A Generalization of Similarity Measure in Collection of  Intuitionistic Fuzzy Sets

Authors

  • Dwi Nur Yunianti Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Malang, East Java, Indonesia Department of Mathematics, Faculty of Mathematics and Science, State University of Surabaya, Surabaya, East Java, Indonesia
  • Noor Hidayat Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Malang, East Java, Indonesia
  • Raden Sulaiman Department of Mathematics, Faculty of Mathematics and Science, State University of Surabaya, Surabaya, East Java, Indonesia
  • Abdul Rouf Alghofari Department of Mathematics, Faculty of Mathematics and Natural Sciences, Brawijaya University, Malang, East Java, Indonesia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6514

Keywords:

Intuitionistic fuzzy sets; collection of intuitionistic fuzzy sets; similarity measure; a generalitation of similarity measure

Abstract

A collection of intuitionistic fuzzy sets is a new approach to intuitionistic fuzzy set theory. In collections of intuitionistic fuzzy sets, a similarity measure can determine the degree of similarity based on the information carried by the collections. However, an existing similarity measure is limited to evaluating similarity between two collections defined over the same universal set. To overcome this limitation, thus, in this paper, we propose a generalized similarity measure that can be applied to collections defined over different universal sets. To construct the generalization, we first introduce the concept of inferior and equivalent relations in the collection of intuitionistic fuzzy sets. Then, we present a new formula for the similarity measure. Finally, the proposed measure is illustrated through a pattern recognition problem to demonstrate its effectiveness and practical value. 

Downloads

Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Mathematical and Fuzzy Logic

License

Copyright (c) 2025 Dwi Nur Yunianti, Noor Hidayat, Raden Sulaiman, Abdul Rouf Alghofari

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

A Generalization of Similarity Measure in Collection of  Intuitionistic Fuzzy Sets. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6514. https://doi.org/10.29020/nybg.ejpam.v18i3.6514