Decisions in uncertainty based on entropy

Abstract

At present, the choice of the best solutions out of many possible under conditions of uncertainty is the actual economic task, arising and being solved in many economic situations. Famous classical approaches to its solution are based on various assessments of decision-making practical situations. However, they often give insufficiently accurate or incorrect results and do not satisfy sustainability requirements, when the only invariant calculation result relative to calculation methodology is a reliable one and corresponds to the real result. This article describes an alternative approach to the justification of decisions under conditions of uncertainty without the construction and use of assumptions about the decision-making situation and in conformity with the approaches of the stability theory. The problem of multi-criteria decision-making in conditions of complete uncertainty, wherein structuring of alternatives is performed using the fuzzy entropy, has been formulated and conceptually investigated. The idea of the described method assumes that the criteria conformity is estimated by fuzzy numbers and (or) linguistic allegations, i.e. formalizes by tools of fuzzy set theory. In opposition to classical approaches, this approach does not require the construction of hypotheses about the possible circumstances of decision-making and meets the requirements of stability theory. As a confirmation, it has been shown that the calculation of fuzzy entropy by various methods does not lead to contradictory results. In this work appropriateness and practicality of using the fuzzy entropy criterion for ordering sets of alternatives in fuzzy conditions of decision-making have been substantiated. The method for calculating the fuzzy entropy when evaluating criteria in linguistic form has been grounded. The paper presents numerical examples for which the fuzzy entropy calculation allows generating grounded clear recommendations and choosing the best solution, which does not provide, under the given concrete numeric data, classical methods. The proposed approach for ordering and searching for alternative solutions with a strong uncertainty using fuzzy entropy makes it possible to significantly enhance the validity of the required multi-criteria decision through the achievement of the invariance of the calculation results regarding the models and methods of processing fuzzy input data.