Fuzzy Model for Decision Support under Uncertainty Based on the «Fztotriangle» Transformation

Abstract

One of the problems of operations research is the problem of choosing the best solution from the set of possible solutions in conditions of uncertainty, when there is no reliable data about the situation requiring a decision. Classical methods of mathematical modeling are focused on point, numerical estimates that characterize the results of possible choice. Moreover, in a situation of significant uncertainty, these methods do not provide unambiguous and mathematically rigorous recommendations for the choice of a solution method. One of the options to overcome these limitations is the use of the apparatus of the theory of fuzzy sets. We propose the method of finding the best solution on the set of fuzzy elements of the evaluation matrix, when the uncertainties of initial data are represented by fuzzy sets (numbers) with different functions of affiliation, which allows you to represent different levels of incomplete information about the situation requiring a decision. The choice of the best decision in conditions when the assessment of possible consequences is represented in the form of fuzzy sets is based on the application to these assessments of FztoTriangle transformation, which allows to obtain integral values for the results of possible decisions on the whole set of conditions characterizing the situation under study, in the form of an equivalent fuzzy set with a triangular identity function. This simplifies the comparison of fuzzy sets representing possible solutions. Performing such transformations does not impose restrictions on the type of affiliation functions of the evaluations used. The final result will be estimates of the consequences of the chosen solution, as well as the possibility of its implementation. The proposed method does not require complex mathematical transformations and can be easily implemented in software as a component of decision support system.