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Defuzzification method for ranking fuzzy numbers based on centroids and maximizing and minimizing set

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This paper proposes a new method on ranking fuzzy numbers through the process of defuzzification by using maximizing and minimizing set on the triangular fuzzy numbers formed from generalized trapezoidal fuzzy numbers. | Nội dung Text Defuzzification method for ranking fuzzy numbers based on centroids and maximizing and minimizing set Decision Science Letters 8 2019 411 428 Contents lists available at GrowingScience Decision Science Letters homepage www.GrowingScience.com dsl Defuzzification method for ranking fuzzy numbers based on centroids and maximizing and minimizing set PhaniBushan RaoPeddia aDepartment of Mathematics Institute of Technology GITAM Deemed to be University Visakhapatnam Andhra Pradesh 530045 India CHRONICLE ABSTRACT Article history This paper proposes a new method on ranking fuzzy numbers through the process of Received November22 2018 defuzzification by using maximizing and minimizing set on the triangular fuzzy numbers formed Received in revised format from generalized trapezoidal fuzzy numbers. In this method a total utility value of each fuzzy December28 2018 number is defined by considering two left and two right utility values along with decision Accepted May25 2019 Available online maker s optimism which serves as a criterion for ranking fuzzy numbers and overcomes the May25 2019 limitations of Chen s 1985 Chen S. H. 1985 . Ranking fuzzy numbers with maximizing set Keywords and minimizing set. Fuzzy sets and systems 17 2 113-129 ranking method. Fuzzy numbers Centroids Maximizing set Minimizing set Index of optimism 2018 by the authors licensee Growing Science Canada. 1. Introduction Ranking fuzzy numbers is an important tool in decision making artificial intelligence data analysis and applications. Since the inception of fuzzy set theory by Zadeh 1965 and the first paper on ranking fuzzy numbers by Jain 1978 different scholars offered various techniques for ranking fuzzy numbers by representing the ill-defined quantities as fuzzy sets. Thus several studies have proposed various methods for ranking fuzzy numbers developed by applying maximizing set and minimizing set of fuzzy numbers considered to be an important breakthrough in ranking of fuzzy numbers.