On spherical fuzzy distance measure and TAOV method for decision-making problems with incomplete weight information

A spherical fuzzy set is one of the reliable tools to handle the uncertainties in the data with the help of the three membership degrees: Positive, neutral, and negative. Under this environment, the paper aims to present a novel decision-making algorithm named as MCDM-TAOV with some novel distance measures using matrix norms. In the literature, several kinds of distance measures occur, but they fail to meet certain axioms of the measure. To overwhelm this, the proposed measure satisfies all axiomatic requirements and overcomes the hindrances in the existing distance measures. Several counter-intuitive examples are provided to justify the superiority of the proposed measures. Furthermore, we addressed the total area based on orthogonal vector (TAOV) methodology to solve the MCDM ("multi-criteria decision-making") problems. A distance-based criteria weight determination method is presented to compute the unknown criteria weight. The approach has been demonstrated by assessing the third-party reverse logistics provider (3PRLP) problem. The practical applicability, comparative analysis and advantages of the study with other decision-making methods are furnished to depict the efficiency of the moulded process.