Journal of Intelligent & Fuzzy Systems - Volume 31, issue 3

Authors: Veeramani, C. | Sumathi, M.

Article Type: Research Article

Abstract: Fuzzy Linear Fractional Programming problem has been used as an important planning tool for the different disciplines such as engineering, business, finance, economics, etc. In this paper, a new algorithm is developed to solve the Fuzzy Linear Fractional programming Problem (FLFPP) where the cost of the objective function, the resources and the technological coefficients are triangular fuzzy numbers. For this, the FLFPP is transformed into an equivalent deterministic Multi Objective Linear Fractional Programming Problem (MOLFPP) and solved them each objective function. From the obtained solutions, we define an imprecise and aspiration level for each objectives. Hence, the objectives are transformed …as fuzzy goal. Then the goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables. Finally, two real examples and one case study problem will be used to illustrate our algorithm and compare it with the existing method. Show more

Keywords: Triangular fuzzy number, linear programming problem, multi objective linear programming problem, goal programming

DOI: 10.3233/JIFS-15712

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1831-1843, 2016

Authors: Liu, Jian | Zhang, X.X.

Article Type: Research Article

Abstract: With the increase of massive data, a large number of business applications began to seek effective and scalable frameworks for data storages and processing. Under this background, emerging technologies for big data, such as Hadoop-based systems that use scalable distributed storage system HBase, become available. Since most of business data nowadays are stored in relational databases, and information imprecision and uncertainty widely exist in real-world applications, there is an increasing willingness to manage large-scale fuzzy relational data in the Hadoop-based platform. This paper concentrates on fuzzy information modeling in HBase. In particular, we investigate the formal transformation from the fuzzy …relational data model to the HBase model and develop a set of mapping rules to assist in the transformation process. In addition, we present a generic approach to transform the fuzzy relational algebra into the fuzzy HBase manipulation language. Show more

Keywords: HBase, fuzzy relational data, modeling, mapping

DOI: 10.3233/JIFS-15899

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1845-1857, 2016

Authors: Hou, Shixi | Fei, Juntao

Article Type: Research Article

Abstract: This paper proposed an adaptive fuzzy state feedback controller for a three-phase active power filter (APF) based on a Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy model is based on the APF dynamic model in the dq frame, which ensures that the current control dynamic and DC capacitor voltage dynamic become decoupled. By using the parallel distributed compensation (PDC), local linear state feedback controller could be designed for each T-S fuzzy sub-model. To deal with the parametric uncertainties and external disturbances, a parameter estimation scheme for tuning the parameters of T-S fuzzy model is designed and the parameters are adjusted …online by the adaptive law derived from the Lyapunov stability analysis. Simulation studies demonstrate that the proposed control method exhibit excellent performance in both steady state and transient operation during balanced and unbalanced load, and source voltage. Show more

Keywords: T-S fuzzy, active power filter, parameter estimation, Lyapunov stability analysis

DOI: 10.3233/JIFS-15997

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1859-1868, 2016

Authors: Akbaş, Serkan | Dalkiliç, Türkan Erbay

Article Type: Research Article

Abstract: Multi-criteria decision making method is used in such cases having multiple targets. Multi-objective linear programming problems, which deal with uncertain measurements for both objectives and constraints, are solved by fuzzy multi-objective linear programming methods. Analytic hierarchy process (AHP), one of the multi-criteria decision-making methods based on weighting of objectives, is designed to solve complex problems. In this study, multiple criteria decision making problems and decision makers’ opinions on these problems as well as their solution processes are discussed. Firstly, a fuzzy multi objective linear programming problem is solved using the approaches of Zimmerman and Hybrid. In the literature, these methods …are applied using triangular fuzzy numbers based on decision makers’ opinions only in cases where the objective function is minimization. In this study, as an alternative to the triangular fuzzy numbers, trapezoidal fuzzy numbers are defined, and both minimization and maximization of objective functions are examined. Finally, a solution algorithm for a fuzzy multi-objective linear programming problem is proposed under some given conditions. The algorithm is applied to a sample problem that involves modeling of a congress organizing which aims to place attendees to accommodations under specific objectives and constraints. In the evaluation phase of the algorithm, targets are weighted by using triangular and trapezoidal fuzzy numbers. At the end, the results of the proposed algorithm are compared with the results of other methods in the literature. Show more

