Triangular approximation of intuitionistic fuzzy numbers on multi-criteria decision making problem
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Triangular approximation of intuitionistic fuzzy numbers on multi-criteria decision making problem Velu Lakshmana Gomathi Nayagam1
· Jagadeeswari Murugan1
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Most of the engineering applications depend on incomplete and imprecise information which are represented by nonlinear mathematical functions for defining membership and nonmembership functions in intuitionistic fuzzy setup. Shuyang Li and Hongxing Li have studied the approximation of conventional intuitionistic fuzzy numbers in which the membership function is bounded and nonmembership function is unbounded in nature. The concepts of intuitionistic fuzzy sets (IFSs) and interval valued intuitionistic fuzzy sets (IVIFSs) have bounded membership function and bounded nonmembership function. As the generalization of both IFSs and IVIFSs, the notion of intuitionistic fuzzy numbers of new type with bounded membership function and bounded nonmembership function has been introduced by Lakshmana et al. In this paper, the procedure for weighted triangular approximation of intuitionistic fuzzy number of new type is provided with some suitable illustrations. Moreover, some useful properties of the triangular approximation on intuitionistic fuzzy numbers have also been discussed. Keywords Intuitionistic fuzzy number · Generalized parabolic intuitionistic fuzzy numbers · Distance function · Weighting function
1 Introduction Defuzzification methods have been broadly studied and applied in many fields such as fuzzy control, data analysis, fuzzy expert system, fuzzy clustering, etc. Approximation is a kind of defuzzification with a reliable agreement balancing between the two opposite characteristics of introducing appropriate form of approximation to enhance better computation and preventing loss of information. Initially, many researchers have investigated the approximation of fuzzy numbers (FN) by interval fuzzy numbers with different assumptions in Ban (2006) and Grzegorzewski (2002). In that queue, Abbasbandy and Asady (2004) have introduced an approach to defuzzify a fuzzy quantity by the notion of trapezoidal fuzzy numbers. Grzegorzewski and Mrowka (2005) have recommended an approximation operator which Communicated by Kannan.
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Jagadeeswari Murugan [email protected] Velu Lakshmana Gomathi Nayagam [email protected]
1
Department of Mathematics, National Institute of Technology, Tiruchirappalli, India
provides a trapezoidal fuzzy number that is proximate to the original fuzzy number and having identical expected interval with the original one. Abbasbandy and Amirfakhrian (2006a) have presented a unique method to compute the nearest approximation of a fuzzy number as a polynomial. Abbasbandy and Amirfakhrian (2006b) have proposed a nearest trapezoidal form of fuzzy numbers for a generalized left right fuzzy number using the pseudo-metric on the set of all fuzzy numbers. Grzegorzewski and Mrowka (2007) have revisited the trapezoidal approximation operator which preserves the exp
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