COPRAS method based on interval-valued hesitant Fermatean fuzzy sets and its application in selecting desalination technology

Abstract

This paper firstly introduces the idea of interval-valued hesitant Fermatean fuzzy set (IVHFFS). It is one of the significant theoretical and practical features, which derive from the integration of hesitant Fermatean fuzzy set (HFFSs) and interval number. In this study, we firstly present the basic concept, various operations and distance measures of IVHFFSs. Then, based on the operations of IVHFFSs, some aggregation operators (AOs) are proposed for aggregating the interval-valued hesitant Fermatean fuzzy information. Furthermore, some elegant properties of these operators are discussed in detail. To show the applicability, we discuss a decision analysis process on IVHFFSs environment with the help of conventional complex proportional assessment (COPRAS) methodology. Finally, the selection process of desalination technology for treating the feed water is also taken to validate the developed decision analysis procedure on IVHFFSs. This paper considers various criteria and sub-criteria in the assessment procedure and determines the most significant criteria influencing the desalination technology selection process are technical, social, environment and economic criteria, with significance weights of 0.3972, 0.289, 0.1653 and 0.1486, respectively. The work concludes that the reverse osmosis (RO) is the suitable desalination technology under the considered criteria followed by electrodialysis (ED), and multiple-effect distillation (MED). Moreover, the sensitivity investigation and comparative study are presented to verify the robustness and stability of the proposed method. The findings of this study show that the proposed model can suggest more feasible performance while facing several input uncertainties and influencing factors.