Keywords: Analytic hierarchy process, fuzzy multi-objective linear programming, trapezoidal fuzzy numbers

DOI: 10.3233/JIFS-16041

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1869-1879, 2016

Authors: Shahzadi, Sundas | Akram, Muhammad

Article Type: Research Article

Abstract: In this research article, we present a novel frame work for handling intuitionistic fuzzy soft information by combining the theory of intuitionistic fuzzy soft sets with graphs. We present the concepts of intuitionistic fuzzy soft graphs, regular intuitionistic fuzzy soft graphs and irregular intuitionistic fuzzy soft graphs. We illustrate these concepts by describing several examples. We investigate some of their related properties. We introduce the notion of edge regular intuitionistic fuzzy soft graphs and present some of their interesting properties. We also present an application of intuitionistic fuzzy soft graphs in decision-making.

Keywords: Regular intuitionistic fuzzy soft graphs, irregular intuitionistic fuzzy soft graph, edge regular intuitionistic fuzzy soft graphs, decision-making

DOI: 10.3233/JIFS-16120

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1881-1895, 2016

Authors: Jamwal, Prashant K. | Hussain, Shahid

Article Type: Research Article

Abstract: Robotic devices can be potentially used to assist physical therapy treatments in order to restore musculoskeletal system malfunctions owing to neurological disorders. Cable actuated parallel robots, despite their obvious benefits such as enhanced workspace, light weight, and flexibility, are not popularly used in ankle rehabilitation treatments, due to their complex mechanism and cable actuation issues. In order to address these issues, it is recommended to carry out robot design optimization. However, design synthesis of the cable actuated parallel ankle robot calls for multi-objective optimization (MOO), since there are multiple and conflicting objectives to achieve. To acquire more choices between actuator …forces, overall stiffness of robot (which is crucial for a cable based ankle robot) and other vital design objectives, it is required to explore the extreme ends of the Pareto Front (PF) more carefully. Existing multi-objective evolutionary algorithms (MOEAs) normally focus on the convergence and may not provide solutions at the extremities of PF. Capitalizing on this improvement opportunity, this paper presents a fuzzy based MOEA, namely, biased fuzzy sorting genetic algorithm (BFSGA) which encourages solutions in the extreme zones of the PF. It is shown in this paper that using proposed method, diversity in the populations is supported and in the process wider trade-off choices of objectives can be obtained. During ankle robot design optimization, crisp objectives are defined as fuzzy objectives and competing solutions are provided an overall activation score (OAS). Subsequently OAS is used to assign a fuzzy dominance ranking to the design solutions. It is found that the BFSGA approach performs well in exploring the extreme zones of the Pareto front, which are normally overlooked by other MOEA such as NSGA-II due to their inherent mechanism. Show more

Keywords: Ankle robot, parallel mechanism, rehabilitation, design optimization, fuzzy methods

DOI: 10.3233/JIFS-16030

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1897-1908, 2016

Authors: Yuan, Jiahang | Li, Cunbin | Xu, Fangqiu | Sun, Baojun | Li, Wenle

Article Type: Research Article

Abstract: The main purpose of this paper is to research the multi-attribute group decision making (MAGDM) problems with interval-valued hesitant fuzzy numbers based on the confidence level. In this paper, we provide the confidence level of decision-making information which is applicable to put forward an optimized weight solution. Then we define the interval-valued intuitionistic hesitant fuzzy operator to aggregate decision information combing the φs transformation and Choquet integral. Taking the disadvantage of ranking by distance into account, we propose a ranking approach using the interval-valued intuitionistic hesitant fuzzy entropy. Finally, an illustrative example has been made to demonstrate the validity …and feasibility of the proposed method. Show more

