A constrained non-linear optimization model for fuzzy pairwise comparison matrices using teaching learning based optimization

Abstract

Non-linear optimization models have been recently proposed to derive crisp weights from fuzzy pairwise comparison matrices. In this paper, a TLBO (Teaching Learning Based Optimization) based solution is presented for solving an optimization model as a system of non-linear equations to derive crisp weights from fuzzy pairwise comparison matrices in AHP (Analytic Hierarchy Process). This fuzzy-AHP method is named as TLBO-1. It has been found that TLBO-1 can lead to inconsistent or less consistent weights. To solve the problem of inconsistent weights, a new constrained non-linear optimization model is proposed in this paper. This model is based on the min-max approach for fuzzy pairwise comparison ratios of weights. TLBO is again used to solve this optimization model, and crisp weights are derived. This fuzzy AHP method is named as TLBO-2. The effectiveness of the proposed model is illustrated by three examples. For each example, the consistency of the derived crisp weights is compared with other optimization models. The results show that the TLBO-2 method can derive more consistent weights for the fuzzy AHP based Multi-Criteria Decision Making (MCDM) systems as compared to the other optimization models.