MULTI-CRITERIONAL CHOICE OF AN ALTERNATIVE UNDER THE RULES OF FUZZY PRODUCTS WITH SOME RELIABILITY DEGREE

• Published in: Eureka, Physics and Engineering (Online) Physics and Engineering (Online), 2021 (2), p.124-136
• Main Authors: Habibov, Ibrahim Abulfaz, Dyshin, Oleg, Аghаmmadova, Sevda Alipasha, Hasanzade, Irada Sabir
• Format: Article
• Language: English
• Subjects: Algorithms; Alternatives; Assessments; Bayesian analysis; Centroids; Decision making; Decision theory; Estimates; Fuzzy sets; Gas pipelines; Intervals; Multiple criterion; Natural gas; Statistical inference
• ISSN: 2461-4254; 2461-4262
• DOI: 10.21303/2461-4262.2021.001708

One of the main problems of decision-making tasks is the need to take into account subjective expert assessments, the complete consistency of which is rare, and the choice of the best alternative. The complexity of the connections between the many-sided aspects of the decision-making situation and the lack of an accurate forecast of the consequences leads to the fact that when assessing and choosing alternatives, it is possible, and often necessary, to use and process qualitatively fuzzy estimates. In decision-making situations, when at least one of the elements (outcomes, criteria, preferences, expert opinions, etc.) is described qualitatively, indistinctly, there are problems of multi-criteria decision-making with fuzzy initial information. Let’s consider the solution to the problem of multi-criteria choice based on the rules of fuzzy conditional inference, which have the form of fuzzy statements, the conditions and conclusions of which, along with expert assessments of the criteria, are presented in the form of interval fuzzy numbers of the second type (IT2FN). The convolution of private implications in each statement is made according to Lukasiewicz's rule. To reduce the type and defuzzify the resulting IT2FN, the Karrnik-Mendel algorithm was used to construct the minimum and maximum centroids of nested fuzzy sets of the first type, which give an estimate of the utility interval for each alternative. To refine the obtained utility estimates, under conditions of incomplete definiteness of statements, using the generalized Bayesian inference mechanism, adjusted estimates of the utility intervals of alternatives are constructed. By comparing these intervals, a larger interval is determined and the corresponding alternative is taken as a solution to the problem under consideration. The application of the proposed approach to solving the problem of multicriteria selection of the most corroded section of a gas pipeline with ambiguous expert opinions is shown. To date, specific practical and theoretical results have been obtained for decision-making problems with fuzzy initial information