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.
Highlights
In majority economic and industrial engineering problems, one must make a decision, and the decision must be optimal
As far as we know, all approaches to solving full fuzzy linear fractional programming problems, found in the literature, yield crisp solutions, or solutions expressed by triangular or trapezoidal fuzzy numbers
We developed a novel approach to solving the full fuzzy linear fractional programming problem, providing 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
Summary
In majority economic and industrial engineering problems, one must make a decision, and the decision must be optimal. The optimization step consists in finding the best available values of an objective function over a well-defined domain. B. Stanojević et al On the ratio of fuzzy numbers – exact membership function. Of objective functions defined over different types of domains by using different types of constraints. The optimization problems, where the objective function appears as a ratio of functions, form the fractional programming problems. Fractional programming is an important tool for modelling various decision processes, such as maximizing the profit/cost, volume/cost, or other quantities that measure the efficiency of a system. Fractional programming appears in information theory, numerical analysis, decomposition algorithms for large linear systems, and in many other fields that are not necessarily economical
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