A Parametric Family of Fuzzy Similarity Measures for Intuitionistic Fuzzy Sets

Madiha Qayyum, Etienne E. Kerre () and Samina Ashraf
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Madiha Qayyum: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
Etienne E. Kerre: Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281, S9, B-9000 Gent, Belgium
Samina Ashraf: Department of Mathematics, University of Education, Bank Road Campus, Lahore 54000, Pakistan

Mathematics, 2023, vol. 11, issue 14, 1-10

Abstract: Measuring the similarity between two objects and classifying them on the basis of their resemblance level has been a fundamental tool of the human mind. In an intuitionistic fuzzy environment, we find researchers that have attempted to generalize the fuzzy versions of similarity measures between fuzzy sets to their intuitionistic forms for measuring the level of similarity between the intuitionistic fuzzy sets. Though many different forms of intuitionistic fuzzy similarity measures have been introduced so far, a comparative study reveals that among all these measures, it is difficult for one to claim the existence of a single measure that alone has the capability to recognize every single pattern assigned to it. This paper presents a four-parametric family of similarity measures for intuitionistic fuzzy sets employing weighted average cardinality and intuitionistic fuzzy t-norms along with their dual t-co-norms. A combinational variation of the parameters involved in this family resulted in some of the famous similarity measures having an intuitionistic version. These new measures are analyzed for their properties, and they have shown some remarkable results. Moreover, the proposed family has a practical advantage over the other measures in the existing literature because every member not only possesses the capability of successfully recognizing any pattern assigned to it up to a fine accuracy but also a choice of different t-norms and co-norms within a single measure equips it with the capacity to portray different mindsets of a decision-maker who, besides being unbiased, can possess a deep psychology of being an optimist, pessimist, or possessing neutral behavior in general. Lastly, the members of this family are tested for their feasibility in a sensitive medical decision process of detection of COVID-19.

Keywords: intuitionistic fuzzy set (IFS); weighted average cardinality measure (WACM); fuzzy measure for IFS; pattern recognition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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