Soergel Distance Measures for q-Rung Orthopair Fuzzy Sets and Their Applications

Abstract

AbstractThe virtue of the q-rung orthopair fuzzy set inherits those of the intuitionistic fuzzy set and the Pythagorean fuzzy set in loosening the constraint on support and counter-support. The very lax requirement gives the evaluators great freedom in expressing their beliefs about membership degrees and non-membership degrees, which makes q-rung orthopair fuzzy sets having a wide scope of application in practice. A distance measure is an important mathematical tool for distinguishing the difference between q-rung orthopair fuzzy sets and allows to deal with problems such as multi-criteria decision-making, medical diagnosis, and pattern recognition under a q-rung orthopair fuzzy environment. Unfortunately, many of the existing q-rung orthopair fuzzy distance measures have their limitations. To eliminate such restrictions, in this chapter, the Soergel-type distances of q-rung orthopair fuzzy sets are introduced and the basis on which the orthopairs can be ranked is established. The weighted types of the proposed Soergel distances and their corresponding similarity coefficients are derived. In addition, the validity of the emerging distance measures is shown by comparing them with the distance measures described in some recent research studies through numerical examples. Some charts are provided to visually display the various characteristics and to analyze the properties of the proposed distance measures. The outputs verify that these Soergel distance measures of q-rung orthopair fuzzy sets outperform other existing metrics in measuring uncertainty and avoiding counterintuitive cases. Some illustrative examples of decision-making in real life are presented, demonstrating the strong discrimination capability and effectiveness of the proposed Soergel distance measures.KeywordsFuzzy setq-Rung orthopair fuzzy setSoergel distance measureMedical diagnosisPattern recognitionBenchmarking