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

Abstract

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.

Keywords:

• Decision analysis
• multi-criteria
• fuzzy sets

Acknowledgements(s)

We thank the anonymous referees for their valuable suggestions; we thank Tamoor Qureshi and Muhammad Ali for their support and comments to improve the quality of the images.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Table 17. Pairwise judgement of alternatives with respect to Criterion 3 Q₃.

Table 18. Pairwise judgment of alternatives with respect to Criterion 4 Q₄.

Table 19. Pairwise judgment of alternatives with respect to Criterion 5 Q₅.

Table 20. Spherical fuzzy weight matrix.

Table 21. Score values and ranking.