Abstract
This paper suggests a fuzzy MCDM (multiple criteria decision-making) approach, where ratings of alternatives versus criteria and weights of criteria are assessed in fuzzy numbers or linguistic values represented by fuzzy numbers. Criteria are classified into cost and benefit ones. In the proposed method, the ratings assigned by decision makers to each alternative versus each criterion and the weights assigned by decision makers to each criterion are averaged. The averaged cost and benefit ratings are further normalized into comparable scales respectively. The membership function of subtracting the summation of weighted normalized benefit ratings from that of weighted normalized cost ratings for each alternative can be developed by interval arithmetic of fuzzy numbers. The fuzzy number ranking method of centroid is then applied to determine the ordering of the alternatives. A numerical example of robot selection demonstrates feasibility of the proposed method.
Highlights
Fuzzy multiple criteria decision-making (MCDM) is a powerful tool for evaluation and selection of alternatives versus different criteria, where ratings of alternatives under different criteria and the importance weights of criteria are usually assessed in fuzzy numbers or linguistic values (Zadeh, 1975) represented by fuzzy numbers
Criteria are categorized into cost and benefit ones
Since criteria may have incommensurable units (Chen and Hwang, 1992), all averaged cost and benefit ratings are further normalized into comparable scales respectively before weighted
Summary
Fuzzy multiple criteria decision-making (MCDM) is a powerful tool for evaluation and selection of alternatives versus different criteria, where ratings of alternatives under different criteria and the importance weights of criteria are usually assessed in fuzzy numbers or linguistic values (Zadeh, 1975) represented by fuzzy numbers. Clear development for the membership function of the aggregation of the fuzzy weighted ratings of each alternative cannot be found in the above works. This limitation deters their applicability to real world problems. Using interval arithmetic of fuzzy numbers can develop the membership function of subtracting SWNBR from SWNCR for each alternative. Because the final fuzzy evaluation values are still fuzzy numbers, a ranking method is needed. Some methods are computational complex and others are difficult to present connection by formula between the ranking procedure and the final fuzzy evaluation values of alternatives under fuzzy MCDM model.
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