Keywords: Interval-valued intuitionistic hesitant fuzzy numbers, confidence levels, Choquet integral, φs transformation

DOI: 10.3233/JIFS-16092

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1909-1919, 2016

Authors: Gong, Yanbing | Dai, Liangliang | Hu, Na

Article Type: Research Article

Abstract: Determining the ordered weighted averaging (OWA) operator weights is important in decision making applications. Several approaches have been proposed in the literature to obtain the associated weights. This paper provides two new disparity models to obtain the associated weights, which is determined by considering the absolute deviation and relative deviation of any distinct pairs of weights. The proposed mathematical models improve the existing minimize disparity approach and chi-square method, which is suggested by Amin and Emrouzenjad (2006, 2010) and Wang (2007). A numerical example and an application in search engines prove the usefulness of the generated OWA operator weights.

Keywords: OWA operator, absolute difference, relative difference

DOI: 10.3233/JIFS-16108

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1921-1927, 2016

Authors: Altunkaynak, Abdusselam | Elmazoghi, Hasan G.

Article Type: Research Article

Abstract: Neuro-fuzzy (NF) systems were applied to develop a new model for enhancing the prediction accuracy of breach formation time of embankment dams (t f ), which is widely recognized to have uncertainty and affects the accuracy of dam breaks simulations. NF is based on expert knowledge which is trained by a learning algorithm derived from neural network theory and defined by a set of IF-THEN rules, each of which establishes a local linear input-output relationship between the variables of the model. The erodibility of the embankment material, the height of water and volume of water above the breach invert …were taken as the input variables that contribute to t f . Historical data from 45 embankment dam failures were randomly divided into two sets and used to train and test the performance of the developed model. Two models, without and with inclusion of the erodibility as input variable, were addressed. To train the models two different output types with ten different combinations of input fuzzy sets were examined. Therefore, 40 different NF models were investigated in order to obtain the best model that adequately resembles the observed t f values of the testing dataset. The results of the NF model were also compared with the results of the best available regression models (RM) and a recent gene expression programming (GEP). Three statistical evaluation parameters were used to evaluate the results of the models. Test results show the potential of the developed NF model which performed better than the available RM and GEP. Show more

Keywords: Breach time, dam breach, embankment, erodibility, neuro-fuzzy

DOI: 10.3233/JIFS-16115

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1929-1940, 2016

Authors: Bhardwaj, Amit Kumar | Gajpal, Yuvraj | Singh, Maninder

Article Type: Research Article

Abstract: Integrated Network Traffic Visualization System (INTVS) is a security system used for decision making against the malicious traffic. This paper presents usage of fuzzy fault tree analysis (FFTA) technique to get the reliability of INTVS. Fault-tree analysis incorporates the trapezoidal fuzzy numbers and minimal cut sets (MCSS) approach for reliability assessment of INTVS. The analysis performed in this paper can be used to calculate reliability of network security system. A case study is demonstrated to calculate the reliability of INTVS security system, which is implemented in Thapar University, India.

Keywords: Security system, fuzzy reliability analysis, fuzzy fault tree analysis, integrated network traffic visualization system, trapezoidal fuzzy number

DOI: 10.3233/JIFS-16128

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1941-1953, 2016

Authors: Kaur, Jeevan Jot | Kumar, Amit

Article Type: Research Article

Abstract: In this paper, it is pointed out that in the existing methods [Sarangam Majumdar, Numerical solutions of fuzzy complex system of linear equations, German Journal of Advanced Mathematical Sciences 1 (2013), 20–26] for solving fuzzy complex system of linear equations in which all the parameters except variables are represented by triangular/trapezoidal fuzzy complex numbers as well as the fuzzy complex system of linear equations in which all the parameters except coefficients are represented by triangular/trapezoidal fuzzy complex numbers, Majumdar has assumed that on subtracting a fuzzy number from itself, the obtained value is a zero fuzzy number as well …as on dividing a fuzzy number by itself, the obtained value is a unit fuzzy number. To resolve these flaws of the existing methods, two new methods (named as Mehar method and Keerat method) are proposed for solving the same systems of fuzzy complex linear equations. Show more

