Proportional neutrosophic sets and their AHP & TOPSIS extension

Abstract

A problem with the neutrosophic sets, as other fuzzy set extensions, is that they require decimal numbers for truthiness, falsity, and indecision degrees of an element from experts, which cannot be easily assigned. This will be more difficult when three or more digits’ membership degrees are required to assign. Instead, proportion-based relations between the elements of a neutrosophic set can make easier to determine the truthiness, falsity, and indecision degrees. We introduce proportional neutrosophic sets in this study, together with associated aggregation operators and arithmetic operations. The proportional judgments between truthiness, falsity, and indeterminacy are enough for proportional neutrosophic sets. With these data more accurately reflecting the opinions of experts, proportional neutrosophic sets facilitate the use of neutrosophic sets. The provided models also incorporate the ambiguous concept of proportionality. According to the application and comparative analyses, proportional neutrosophic sets yield reliable results and are readily applicable to any kind of issue. Multi-criteria decision methodology using proportional neutrosophic sets based analytic hierarchy process and TOPSIS methods has been developed and used in a personnel selection problem. Additionally, we compare the proposed methodology with its classical version. Proportional neutrosophic sets are very successful in determining the degrees and ease neutrosophic multi-criteria decision making process.