Norm-oriented similarity modeling for quasirung orthopair fuzzy sets: a framework for pattern recognition and medical diagnosis

Afnan Albahli; Yasir Akhtar; Adwan A. Alanazi; Darjan Karabasevic; Pavle Brzakovic; Afnan Albahli; Yasir Akhtar; Adwan A. Alanazi; Darjan Karabasevic; Pavle Brzakovic

doi:10.3934/math.20261227

AIMS Mathematics

2026, Volume 11, Issue 9: 31005-31040. doi: 10.3934/math.20261227

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Research article

Norm-oriented similarity modeling for quasirung orthopair fuzzy sets: a framework for pattern recognition and medical diagnosis

1.
Department of Information Technology, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia; AMAlbahli@pnu.edu.sa
2.
Department of Applied Mathematics, Chung Yuan Christian University, Taoyuan 32023, Taiwan; g11101102@cycu.edu.tw
3.
Department of Computer Science and Information, College of Computer Science and Engineering, University of Hail, Hail, Saudi Arabia; a.alanazi@uoh.edu.sa
4.
College of Global Business, Korea University, Sejong 30019, Republic of Korea
5.
Faculty of Applied Management, Economics, and Finance, University Business Academy in Novi Sad, Jevrejska 24, Belgrade 11000, Serbia; pavle.brzakovic@mef.edu.rs
6.
Institute of Dynamic Management, Vilnius Gediminas Technical University, Vilnius, Saulėtekio al. 11 LT-10223, Lithuania

Received: 31 July 2026 Revised: 25 August 2026 Accepted: 02 September 2026 Published: 21 September 2026
MSC : 03E72, 94A17

The quasirung orthopair fuzzy sets (QOFSs) provide a flexible framework for representing uncertainty through membership degree (MD) and non-membership degree (NMD). This study developed a unified framework for constructing similarity measures (SMs) under the QOFS environment using cosine-, entropy-, and norm-based structures. The proposed measures incorporate membership, non-membership, and hesitancy information to provide flexible similarity assessment through tunable parameters. The theoretical properties of the proposed measures were established, and a dual-perspective analysis was conducted at microscopic and macroscopic levels to examine their mathematical and numerical behavior. Comparative numerical experiments were performed to investigate the discrimination, sensitivity, stability, and computational characteristics of the proposed measures. Their applicability was further illustrated through pattern recognition and medical decision-making examples. The main contributions are as follows: (1) A systematic framework was developed to characterize similarity relationships between quasirung orthopair fuzzy numbers (QOFNs) through multiple complementary mathematical formulations; (2) treatment of numerical issues, including division-by-zero cases, through appropriate similarity constructions; (3) establishment of essential mathematical properties and a systematic micro–macro evaluation framework; and (4) comprehensive numerical comparison and illustrative applications demonstrating the computational applicability of the proposed measures.
- similarity measures,
- quasirung orthopair fuzzy information,
- uncertainty quantification,
- decision-making,
- applications
Citation: Afnan Albahli, Yasir Akhtar, Adwan A. Alanazi, Darjan Karabasevic, Pavle Brzakovic. Norm-oriented similarity modeling for quasirung orthopair fuzzy sets: a framework for pattern recognition and medical diagnosis[J]. AIMS Mathematics, 2026, 11(9): 31005-31040. doi: 10.3934/math.20261227

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Abstract

The quasirung orthopair fuzzy sets (QOFSs) provide a flexible framework for representing uncertainty through membership degree (MD) and non-membership degree (NMD). This study developed a unified framework for constructing similarity measures (SMs) under the QOFS environment using cosine-, entropy-, and norm-based structures. The proposed measures incorporate membership, non-membership, and hesitancy information to provide flexible similarity assessment through tunable parameters. The theoretical properties of the proposed measures were established, and a dual-perspective analysis was conducted at microscopic and macroscopic levels to examine their mathematical and numerical behavior. Comparative numerical experiments were performed to investigate the discrimination, sensitivity, stability, and computational characteristics of the proposed measures. Their applicability was further illustrated through pattern recognition and medical decision-making examples. The main contributions are as follows: (1) A systematic framework was developed to characterize similarity relationships between quasirung orthopair fuzzy numbers (QOFNs) through multiple complementary mathematical formulations; (2) treatment of numerical issues, including division-by-zero cases, through appropriate similarity constructions; (3) establishment of essential mathematical properties and a systematic micro–macro evaluation framework; and (4) comprehensive numerical comparison and illustrative applications demonstrating the computational applicability of the proposed measures.

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