Keywords: Fuzzy number, fuzzy complex number, system of fuzzy complex linear equations

DOI: 10.3233/JIFS-16134

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1955-1965, 2016

Authors: Zhang, Chun-Lian

Article Type: Research Article

Abstract: Supply chain finance is a new financing model that makes the industry chain as an organic whole chain to develop financing services. Its purpose is to combine with financial institutions, companies and third-party logistics companies to achieve win-win situation. The supply chain is designed to maximize the financial value. The supply chain finance business in our country is still in its early stages. Conducting the research on risk assessment and control of the supply chain finance business has an important significance for the promotion of the development of our country supply chain finance business. The paper investigates the dynamic multiple …attribute decision making problems, in which the decision information, provided by decision makers at different periods, is expressed in intuitionistic fuzzy numbers. We first develop one new aggregation operators called dynamic intuitionistic fuzzy Hamacher weighted averaging (DIFHWA) operator. Moreover, a procedure based on the DIFHWA and IFHWA operators is developed to solve the dynamic multiple attribute decision making problems where all the decision information about attribute values takes the form of intuitionistic fuzzy numbers collected at different periods. Finally, an illustrative example for risk assessment of supply chain finance is given to verify the developed approach and to demonstrate its practicality and effectiveness. Show more

Keywords: Dynamic multiple attribute decision making, dynamic intuitionistic fuzzy Hamacher weighted averaging (DIFHWA) operator, intuitionistic fuzzy Hamacher weighted averaging (IFHWA) operator, risk assessment, supply chain finance

DOI: 10.3233/JIFS-16174

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1967-1975, 2016

Authors: Zhao, Yi-Ding | Li, Zhi-Min | Zhang, Xi-Guang

Article Type: Research Article

Abstract: Software is omnipresent in our daily lives. Delivering quality software on schedule and in budget has become the challenge for most companies. As software size and complexity are increasing at a geometric rate, assuring software quality is becoming more difficult. Thus, how to control and manage software quality has attracted more and more attentions. In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. We first introduce some operations on the fuzzy number intuitionistic fuzzy sets. Then, we further develop the fuzzy number intuitionistic fuzzy Hamacher power weighted average (FNIFHPWA) operator. Then, we …apply the fuzzy number intuitionistic fuzzy Hamacher power weighted average (FNIFHPWA) operator to deal with multiple attribute decision making under the fuzzy number intuitionistic fuzzy environments. Finally, an illustrative example for evaluating the software quality is given to verify the developed approach. Show more

Keywords: Multiple attribute decision making (MADM), fuzzy number intuitionistic fuzzy sets, Hamacher aggregation operators, fuzzy number intuitionistic fuzzy Hamacher power weighted average (FNIFHPWA) operator, software quality evaluation

DOI: 10.3233/JIFS-16190

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1977-1985, 2016

Authors: Hung, Jui-Chung

Article Type: Research Article

Abstract: Stock market volatility exhibits characteristics such as clustering and time-varying fluctuations. This paper proposes a two-stage method for addressing these concerns. The involved procedure is as follows: First, a fuzzy system is used to analyze clustering regimes according to the size of fluctuations. Second, the clustering regimes of Stage I are used to establish a support vector regression (SVR) model, which is used to reduce the time-varying complexity. However, the fuzzy-SVR model combines the parameters of membership functions and SVR models, further complicating the problem. Thus, this paper presents parallel research based on a genetic algorithm (GA) for estimating the …parameters of the membership functions and SVR model. Data from four stock markets—the Taiwan Stock Exchange weighted stock index (Taiwan), the NASDAQ Composite index, the Hang Seng index (Hong Kong), and the Shanghai Composite index (Shanghai)—were analyzed in this study to illustrate the performance of the proposed model. According to the simulation results, the forecasting of out-of-sample volatility performance was significantly improved when the model accounted for the behavioral effect of both clustering and time-varying fluctuations. Show more

