Arithmetic operations on generalized intuitionistic fuzzy number and its applications to transportation problem

Abstract

Intuitionistic fuzzy has always been a subject of keen interest, and a rigorous research has also been done on it. However, those research works were mainly based on normal intuitionistic fuzzy- a generalized approach to it could hardly be seen. So in this paper, we have developed a generalized intuitionistic fuzzy number and its arithmetic operations. It is a unique attempt made by us in which for the first time two basic generalized intuitionistic fuzzy numbers namely generalized trapezoidal and generalized triangular intuitionistic fuzzy numbers have been considered to serve the purpose. All arithmetic operations have been formulated on the basis of (α, β)-cut method, vertex method and extension principle method. Comparison among those three methods using an example is given and numerical results have been presented graphically. A new method is proposed to solve generalized intuitionistic fuzzy transportation problem (GIFTP) using ranking function. To validate the proposed method we have solved a GIFTP by assuming transportation cost, supply and demand of the product in generalized intuitionistic fuzzy numbers and the optimum results have been compared with the results of normal intuitionistic fuzzy transportation problem.