A new spherical aggregation function with the concept of spherical fuzzy difference for spherical fuzzy EDAS and its application to industrial robot selection

In this article, a new fully fuzzy approach is developed for the evaluation based on distance from average solution (EDAS) for multi-criteria decision-making (MCDM) using spherical fuzzy sets (SFSs). The proposed approach avoids the current limitations and drawbacks of distance-based methods in general and the EDAS method in particular using spherical fuzzy information namely, early defuzzification, the flaws of distance measures, and the undefined spherical fuzzy subtraction and division operations. First, the approach employs the score function only in the final step for ranking. Second, the concept of the spherical fuzzy difference is introduced to make up for the subtraction operation which is the backbone of EDAS and as a substitute for distance measures. The spherical fuzzy difference is utilized to indicate any increase or decrease in the membership degree, the non-membership degree, and the hesitancy degree in the performance of an alternative for a criterion than that of its peer in the average solution. Then, the weighted spherical differences are calculated. The total weighted spherical differences from the average solution of each alternative for the assessment criteria are aggregated in the appraisal score. Due to a flaw in the extant aggregation operators, their results might be misleading. Therefore, an aggregation function is introduced that guarantees a balanced and fair aggregation. The appraisal scores are defuzzified, and the alternative with the highest appraisal score is the best. Two practical examples in MCDM are solved and a comparative study is presented to demonstrate and validate the algorithm.