Keywords: Support vector regression, forecasting volatility, fuzzy system, genetic algorithm, clustering

DOI: 10.3233/JIFS-16209

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1987-2000, 2016

Authors: Zhao, Xiqing | Yang, Lianhe | Wang, Lijun

Article Type: Research Article

Abstract: As the basic necessities of human life, food, clothing, housing and transportation are of great importance to everyone, and the changes in these essential requirements of people can clearly manifest the development level of a society. China is a dominant textile producer in the world, with the textile export accounting for a large proportion of its overall trade export. In recent years, however, our textile export has encountered great challenges from both home and abroad. On the one hand, Green Barrier has raised its limits to China’s textile export; on the other hand, people have laid a greater emphasis on …environmental protection and their health, both of which call for advanced technology in the field of ecological textile. Yet the fact is that the development of China’s ecological textile is still confined to the use of innocuous raw materials and its processing confined to the category of cleaner production and industrial communities. In this paper, we investigate the multiple attribute decision making (MADM) problems for evaluating the resource integration capability of textile enterprise with hesitant fuzzy uncertain linguistic information. Then, motivated by the ideal of traditional power geometric aggregation operator, we have developed hesitant fuzzy uncertain linguistic power weighted geometric (HFULPWG) operator. Then, we have utilized hesitant fuzzy uncertain linguistic power weighted geometric (HFULPWG) operator to develop some approaches to solve the hesitant fuzzy uncertain linguistic multiple attribute decision making problems. Finally, a practical example for evaluating the resource integration capability of textile enterprise is given to verify the developed approach. Show more

Keywords: Multiple attribute decision making (MADM), hesitant fuzzy uncertain linguistic values, hesitant fuzzy uncertain linguistic power weighted geometric (HFULPWG) operator, resource integration capability, textile enterprise

DOI: 10.3233/JIFS-16216

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2001-2008, 2016

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

Article Type: Research Article

Abstract: In this paper, a new method is proposed to find the feasible (strong) fuzzy solution of a square (n  × n ) fully fuzzy linear equation system (FFLS) with triangular fuzzy numbers. The main purpose of the proposed method is to remove all the sign restrictions on the parameters and variables. Our method, which is based on the multiplication of two arbitrary triangular fuzzy numbers, converts the FFLS to a mixed integer programming problem. The method is illustrated with numerical examples.

Keywords: Linear equation system, fuzzy number, fuzzy decision making, mixed integer programming

DOI: 10.3233/JIFS-16227

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2009-2015, 2016

Authors: Wang, Jian-Bo | Wang, Ming-Zhe

Article Type: Research Article

Abstract: Communication network has been focused by a lot of researchers for years. The communication network solution is used to solve the bottleneck of the on chip communication between processors, to improve the performance of overall system, and to promote the development of high performance computer. In order to improve the efficiency of communication network design and reduce the time-to-market of communication network product, it is important to develop a useful tool to evaluate the communication network performance. Moreover, since the communication network is limited by the on-chip resources, area and power consumption, it is crucial to research the optimization method …with various constraint conditions to enhance the communication network performance. This paper demonstrates on the multiple attribute decision making problems to testify the comprehensive performance of communication network with the fuzzy number intuitionistic fuzzy information. Some operations on the fuzzy number intuitionistic fuzzy sets are provided in advance. Afterwards, we propose the fuzzy number intuitionistic fuzzy Hamacher correlated geometric (FNIFHCG) operator. Then, we apply the FNIFHCG operator to tackle the multiple attribute decision making with the fuzzy number intuitionistic fuzzy information. At last, an example to test the performance of communication network is proposed. Show more

Keywords: Comprehensive performance evaluation, fuzzy number intuitionistic fuzzy sets, fuzzy number intuitionistic fuzzy Hamacher correlated geometric (FNIFHCG) operator, communication network

DOI: 10.3233/JIFS-16238

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2017-2025, 2016

Authors: Ali, Javid | Ahmed, M.A. | Nafadi, H.A.

