approach, the production possibility set is spanned by all the DMUs except the DMU under evaluation, and expressed in terms of fuzzy inequalities. In addition, the line segment joining the origin to the evaluated DMU is employed in the proposed approach, and its mathematical expression is expressed by fuzzy inequality. Fuzzy efficiency of the evaluated DMU is dependent upon the number of solutions of fuzzy inequalities, and the fuzzy inequalities consist of inequalities of the production …possibility set and the line segment. Moreover, the partially ordered set and maximal element are introduced to distinguish the weak efficiency and efficiency. Finally, the use of the fuzzy approach is illustrated by means of an example. Show more

Keywords: Fuzzy evaluation, inequality approach, data envelopment analysis, decision making unit, maximal element

DOI: 10.3233/JIFS-17267

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 459-465, 2018

Authors: Phiangsungnoen, Supak | Thounthong, Phatiphat | Kumam, Poom

Article Type: Research Article

Abstract: In this paper, we introduce and prove some classes of fuzzy contractive mappings with altering distance function via α and β κ –admissible mappings in the fuzzy metric spaces. We also give some example and graph which demonstrate the validity of the hypotheses of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature. As an application to our main result a fixed point for contraction mappings of integral type in fuzzy metric spaces are presented.

Keywords: α-admissible mapping, altering distance, βκ–admissible mapping, fixed point, fuzzy metric spaces

DOI: 10.3233/JIFS-17350

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 467-475, 2018

Authors: Wang, Yan | Zacharewicz, Grégory | Traoré, Mamadou Kaba | Chen, David

Article Type: Research Article

Abstract: System inference, i.e., the building of system structure from system behavior, is widely recognized as a critical challenging issue. In System Theory, structure and behavior are at the extreme sides of the hierarchy that defines knowledge about the system. System inference is known as climbing the hierarchy from less to more knowledge. In addition, it is possible only under justifying conditions. In this paper, a new system inference method is proposed. The proposed method extends the process mining technique to extract knowledge from data and to represent complex systems. The modularity, frequency and timing aspects can be extracted from the …data. They are integrated together to construct the Fuzzy Discrete Event System Specification (Fuzzy-DEVS) model. The proposed approach consists of three stages: (1) extraction of event logs from data by using the System Entity Structure method; (2) discovery of a transition system, using process discovery techniques; (3) integration of fuzzy methods to automatically generate a Fuzzy-DEVS model from the transition system. The last stage is implemented as a plugin in the Process Mining Framework (ProM) environment. A case study is presented in which Fuzzy-DEVS model is inferred from real life data, and the SimStudio tool is used for its simulation. Show more

Keywords: System inference, process mining, fuzzy-DEVS, system entity structure, event logs

DOI: 10.3233/JIFS-17403

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 477-490, 2018

Authors: Kumar, Naresh | Antwal, Shobha | Jain, S.C.

Article Type: Research Article

Abstract: Focus of this research work is optimizing the deduplication system by adjusting the pertinent factors in content defined chunking (CDC) to identify as the key ingredients by declaring chunk cut-points and efficient fingerprint lookup using bucket based index partitioning. For efficient chunking, proposed Differential Evolution (DE) algorithm based approach is optimized Two Thresholds Two Divisors (TTTD-P) CDC algorithm where significantly it reduces the number of computing operations by using single dynamic optimal parameter divisor D with optimal threshold value exploiting the multi-operations nature of TTTD. Therefore, proposed DE based TTTD-P optimize chunking to maximize chunking throughput with increased deduplication ratio …(DR); and bucket indexing approach reduces hash values judgment time to identify and declare redundant chunk about 16 times faster than Rabin CDC, 5 times than Asymmetric Extremum (AE) CDC, 1.6 times than FAST CDC. Experimental results comparative analysis reveal that TTTD-P using fast BUZ rolling hash function with bucket indexing on Hadoop Distributed File System (HDFS) provide a comparatively maximum redundancy detection with higher throughput, higher deduplication ratio, lesser computation time and very low hash values comparison time as being best distributed deduplication for big data storage systems. Show more

Keywords: Big data, data deduplication, content defined chunking, Differential Evolution, TTTD, HDFS

DOI: 10.3233/JIFS-17593

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 491-505, 2018

Authors: Wang, Xiaosheng | Chen, Dan | Ahmadzade, Hamed | Gao, Rong

Article Type: Research Article

Abstract: An uncertain random variable is a measurable function on the chance space. It is used to describe the mixing phenomena with both randomness and uncertainty. The uncertain random sequence is a sequence of uncertain random variables indexed by integers. Three types of convergence concept of uncertain random sequence have been defined, namely, convergence in distribution, convergence almost surely and convergence in measure, and some convergence theorems have been obtained. The main purpose of this paper is to provide some limit theorems on uncertain random sequences. First, we construct two examples to illustrate the concepts of convergence almost surely and convergence …in measure for a sequence of uncertain random variables. Then an inequality for uncertain random variable is presented, which states the relationship among chance measure, probability and uncertain measure. Several theorems about convergence of uncertain random sequences are obtained by Borel-Cantelli lemma which is given based on the properties of limit superior. Finally, a convergence theorem for uncertain random series is established. The main results of this paper contain the relevant conclusions for random sequence and uncertain sequence. Show more

Keywords: Uncertain random variable, chance measure, limit theorem

DOI: 10.3233/JIFS-17599

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 507-515, 2018

Authors: Abd El-Latif, A.M.

Article Type: Research Article

Abstract: Soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. The main purpose of soft rough set is reducing the soft boundary region by increasing the lower approximation and decreasing the upper approximation. This paper is devoted to the further generalization of the soft rough set theory by using the ideal notion to reduce the soft boundary region. A new soft rough set model, called soft ideal approximation space, is proposed and its properties are derived. The new soft ideal lower and upper approximation operators are presented and their related properties are …surveyed. Show more

Keywords: Rough sets, soft rough set, Pawlak approximation space, soft ideal rough topology

DOI: 10.3233/JIFS-17610

Citation: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 1, pp. 517-524, 2018