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This article proposes a new version of the technique of order preference by similarity to an ideal solution (TOPSIS) to solve fuzzy multi-attribute group decision making (MAGDM) problems using trapezoidal interval type-2 fuzzy sets (IT2FSs). The traditional TOPSIS ranks the alternatives according to their relative degree of closeness to the ideal solutions. On the other hand, TOPSIS based on similarity measure ranks the alternatives according to their total degree of similarity to the ideal solutions. This study extends TOPSIS using similarity measure using map distance to IT2FSs. First, the similarity measure based on map distance for interval-valued fuzzy sets (IVFSs) is extended to encompass IT2FSs due to the deficiency in IT2FSs similarity measures. Then, TOPSIS using similarity measure is applied. Hence, fuzzy MAGDM problems can be handled in a more flexible intelligent manner and avoiding defuzzification with its drawbacks. An illustrative example is given to explain the approach. Then, a practical problem in assessing thermal energy storage technologies in solar power systems is solved, where the weights of the attributes and the performance of the qualitative attributes are linguistic variables modeled by IT2FSs. The reliability of two normalization techniques is examined and the impact of the theoretical and empirical reference points on the solution is investigated.
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