Solving Fuzzy Quadratic Programming Problems with a Proposed Algorithm

TL;DR

This paper introduces a new algorithm for solving fuzzy quadratic programming problems with triangular fuzzy numbers, converting them into parametric quadratic problems to find bounds and optimal solutions efficiently.

Contribution

The paper proposes a novel algorithm that transforms fuzzy quadratic programming into parametric problems, enabling effective bounds and solutions for FQP with TFN coefficients.

Findings

The algorithm successfully computes bounds for FQP objectives.

Numerical example demonstrates the algorithm's effectiveness.

Comparison shows advantages over existing methods.

Abstract

The theory of fuzzy mathematics has been proven very effective for defining and solving optimization problems. Fuzzy quadratic programming (FQP) is a consequence of this approach. In this paper, an algorithm has been proposed to solve FQP with coefficients as triangular fuzzy numbers (TFN). The proposed algorithm converts FQP into two parametric quadratic programming (QP) problems. These QP solutions provide a lower and upper bound on the objective function of FQP. When these two values coincide, an optimal solution is achieved. This algorithm has been analyzed using a numerical example and compared with existing methods.