Obtaining Crisp Priorities for Triangular and Trapezoidal Fuzzy Judgments

Abstract

This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices. Crisp judgments cannot be given for real-life situations, as most of these include some level of fuzziness and complexity. In these situations, judgments are represented by the set of fuzzy numbers. Most of the fuzzy optimization models derive crisp priorities for judgments represented with Triangular Fuzzy Numbers (TFNs) only. They do not work for other types of Triangular Shaped Fuzzy Numbers (TSFNs) and Trapezoidal Fuzzy Numbers (TrFNs). To overcome this problem, a sum of squared error (SSE) based optimization model is proposed. Unlike some other methods, the proposed model derives crisp weights from all of the above-mentioned fuzzy judgments. A fuzzy number is simulated using the Monte Carlo method. A threshold-based constraint is also applied to minimize the deviation from the initial judgments. Genetic Algorithm (GA) is used to solve the optimization model. We have also conducted casestudiesto show the proposed approach’s advantages over the existingmethods. Results show that the proposed model outperforms other models to minimize SSE and deviation from initial judgments. Thus, the proposed model can be applied in various real time scenarios as it can reduce the SSE value upto 29% compared to the existing studies.