Applied Research Advances

Vol. 2 No. 1 (2026): Applied Research Advances
Articles

A New Similarity Measure of q-Rung Orthopair Fuzzy Sets based on the Jaccard Index with its Application to the Orthopairian TOPSIS Method

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  • Zahid Hussain,
  • Kashif Ali,
  • Mehboob Ali
Zahid Hussain
Department of Mathematical Sciences, Karakoram International University, Gilgit-Baltistan, Pakistan
Kashif Ali
College of Business Management and Applied Sciences, Danyor, Gilgit-Baltistan, Pakistan
Mehboob Ali
Department of Statistics, Government College Gilgit, Gilgit-Baltistan, Pakistan

Published 2026-09-19

Keywords

  • Similarity Measure,
  • Jaccard Index,
  • q-Rung Orthopair Fuzzy Sets,
  • Multi-Criteria Decision-Making,
  • Technique for Order of Preference by Similarity to Ideal Solution,
  • Orthopairian TOPSIS
    • ...More
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Copyright (c) 2026 Zahid Hussain, Kashif Ali, Mehboob Ali (Author)

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

How to Cite

Hussain, Z., Ali, K., & Ali, M. (2026). A New Similarity Measure of q-Rung Orthopair Fuzzy Sets based on the Jaccard Index with its Application to the Orthopairian TOPSIS Method. Applied Research Advances, 2(1), 325-336. https://doi.org/10.65069/ara21202635
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Abstract

This paper introduces a novel similarity measure for q-rung orthopair fuzzy sets (q-ROFSs) based on the Jaccard index, aimed at improving decision-making processes under uncertainty. The q-ROFSs are flexible generalizations of intuitionistic fuzzy sets and Pythagorean fuzzy sets, offering improved flexibility in representing uncertainty. Hence, we proposed a novel SM using the Jaccard index for q-ROFSs. The suggested similarity measure considers both the membership and non-membership degrees of q-ROFSs and adheres to key properties such as boundedness, commutativity, and sensitivity. Numerical examples validate the measure, showing it to be both reasonable and effective. The proposed similarity measure is further integrated with the technique for order of preference by similarity to ideal solution (TOPSIS) method, forming orthopairian TOPSIS (OTOPSIS), which enables more accurate ranking of alternatives in uncertain environments. A practical example demonstrates the method's effectiveness, emphasizing its potential for multi-criteria decision-making applications in complex scenarios. The results confirm that the proposed measure is well-suited for decision-making in uncertain, multi-attribute settings.

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