Abstract
This paper presents a solution approach for multi-objective linear programming problem. We propose to involve fuzzy order relations to describe the objective functions where in ”classical” fuzzy approach the membership functions which illustrate how far the concrete point is from the solution of individual problem are studied. Further the global fuzzy order relation is constructed by aggregating the individual fuzzy order relations. Thus the global fuzzy relation contains the information about all objective functions and in the last step we find a maximum in the set of constrains with respect to the global fuzzy order relation. We illustrate this approach by an example.
Highlights
In the paper we work in the field of multi-objective linear programming (MOLP), which is an important tool for solving real-life optimization problems such as production planning, logistics, environment management, banking/finance planning etc
Our investigations are based on the fuzzy approach [16] where the membership functions are involved to prescribe how far the concrete point is from the solution of an individual problem
The paper is structured in the following way: Section 2 contains some known facts about fuzzy logic important for the further understanding of the material; we propose the general information about fuzzy relations and build the essential fuzzy relations for the realization of our scheme in Section 3; we study the aggregation of fuzzy relations in Section 4; We propose the solution approach in Section 5; we observe the numerical example in Section 6 and we conclude our paper by Section 7
Summary
In the paper we work in the field of multi-objective (or Multiple Objective) linear programming (MOLP), which is an important tool for solving real-life optimization problems such as production planning, logistics, environment management, banking/finance planning etc. Involving Fuzzy Orders for Multi-Objective Linear Programming 367 MOLP problem can be represented as follows: max Z, where Z = To justify the choice of fuzzy order let us first observe the classical linear programming problem when we should maximize the unique function z=. The paper is structured in the following way: Section 2 contains some known facts about fuzzy logic important for the further understanding of the material; we propose the general information about fuzzy relations and build the essential fuzzy relations for the realization of our scheme in Section 3; we study the aggregation of fuzzy relations in Section 4; We propose the solution approach in Section 5; we observe the numerical example in Section 6 and we conclude our paper by Section 7
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