Article Type: Research Article

Abstract: The purpose of this paper is to introduce the notion of hybrid tangential property for pairs of single-valued and multi-valued mappings in modified intuitionistic fuzzy metric spaces and we prove common fixed point theorems for such mappings in modified intuitionistic fuzzy metric spaces.

Keywords: Modified IFMS, hybrid map, common fixed point

DOI: 10.3233/JIFS-16315

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2027-2033, 2016

Authors: Zhou, Ge

Article Type: Research Article

Abstract: From the beginning of 21th, enterprise’s competition predominance depends on capability of green supply chain. Suppliers are fountains of green supply chain, and the performance will directly influence the whole supply chain performance. The green supplier performance management is a key and difficult question in green supply chain manage system, which contains two cores, supplier performance evaluation and performance improvement. With the practice of two items, enterprise can control supplier performance continuously, and take improve actions in time, make the supplier performance to achieve requested level. Finally, enterprise can optimize the competition capability. In this paper, we investigate the multiple …attribute decision making (MADM) problems for supplier performance evaluation with triangular fuzzy information. Motivated by the idea of Bonferroni mean and Einstein operations, we develop the aggregation techniques called the triangular fuzzy Einstein Bonferroni mean (TFEBM) operator for aggregating the triangular fuzzy information. For the situations where the input arguments have different importance, we then define the triangular fuzzy weighted Einstein Bonferroni mean (TFWEBM) operator, based on which we develop the procedure for multiple attribute decision making under the triangular fuzzy environments. Finally, a practical example for supplier performance evaluation is given to verify the developed approach. Show more

Keywords: Multiple attribute decision making (MADM), triangular fuzzy numbers, Bonferroni mean, triangular fuzzy Bonferroni mean (TFBM) operator, triangular fuzzy weighted Bonferroni mean (TFWBM) operator, Chinese traditional medicine industry, modernization development

DOI: 10.3233/JIFS-16396

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2035-2042, 2016

Authors: Ghorai, Ganesh | Pal, Madhumangal

Article Type: Research Article

Abstract: Recently, Ghorai and Pal [12 ] introduced the notion of m -polar fuzzy planar graphs using the concept of m -polar fuzzy multisets. In this paper, m -polar fuzzy faces and strong m -polar fuzzy faces are defined. Then m -polar fuzzy dual graph of an m -polar fuzzy planar graph is introduced with example. Some isomorphism properties of m -polar fuzzy planar graphs are also studied.

Keywords: m-polar fuzzy planar graphs, faces of m-polar fuzzy planar graphs, m-polar fuzzy dual graphs, isomorphism of m-polar fuzzy planar graphs

DOI: 10.3233/JIFS-16433

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2043-2049, 2016

Authors: Touqeer, Muhammad | Çağman, Naim

Article Type: Research Article

Abstract: The fuzzification of (weak, strong, reflexive) hyper h -ideals in hyper BCK-algebras is considered. It is shown that every fuzzy (weak, strong, reflexive) hyper h -ideal is a fuzzy (weak, strong, reflexive) hyper BCK-ideal. Relations among (fuzzy) weak hyper h -ideals, (fuzzy) hyper h -ideals, (fuzzy) strong hyper h -ideals and fuzzy reflexive hyper h -ideals are given. The hyper homomorphic pre-image of a fuzzy hyper h -ideal is discussed. It is proved that the product of fuzzy hyper h -ideals is also a fuzzy hyper h -ideal.

Keywords: Hyper BCK-algebras, fuzzy hyper h-ideal, fuzzy weak hyperh-ideal, fuzzy strong hyper h-ideal, fuzzy reflexive hyperh-ideal

DOI: 10.3233/IFS-162194

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 2051-2058, 2016