Volume 18, Issue 5 , September and October 2021
T. T. Lei; Y. Qin; Z. S. Xu; R. A. Borzooei
Volume 18, Issue 5 , September and October 2021, Pages 1-17
Abstract
Iranian Journal of Fuzzy Systems (IJFS) is an international journal, based on the WoS core collection, this paper uses bibliometric methods and tools (VOSviewer and Bibliometrix) to analyze the publications of IJFS from 2007 to 2020. A total of 716 publications are analyzed. Firstly, according to the ...
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Iranian Journal of Fuzzy Systems (IJFS) is an international journal, based on the WoS core collection, this paper uses bibliometric methods and tools (VOSviewer and Bibliometrix) to analyze the publications of IJFS from 2007 to 2020. A total of 716 publications are analyzed. Firstly, according to the basic information of the publications, including the type of publications, the number of publications, the number of citations, the average number of citations and the h-index, we conduct a general statistical analysis to explore the basic characteristics and internal structure of the publications. Afterwards, by studying the citation structure of publications, this paper analyzes which groups and fields the journal is more concerned about. For the journal itself, we combine the number of citations and the number of publications to identify the most popular publications, the most productive and influential authors/institutes/countries/regions. In the collaboration network analysis, we map the collaboration network of countries/regions, institutes and authors to explore the different levels of collaboration. The co-citation network of the journal is studied to explore the relationship between IJFS and other international academic journals. In the analysis of keywords, we discuss the development trend and hot topics of keywords over time through co-occurrence analysis, word growth graph and thematic evolution analysis. Finally, based on the above analysis, we discuss the problems and challenges that the journal may face, and some main conclusions are drawn. This study has certain reference value for the further development of the related researchers�� scientific research and the journal.
A. Piegat; M. Landowski
Volume 18, Issue 5 , September and October 2021, Pages 19-36
Abstract
The article presents a new, multidimensional arithmetic of type 2 fuzzy numbers (M-IT2-F arithmetic) in which the result is a multidimensional fuzzy set. This arithmetic increases the accuracy of calculations and the scope of problems solved in relation to the currently used interval type 2 standard ...
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The article presents a new, multidimensional arithmetic of type 2 fuzzy numbers (M-IT2-F arithmetic) in which the result is a multidimensional fuzzy set. This arithmetic increases the accuracy of calculations and the scope of problems solved in relation to the currently used interval type 2 standard fuzzy arithmetic (IT2-SF arithmetic). The proposed M-IT2-F arithmetic has mathematical properties that IT2-SF arithmetic does not have. Thanks to these properties, it provides accurate calculation results that are not over- or under-estimated in terms of uncertainty. The paper contains comparisons of both types of arithmetic in application to two problems. Fuzzy arithmetic is not a finished work and is in a phase of continuous improvement and development. M-IT2-F arithmetic is a higher form of M-IT2 (non-fuzzy) arithmetic.
N. Q. Liu; Y. J. Chen; Y. K. Liu
Volume 18, Issue 5 , September and October 2021, Pages 37-51
Abstract
This paper studies a class of credibilistic optimization (CO) problems, in which a convex objective is minimized subject to ambiguous credibilistic constraints. The considered CO problem is usually computational intractable. Our purpose in this paper is to discuss the robust counterpart approximations ...
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This paper studies a class of credibilistic optimization (CO) problems, in which a convex objective is minimized subject to ambiguous credibilistic constraints. The considered CO problem is usually computational intractable. Our purpose in this paper is to discuss the robust counterpart approximations of ambiguous credibilistic constraints. Under mild assumptions, the closed property about the feasible region of credibilistic constraint is discussed. Using the obtained results, this paper deals with the robust counterpart approximations of credibilistic constraints under two types of ambiguity sets of possibility distributions. The first type is exponential function-based ambiguity set of possibility distribution, while the second type of ambiguity set is a particular case of the first one, and it is based on range and expectation information of fuzzy variables. The developed approximation techniques are capable to utilize the knowledge of ambiguity sets of possibility distributions when building distribution uncertainty-immunized solutions. As a result, the obtained safe approximations of ambiguous credibilistic constraints are computationally tractable convex/linear constraints. To apply the proposed approximation approach, a portfolio optimization problem is addressed, in which the investor is to find a portfolio to maximize the value-at-risk of his total return under the support and expectation information of uncertain returns. We use two types of robust counterpart approximations to credibilistic constraints. The computational results support our arguments.
M. Kalina; O. Staˇsov´a
Volume 18, Issue 5 , September and October 2021, Pages 53-68
Abstract
The paper deals with uninorms and nullnorms as basic semi-group operations which are commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In [Kalina 2019], they were introduced on bounded posets. This contribution ...
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The paper deals with uninorms and nullnorms as basic semi-group operations which are commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In [Kalina 2019], they were introduced on bounded posets. This contribution is a generalization and extension of the results in [Kalina 2019]. Some necessary and some sufficient conditions for the existence of idempotent uninorms and idempotent nullnorms on bounded posets are studied. Finally, some application examples are provided.
