Determining Normalized Crisp Weights From Fuzzy Comparison Matrices Using an Improved Two-Stage Logarithmic Goal Programming Model

Fuzzy analytical hierarchy process (fahp) is one of the most popular multi-criteria decision making (mcdm) techniques in which the weights of criteria and the evaluation measures of alternatives are generated based on fuzzy pairwise comparisons. there are many approaches for determining the weights from pairwise comparison matrices (pcm). some of them have calculated the interval weights at all alphacuts. however, in some mcdm techniques (like technique for order preference by similarity to ideal solution (topsis), vlsekriterijumska optimizacija i kompromisno resenje (vikor), and fahp), it is needed to calculate normalized crisp weights. in this paper, the authors extend an index where interval weights obtained at all alphacuts are converted into the crisp weight. finally, several illustrative examples in the literature are considered to show the verication of the proposed index and the obtained results are then compared with weights extracted by fuzzy preference programming (fpp). the results show that our approach is suitable for obtaining the crisp weights and also, has the similar ranking orders with those of the others.