Studies on Transportation Problems under Extended Fuzzy Environment

Abstract

The objective of the study is to analyze the transportation problems under extended fuzzy environment. Transportation problem (TP) with fuzzy, falls under the broader category of linear programming and network optimization which provides a powerful framework to address uncertainty and imprecisions. To do this, the mathematical models of TP with extended fuzzy like intuitionistic fuzzy, interval valued intuitionistic fuzzy, type-2 fuzzy and type-2 intuitionistic fuzzy parameters are formulated. Ranking functions are needed to compare and find the equivalent crisp values of these fuzzy set extensions to solve the provided TPs. The new ranking functions are proposed for extended fuzzy numbers based on the mean level sets of membership and non-membership functions. Moreover, the initial transportation cost of the proposed TP can be achieved with fuzzified version of different algorithmic approaches. Then, the optimality is checked via modified distribution method for the obtained initial transportation costs. newlineIn addition, the main focus of this work is to introduce the new and special forms of type-2 intuitionistic fuzzy numbers known as generalized symmetric type-2 intuitionistic fuzzy number, normalized triangular type-2 intuitionistic fuzzy number with its arithmetic operations and ranking functions to deal uncertainties in a more precise way. Furthermore, as an application, TPs are explored using parameters as generalized symmetric type-2 intuitionistic fuzzy numbers and normalized triangular type-2 intuitionistic fuzzy number. Finally, numerical examples are given to validate the proposed approaches and show its applicability and efficiency. newline