Amin Ghodousian; Sara Zal
Abstract
In this paper, we investigate direct solution of FRE and compare their results with expected real consequences. We give an applied example formulated by a FRE problem and show that FRE defined by maximum t-conorm and an arbitrary t-norm can yield different interpretations for our example. A necessary ...
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In this paper, we investigate direct solution of FRE and compare their results with expected real consequences. We give an applied example formulated by a FRE problem and show that FRE defined by maximum t-conorm and an arbitrary t-norm can yield different interpretations for our example. A necessary condition and a sufficient condition are presented that guarantee FRE defined by maximum t-conorm and minimum t-norm attain the same solutions as human mind does. Also, we present a t-conorm and use it instead of maximum t-conorm in FRE to obtain solutions with highest similarity with real ones. Finally, we show that under some conditions, FRE defined by any t-conorm and any t-norm may find a solution which is not reasonable.
A. Ghodousian; Fatemeh Elyasimohammadi
Abstract
Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization ...
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Dombi family of t-norms includes a parametric family of continuous strict t-norms, whose members are increasing functions of the parameter. This family of t-norms covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization problem in which the constraints are defined as fuzzy relational equations (FRE) with the Dombi family of t-norms. We firstly investigate the resolution of the feasible solutions set when it is defined with max-Dombi composition and present some necessary and sufficient conditions for determining the feasibility. Also, some procedures are presented for simplifying the problem. Since the feasible solutions set of FREs is non-convex, conventional nonlinear programming methods may not be directly employed to solve the problem. Based on some theoretical properties of the problem, a genetic algorithm is presented, which preserves the feasibility of new generated solutions. Moreover, a method is presented to generate feasible max-Dombi FREs as test problems for evaluating the performance of our algorithm. The proposed method has been compared with some related works. The obtained results confirm the high performance of the proposed method in solving such nonlinear problems.
A. Ghodousian; Abolfazl Javan; Asieh Khoshnood
Abstract
Yager family of t-norms is a parametric family of continuous nilpotent t-norms which is also one of the most frequently applied one. This family of t-norms is strictly increasing in its parameter and covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, ...
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Yager family of t-norms is a parametric family of continuous nilpotent t-norms which is also one of the most frequently applied one. This family of t-norms is strictly increasing in its parameter and covers the whole spectrum of t-norms when the parameter is changed from zero to infinity. In this paper, we study a nonlinear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Yager t-norm. We firstly investigate the resolution of the feasible region when it is defined with max-Yager composition and present some necessary and sufficient conditions for determining the feasibility and some procedures for simplifying the problem. Since the feasible solutions set of FREs is non-convex and the finding of all minimal solutions is an NP-hard problem, conventional nonlinear programming methods may involve high computation complexity. For these reasons, a method is used, which preserves the feasibility of new generated solutions. The proposed method does not need to initially find the minimal solutions. Also, it does not need to check the feasibility after generating the new solutions. Moreover, we present a technique to generate feasible max-Yager FREs as test problems for evaluating the performance of the current algorithm. The proposed method has been compared with Lu and Fang’s algorithm. The obtained results confirm the high performance of the proposed method in solving such nonlinear problems.
Amin Ghodousian; A. Ahmadi; A. Dehghani
Abstract
Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called ...
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Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-conorms were suggested as addition rules by Sugeno for so-called $\lambda$–fuzzy measures. In this paper, we study a nonlinear optimization problem where the feasible region is formed as a system of fuzzy relational equations (FRE) defined by the Sugeno-Weber t-norm. We firstly investigate the resolution of the feasible region when it is defined with max-Sugeno-Weber composition and present some necessary and sufficient conditions for determining the feasibility of the problem. Also, two procedures are presented for simplifying the problem. Since the feasible solutions set of FREs