Solving Multi-objective Linear Fractional Programming Problem Utilizing ($\alpha , \beta )$-Cut in Triangular Intuitionistic Fuzzy Setup

Abstract

In the present communication, a new model of multi-objective linear fractional programming problem (MOLFPP) with triangular intuitionistic fuzzy parameters has been proposed for finding the permissible deviations in the objective values in view of the constraints under consideration. Here, ($\alpha , \beta )$-cuts of the triangular intuitionistic fuzzy numbers have been utilized in the proposed model to find out the level of satisfaction and to convert the fuzzy parameters into closed intervals. Here, such fuzzification has been incorporated to encounter the uncertainty and inexactness that arises in the available information. Using the variable transformation technique/Taylor’s series, the interval-valued fractional objectives have been mathematically estimated by the intervals of linear functions. The objective functions have also been assigned appropriate weights using the analytic hierarchy process. In order to consolidate the multiple objectives into a single objective, the weighting sum method has been applied. It may be observed that the MOLFPP in the interval-valued form has been analogously reduced to a pair of linear problems which provide the acceptable deviations in the objective values. For the sake of illustration and implementation of the proposed work, a numerical example related to a manufacturing company has been solved in detail.