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fuzzy Multi-Objective Linear Programming Problem Using DM's Perspective

INTERNATIONAL JOURNAL OF DECISION SUPPORT SYSTEM TECHNOLOGY 2022年第1期14卷 1-17页

作者： Singh, Vishnu Pratap Deshmukh, Madhura Sharma, Kirti Visvesvaraya Natl Inst Technol Dept Math Nagpur Maharashtra India

In this paper, a two-stage method has been proposed for solving fuzzy multi-objective linear programming problem (FMOLPP) with interval type-2 triangular fuzzy numbers (IT2TFNs) as its coefficients. In the first stage of problem solving, the imprecise nature of the problem has been handled. All technological coefficients given by IT2TFNs are first converted to a closed interval and then the objectives are made crisp by reducing a closed interval into a crisp number, and constraints are made crisp by using the concept of acceptability index. The amount by which a specific constraint can be relaxed is decided by the decision maker, and thus, the problem reduces to a crisp multi-objective linear programming problem (MOLPP). In the second stage of problem solving, the multi-objective nature of the problem is handled by using fuzzy mathematical programming approach. In order to explain the methodology, two numerical examples of the proposed methodology in production planning and diet planning problems have also been worked out in this paper.

关键词： Acceptability Index fuzzy Programming Approach interval Linear Programming interval type-2 triangular fuzzy numbers Multi-Objective Linear Programming Problem

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