A Multi-Criteria Analysis Model under an Interval Type-2 Fuzzy Environment with an Application to Production Project Decision Problems

Using Multi-Criteria Decision-Making (MCDM) to solve complicated decisions often includes uncertainty, which could be tackled by utilizing the fuzzy sets theory. Type-2 fuzzy sets consider more uncertainty than type-1 fuzzy sets. These fuzzy sets provide more degrees of freedom to illustrate the uncertainty and fuzziness in real-world production projects. In this paper, a new multi-criteria analysis model is introduced based on new compromise ratio and relative preference relation methods by vicinity to positive ideal and distance from negative ideal concepts under an interval type-2 fuzzy environment. Also, qualitative criteria are expressed as linguistic variables. Relative preference relation is more reasonable than defuzzification, because defuzzification cannot provide preference degree between two fuzzy numbers and cannot keep all the information. In this paper, an extended relative preference relation over the average is presented to deal with numeral values. Finally, a real application to designing and manufacturing of small electronic components, particularly for the aviation, defense, and space industries, is adopted from the literature and solved to determine the critical path by considering efficient criteria such as time, cost, risk, and quality.