A Novel Pythagorean Fuzzy MULTIMOORA Applied to the Evaluation of Energy Storage Technologies

This chapter develops a new version of the multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) in the Pythagorean fuzzy environment. MULTIMOORA is one of the most robust multi-criteria decision-making (MCDM) techniques since it combines the additive, multiplicative, and reference point utility functions. There are two main approaches when implementing MULTIMOORA. Either using the dominance theory or by aggregating the values of three utility functions. In the latter approach, the results of the additive and multiplicative functions are defuzzified, while the result of the reference point function is already a crisp value since it relies on the distance from the ideal situation. In fact, a distance between two fuzzy values cannot be definitely determined. Hence, it is more convenient to define distance using fuzzy sets rather than a crisp value. Consequently, this study will adopt the aggregation approach in which distances are defined by Pythagorean fuzzy sets. As a result, defuzzification is employed only in the final step for ranking. At this point, the accuracy function can be also employed with the score function to make the comparison more discriminatory. In addition, newly proposed aggregation operators are exploited. These operators guarantee fair treatment among the evaluation criteria since most of the aggregation operators have a flaw that might result in a biased treatment and false ranking in certain situations. A practical example that considers the evaluation of energy storage technologies is provided to illustrate the developed technique and to make a comparative analysis.