α-Cut Approach for Solving Fuzzy Rough Multi-Objective Quadratic Programming Problem

Abstract

In this paper, we introduce a new operation on alpha cut for fuzzy rough and fully fuzzy rough multi-objective quadratic programming problems. Realistic quadratic programming problems often encounter uncertainty as well as indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy and fuzzy rough approaches are applied to such a problem. This paper proposes an effective method to solve the problem of fully fuzzy and fuzzy rough multi-objective quadratic programming where all the variables and parameters are fully fuzzy rough and fuzzy rough triangular numbers. Firstly, a fuzzy rough multi-objective quadratic problem has turned into an equivalent rough multi-objective quadratic programming problem with α-cut. Moreover, from the problem obtained, four crisp multi-objective quadratic programming problems are generated, and the resulting problems are solved as a crisp quadratic programming problem using a weighted method. We use Kuhn-Tucker conditions to solve the four crisp quadratic programming problems. An algorithm to solve (FRMOQP) problem with α-cut will be introduced. An illustrative example will be given. Secondly, a fully fuzzy rough multi-objective quadratic problem has turned into an equivalent fully rough multi-objective quadratic programming problem. Moreover, from the problem obtained four crisp multi-objective quadratic programming problems are generated, and the resulting problems are solved as a crisp quadratic programming problem using a weighted method. An algorithm to solve problems will be introduced. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.