A multi-criteria decision-making approach for portfolio selection by using an automatic spherical fuzzy AHP algorithm

Portfolio selection for Stock evaluation and selection by an investor is multi-criteria decision-making (MCDM) problem of finding the best portfolio among an efficient set of portfolios, which should be tackled by using the appropriate techniques. The Analytic Hierarchy Process (AHP) is amongst the most widely used MCDM methods, which is often used in operation management. The main feature of AHP is, that, it firstly reduces the complex decision problems in hierarchical structures of objectives, criteria, sub-criteria, and alternatives and then, uses a fundamental scale to construct pairwise comparisons. The Spherical Fuzzy Sets (SFS) have many advantages in handling the uncertainty and vagueness of ordinary and 2D Fuzzy Sets (FS)s. Therefore, taking the advantage of AHP and SFSs in this paper, we modify the Fuzzy Analytic Hierarchy Process (FAHP) into Spherical fuzzy AHP (SFAHP). We introduce the concept of Spherical Fuzzy Preference Relation (SFPR) and develop an automatic algorithm to construct a consistent SFPR from an inconsistent one. The validity of the proposed approach is tested through an illustrative application of portfolio selection on the Pakistan Stock Exchange to make a prototype of our results.