A. Vafamand; A. Fatehi; S. M. Emad Oliaee Oliaee
Volume 18, Issue 5 , September and October 2021, Pages 69-85
Abstract
This paper proposes a fuzzy-GPC based on a mathematical model of human immunodeficiency virus (HIV) to determine the drug dosage and control the progression of the illness. For this purpose, a Takagi-Sugeno (TS) fuzzy model is generated to identify the nonlinear behavior of HIV. The parameters of HIV ...
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This paper proposes a fuzzy-GPC based on a mathematical model of human immunodeficiency virus (HIV) to determine the drug dosage and control the progression of the illness. For this purpose, a Takagi-Sugeno (TS) fuzzy model is generated to identify the nonlinear behavior of HIV. The parameters of HIV are estimated by the least square error (LSE) estimation method. Moreover, three scenarios are proposed to control HIV. In scenario 1, according to TS fuzzy model, generalized Predictive Control (GPC) is designed for a daily base drug therapy. Scenario 2 and 3 are more practical. In scenario 2, since the biological behavior of patients are different, the variation in the patients biology is taken into account by generating data according to a group of patients with varying parameters in their mathematical model. In senario3, since daily diagnosis of patient’s health is costly, it is assumed that a patient information is available every month, and drug dosage is determined each month. As a result of which, the sample time of the measurement increases to 30 make it a multi-rate system. The result shows that the TS fuzzy models the mathematical model of HIV very well, and in all scenarios, the proposed controller has a good performance and the number of healthy cells are controlled in acceptable amount.
O. C¸. S¨okmen; M. Yılmaz
Volume 18, Issue 5 , September and October 2021, Pages 87-105
Abstract
The hierarchical Chinese postman problem (HCPP), one of the kinds of Chinese postman problem (CPP), aims to visit at least once the arcs are classified according to their precedence relations and to find the shortest tour or tours. In HCPP, if the travel time values between two nodes constituting the ...
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The hierarchical Chinese postman problem (HCPP), one of the kinds of Chinese postman problem (CPP), aims to visit at least once the arcs are classified according to their precedence relations and to find the shortest tour or tours. In HCPP, if the travel time values between two nodes constituting the cost are not crisp, this problem type can be said to be the hierarchical Chinese postman problem with fuzzy travel times (HCPP-FTT). In real-life problems, as the travel time between the nodes is not fixed due to various factors, in this study triangular fuzzy numbers are used at objective function coefficients of a small-size sample problem. Different ranking methods are used to defuzzify the fuzzy numbers and the acquired results are compared. The mathematical model formed is resolved using CPLEX solver GAMS 24.2.3 software. Besides, in this study, a large-size real-life problem was discussed. The objective function coefficients representing the travel time between the two nodes in the case study discussed were considered as trapezoidal fuzzy numbers. Due to the NP-hard nature of the problem, the mathematical model cannot find solutions in large size problems in the appropriate time interval. For this reason, in this study, the heuristic method based on the Greedy Search (GS) algorithm and the meta-heuristic method based on ant colony optimization (ACO) is proposed for the solution of the real-life problem. The proposed algorithms are coded using the Matlab-2019b programming language. Using the developed algorithms, the results of different ranking methods and solution times were compared.
M. Akram; Shumaiza Shumaiza
Volume 18, Issue 5 , September and October 2021, Pages 107-127
Abstract
The preference ranking organization method for enrichment of evaluations (PROMETHEE) {constitutes a family of outranking} multiple-attribute decision-making (MADM) methods {that has been adopted by researchers from many areas during} the last years.It provides reliable and clear results {thanks to the} ...
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The preference ranking organization method for enrichment of evaluations (PROMETHEE) {constitutes a family of outranking} multiple-attribute decision-making (MADM) methods {that has been adopted by researchers from many areas during} the last years.It provides reliable and clear results {thanks to the} advantages of different types of preference functions.{In this paper, we incorporate the benefits of $q$-rung orthopair fuzzy set (for short, $q$-ROFS) in this strategy of solution.} {This model, $q$-ROFS, is a generalized form of Pythagorean fuzzy set (PFS)}, as it {broadens} the space of acceptable orthopairs and {has} an ability to deal with more elaborate and vague information.The technique of {our extension of the} PROMETHEE method {uses} $q$-rung orthopair fuzzy numbers to {render} the ratings of alternatives, {which allows us} to express {uncertain and vague information more accurately}.The usual criterion preference function {has} been used to measure the preferences of {the} alternatives.A partial ordering of alternatives is obtained by considering the outgoing and incoming flows of alternatives, which is known as PROMETHEE I.Furthermore, a complete ordering is accomplished by taking into account the procedure of PROMETHEE II.As a numerical {exercise, we consider the selection of a contractor for a construction project}.{A full analysis} is performed {to illustrate the application of the technique that stems from our approach}.{Then we compare the results that we obtain with the results from existing approaches, including $q$-rung orthopair fuzzy ELECTRE, $q$-rung orthopair fuzzy TOPSIS, $q$-rung orthopair fuzzy VIKOR and $q$-rung orthopair fuzzy aggregation operators.In this way the accuracy and effectiveness of the presented work is conclusively validated}.
