Novel Distance Measures of q-Rung Orthopair Fuzzy Sets and Their Applications

Abstract

The q-rung orthopair fuzzy sets (q-ROFSs), a novel concept for processing vague information, offer a more potent and all-encompassing method compared to traditional fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets. The inclusion of the parameter q allows for the q-rung orthopair fuzzy sets to capture a broader range of uncertainty of information. In this paper, we present two novel distance measures for q-ROFSs inspired by the Jensen–Shannon divergence, called DJS_2D and DJS_3D, and we analyze some properties they satisfy, such as non-degeneracy, symmetry, boundedness, and triangular inequality. Then, the normalized distance measures, called DJS_2D˜ and DJS_3D˜, are proposed and we verify their rationality through numerical experiments. Finally, we apply the proposed distance measures to practical scenarios, including pattern recognition and multicriteria decision-making, and the results demonstrate the effectiveness of the proposed distance measures.

A Progressive Outlook on Possibility Multi-Fuzzy Soft Ordered Semigroups: Theory and Analysis

“…, ≤) is denoted by S. A non-empty subset X of an ordered semigroup S is called a left (resp. right) ideal of S [20] and is denoted by 𝑋𝑋 ⊲ 𝑙𝑙 𝑆𝑆 (resp. 𝑋𝑋 ⊲ 𝑟𝑟 𝑆𝑆) if it satisfies the following:…”