Fuzzy goal programming applied to multi-objective programming problem with FREs as constraints

• Main Author: Kailash Lachhwani
• Format: Article
• Language: English
• Published: Growing Science 2015-09-01
• Series: Decision Science Letters
• Subjects: Fuzzy relational equations; Minimal solution; Compromise optimal solution; Fuzzy goal programming
• Online Access: http://www.growingscience.com/dsl/Vol4/dsl_2015_29.pdf

This paper presents an alternate technique based on fuzzy goal programming (FGP) approach to solve multi-objective programming problem with fuzzy relational equations (FREs) as constraints. The proposed technique is more efficient and requires less computational work than that of algorithm suggested by Jain and Lachhwani (2009) [Jain, & Lachhwani (2009). Multiobjective programming problem with fuzzy relational equations. International Journal of Operations Research, 6(2), 5563.]. In FGP formulation, objectives are transformed into the fuzzy goals using maximum and minimal solutions elements of FREs feasible solution set. A pseudo code computer algorithm is developed for computation of maximum solution of FREs. Suitable linear membership function is defined for each objective function. Then achievement of the highest membership value of each of the fuzzy goals is formulated by minimizing the sum of negative deviational variables. The aim of this paper is to present a simple and efficient solution procedure to obtain compromise optimal solution of multiobjective optimization problem with FREs as constraints. A comparative analysis is also carried out between two methodologies based on numerical examples.