A spherical fuzzy methodology integrating maximizing deviation and TOPSIS methods

Abstract Due to the uncertainty and vagueness, ambiguity and subjectivity of the information in an intricate decision-making environment, the assessment data specified by experts are mostly fuzzy and uncertain. As an extension of Pythagorean fuzzy sets (PyFSs) and picture fuzzy sets (PFSs), spherical fuzzy sets (SFSs) are used frequently for presenting fuzzy and indeterminate information. In multi-criteria decision-making (MCDM) problems, the weights of criteria are not known generally. The maximizing deviation technique is a useful tool to handle such problems that we have partially or incomplete information about the criteria’ weights. This research expands the classical maximizing deviation technique to the spherical fuzzy maximizing deviation technique using single-valued (SV) and interval-valued (IV) spherical fuzzy sets to determine criteria weights. To rank the alternatives and specify the preeminent preference, we proposed the Interval Valued Spherical Fuzzy TOPSIS method based on the similarity measure instead of distance measure. For this purpose, we proposed an IVSF cosine similarity measure. To present its effectiveness and practicability, we apply the proposed methodology to an advertisement strategy selection problem, where IVSF sets are used to represent the evaluations about alternatives and criteria. A sensitivity analysis with different similarity measurements is performed to show the reliability of the proposed methodology.