A novel extended approach to evaluate criteria weights in MADM problems in fuzzy framework

Determining weights of criteria is a pivotal challenge that arises in Multi-Attribute Decision Making (MADM) problems. Different methods have been suggested in the literature which can be classified into three main categories: subjective, objective and integrated. Especially when the decision maker does not have a specific judgment regarding the weights of the criteria of the decision problem or the number of criteria is large, the methods based on pairwise comparisons are not effective due to the large number of required judgments as well as the natural increase in inconsistency in the judgments. In this paper, we propose an integrated model to determine criteria weights in MADM problems while combining the Ordered Weighted Average (OWA) Yager, entropy, fuzzy/crisp initial decision maker’s judgments about the preferences of alternatives, and the information of decision matrix. In this regard, by considering a decision matrix, we formulate the idea as an optimization problem including an extended TOPSIS, L-p metric and ~L-p metric, or goal programming model in order to provide an extension of OWA operator and entropy method, simultaneously. Then, we use the proposed method in a real-world dataset to evaluate the priorities of mining opportunities in 17 provinces of Iran (including 235 alternatives by considering 48 criteria). In this regard, a comprehensive list of economic, political, social, strategic and environmental criteria has been used. A full analysis is performed to illustrate the application of the technique that stems from our approach. Finally, we compare the results that we obtain with the results from existing approaches, including Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Simple Additive Weighting (SAW) method and Yager. In this way the accuracy and effectiveness of the presented work is conclusively validated.