Abstract
The aim of this paper is to develop a new ranking technique for intuitionistic fuzzy numbers using the method of defuzzification based on probability density function of the corresponding membership function, as well as the complement of nonmembership function. Using the proposed ranking technique a methodology for solving linear bilevel fuzzy stochastic programming problem involving normal intuitionistic fuzzy numbers is developed. In the solution process each objective is solved independently to set the individual goal value of the objectives of the decision makers and thereby constructing fuzzy membership goal of the objectives of each decision maker. Finally, a fuzzy goal programming approach is considered to achieve the highest membership degree to the extent possible of each of the membership goals of the decision makers in the decision making context. Illustrative numerical examples are provided to demonstrate the applicability of the proposed methodology and the achieved results are compared with existing techniques.
Highlights
The concept of bilevel programming problem (BLPP) was first introduced by Candler and Townsley [1]
The BLPP is considered as a class of optimization problems where two decision makers (DMs) locating at two different hierarchical levels independently control a set of decision variables paying serious attention to the benefit of the others in a highly conflicting decision making situation
Let f(x) be the probability density function corresponding to the normal triangular IFNs (TIFNs) Ã which is defined as f (x) = λf1 (x) + (1 − λ) f2 (x), (0 ≤ λ ≤ 1) . (9)
Summary
The concept of bilevel programming problem (BLPP) was first introduced by Candler and Townsley [1]. In fuzzy BLPP [37] it is sometimes realized that the concept of membership function does not provide satisfactory solutions in a highly conflicting decision making situation. In this context IFNs can be used to capture both the membership and nonmembership degrees of uncertainties of both the DMs. there are some real world situations, where randomness and fuzziness occur simultaneously. To explore the potentiality of the proposed approach, two illustrative examples are considered and solved and the achieved solutions are compared with the predefined technique developed by Dubey and Mehra [29]
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