Share:


On the ratio of fuzzy numbers – exact membership function computation and applications to decision making

    Bogdana Stanojević Affiliation
    ; Ioan Dziţac Affiliation
    ; Simona Dziţac Affiliation

Abstract

In the present paper, we propose a new approach to solving the full fuzzy linear fractional programming problem. By this approach, we provide a tool for making good decisions in certain problems in which the goals may be modelled by linear fractional functions under linear constraints; and when only vague data are available. In order to evaluate the membership function of the fractional objective, we use the α-cut interval of a special class of fuzzy numbers, namely the fuzzy numbers obtained as sums of products of triangular fuzzy numbers with positive support. We derive the α-cut interval of the ratio of such fuzzy numbers, compute the exact membership function of the ratio, and introduce a way to evaluate the error that arises when the result is approximated by a triangular fuzzy number. We analyse the effect of this approximation on solving a full fuzzy linear fractional programming problem. We illustrate our approach by solving a special example – a decision-making problem in production planning.

Keyword : full fuzzy program, triangular fuzzy number, fuzzy aggregation, linear fractional programming, error approximation, decision making

How to Cite
Stanojević, B., Dziţac, I., & Dziţac, S. (2015). On the ratio of fuzzy numbers – exact membership function computation and applications to decision making. Technological and Economic Development of Economy, 21(5), 815-832. https://doi.org/10.3846/20294913.2015.1093563
Published in Issue
Sep 29, 2015
Abstract Views
83
PDF Downloads
75