Abstract concept of fuzzy sets. Attanassov & Gargov[3] expanded

Abstract Multiple Attribute Group Decision Making (MAGDM) is a most important scientific, social andeconomic endeavour. Ability to make consistent and correct choices is the essence of any decision processimbued with uncertainty. In situations where the information or the data is of the form of IntuitionisticTrapezoidal Fuzzy Numbers, to construct the MAGDM problem, Intuitionistic Trapezoidal Fuzzy WeightedGeometric (ITzFWG) and Intuitionistic Trapezoidal Fuzzy Hybrid Geometric (ITzFHG) operators are used.In this paper, a novel method of deriving the unknown decision maker weights using sumudu transformcombined with integro-differential equation is proposed and the derived weights are used in computationsfor identifying the best alternative. A numerical illustration is given to show the effectiveness and feasibilityof the proposed approach.Keywords: MAGDM, Intuitionistic Trapezoidal Fuzzy Number, ITzFWG and ITzFHG operator, SumuduTransform, Integro-differential equation.1 Introductionindent Multiple Attribute Group Decision Making (MAGDM) is a process in which multiple decision makersact collectively, analyze problems or situations, consider and evaluate alternative courses of action, andselect from among the alternatives a solution or solutions. When a group makes a decision collectively, itsjudgment can be powerful than that of any of its members. Through discussing, questioning, and collaborativeapproach, group members can identify more complete and robust solutions and recommendations. Themajor challenge of decision making is uncertainty and the major goal of decision analysis is to reduce uncertainty.To deal with qualitative, imprecise and incomplete information in decision problems, Zadeh 32suggested employing the fuzzy set theory as a modelling tool for complex systems. Intuitionistic Fuzzy Sets(IFSs) proposed by Attanassov 2 is a generalization of the concept of fuzzy sets. Attanassov & Gargov3 expanded the IFSs, using interval value to express membership and non membership function of IFSs.Szmidt & Kacprzyk 22, 23 introduced several distance functions and similarity measures for IFSs whichwere later used in various MAGDM problems. Li 8, Wei 25, 26 contributed novel approaches to the1 Department of Mathematics, Bishop Heber College, Trichy-620017, Tamilnadu, India. e-mail: [email protected] 2 Department of Mathematics, Bishop Heber College, Trichy-620017, Tamilnadu, India. e-mail: [email protected] P. John Robinson 1 and s. Jeeva 2field of fuzzy decision making. Gernstenkorn & Manko 5 and Zeng & Li 33 investigated the correlationcoefficient of IFS. Robinson 19, Robinson & Amirtharaj 9-18 and Robinson & Jeeva 20, 21 defined correlationcoefficient for different higher order intuitionistic fuzzy sets and utilized in MAGDM problems.Wu& Cao 27 investigated the same families of geometric aggregation operators with intuitionistic trapezoidalfuzzy numbers. Yager 31, Xu & Yager 30, Xu & Chen 29 and Xu 28, developed some arithmeticaggregation operators with intuitionistic, interval valued intuitionistic fuzzy information.In this work Sumudu transform combined with integro-differential equations will be proposed for determiningweights of decision makers and used for decision making problems. Hukuhara 6, Eltayeb &Kilicman 4, Khan & Razzaq 7 and Bulut et al. 3 discussed the solution of fuzzy differential equationsby fuzzy Sumudu transform. In this paper, sumudu transform are used to obtain the solution of integrodifferentialequation and it is utilized to derive the decision maker weights in MAGDM problems undertrapezoidal fuzzy sets. The feasibility and effectiveness of the proposed method are illustrated using numericalexamples.

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