X. F. Zhang; J. Ai
Volume 18, Issue 5 , September and October 2021, Pages 129-140
Abstract
This paper presents a novel method to investigate the robust stabilization problem of uncertain rectangular singular fractional order Takagi-Sugeno (T-S) fuzzy systems with the fractional order 0 < α < 1. Firstly, the uncertain rectangular singular fractional order T-S fuzzy system is transformed ...
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This paper presents a novel method to investigate the robust stabilization problem of uncertain rectangular singular fractional order Takagi-Sugeno (T-S) fuzzy systems with the fractional order 0 < α < 1. Firstly, the uncertain rectangular singular fractional order T-S fuzzy system is transformed into an augmented uncertain square singular fractional order T-S fuzzy system by designing a new T-S fuzzy dynamic compensator. Secondly, a sufficient condition in the form of linear matrix inequalities (LMI) is obtained for the robust stabilization of the uncertain rectangular singular fractional order T-S fuzzy system. Finally, a numerical example is given to verify the effectiveness of the results proposed.
C. Y. Wang; L. Wan; B. Zhang
Volume 18, Issue 5 , September and October 2021, Pages 141-154
Abstract
This paper further studies topological structures induced by L-fuzzifying approximation operators, where L denotes a completely distributive De Morgan algebra. Firstly, the Alexandrov topologies induced by L-fuzzy relations are investigated with respect to L-fuzzifying approximation operators. Especially, ...
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This paper further studies topological structures induced by L-fuzzifying approximation operators, where L denotes a completely distributive De Morgan algebra. Firstly, the Alexandrov topologies induced by L-fuzzy relations are investigated with respect to L-fuzzifying approximation operators. Especially, the relationships among those Alexandrov topologies are discussed. Secondly, pseudo-similarity sets of L-fuzzy relations are proposed based on the Alexandrov topologies induced by upper and lower L-fuzzifying approximation operators. Meanwhile, the properties of pseudo-similarity sets are discussed, where some examples are presented to show the differences between similarity set of fuzzy relations and pseudo-similarity set of L-fuzzy relations.
M. R. Seikh; S. Karmakar; O. Castillo
Volume 18, Issue 5 , September and October 2021, Pages 155-172
Abstract
The novelty of the type-2 fuzzy variable (T2FV) is its fuzzy secondary possibility distribution. Here, we aim to formulate a new defuzzification model of triangular type-2 fuzzy variables (TT2FVs) based on type reduction. We also show its superiority compared to other existing models by providing some ...
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The novelty of the type-2 fuzzy variable (T2FV) is its fuzzy secondary possibility distribution. Here, we aim to formulate a new defuzzification model of triangular type-2 fuzzy variables (TT2FVs) based on type reduction. We also show its superiority compared to other existing models by providing some numerical examples. Later, we develop a matrix game problem in the type-2 fuzzy environment to show the applicability of the proposed defuzzification method in a real-world situation. Based on this defuzzification method, two crisp linear programming models are derived, which are subsequently solved by the simplex method using LINGO 17.0 software. Also, the expected pay-off for the maximizing player is calculated as TT2FV, which is desirable. Finally, to show the validity and applicability, the proposed methodology is illustrated with the plastic ban problem.
T. N. Luan; D. H. Hoang; T. M. Thuyet
Volume 18, Issue 5 , September and October 2021, Pages 173-180
Abstract
In this paper, we introduce the concept of pseudo-continuous semicopula. We show its relationship with continuity in the second variable and provide a characterization of all semicopulas S such that the smallest semicopula-based universal integral is S-homogeneous. This completely solves Open problem ...
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In this paper, we introduce the concept of pseudo-continuous semicopula. We show its relationship with continuity in the second variable and provide a characterization of all semicopulas S such that the smallest semicopula-based universal integral is S-homogeneous. This completely solves Open problem 2.29 proposed by J. Borzov´a-Moln´arov´a et al. in the paper [2].
M. R. Setayandeh; A. R. Babaei
Volume 18, Issue 5 , September and October 2021, Pages 181-198
Abstract
A novel strategy to design optimization is expressed using the fuzzy preference function concept. This method efficiently uses the designer’s experiences by preference functions and it is also able to transform a constrained multi-objective optimization problem into an unconstrained single-objective ...
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A novel strategy to design optimization is expressed using the fuzzy preference function concept. This method efficiently uses the designer’s experiences by preference functions and it is also able to transform a constrained multi-objective optimization problem into an unconstrained single-objective optimization problem. These two issues are the most important features of the proposed method which using them, you can achieve a more practical solution in less time. To implement the proposed method, two design optimizations of an unmanned aerial vehicle are considered which are: deterministic and non-deterministic optimizations. The optimization problem in this paper is a constrained multiobjective problem that with attention to the ability of genetic algorithm, this algorithm is selected as the optimizer. Uncertainties are considered and the Monte Carlo simulation (MCS) method is used for uncertainties modeling. The obtained results show a good performance of this technique in achieving optimal and robust solutions.
Volume 18, Issue 5 , September and October 2021, Pages 201-212
