Proportional Spherical Fuzzy AHP&TOPSIS Methodology: Application to Smart Solar Panel Selection

When you ask a person what his/her degree of membership in the set of tall people is, he/she usually assigns a one-digit decimal number or, at most, a two-digits decimal number. Moreover, if you ask the same question a short time later, he/she may assign a different membership degree. Proportional fuzzy sets have been proposed for the solution of these problems by Kahraman (2024). Proportional relations between the degrees of parameters of a fuzzy set extension help to determine the membership, non-membership, and indecision degrees with several digits and in a way that does not differ at different time points for better-representing experts’ judgments. In this paper, proportional spherical fuzzy (PSF) sets are introduced and PSF AHP&TOPSIS multi-criteria decision making (MCDM) methodology is developed. PSF AHP is used for computing the weights of the considered criteria whereas PSF TOPSIS is used for prioritizing the alternatives. In the proposed methodology, it is also possible to assign imprecise proportions such as “around k”, “close to k”, or “between k₁ and k₂”. An application of the proposed methodology to a smart solar panel selection problem is presented. The comparative and sensitivity analyses show that that PSFS are easily applicable to any problem and produce valid outcomes and the proposed PSF AHP&TOPSIS is very effective for the solutions of MCDM problems.