A Novel Interval-Valued Intuitionistic Fuzzy Distance Measure Incorporating Min/Max Interaction Terms

Jiulin Jin; Xianlong Yang; Haixin Du; Dragan Pamucar

Authors

Jiulin Jin School of Science, Guiyang University, Guiyang, 550005, Guizhou, China Author https://orcid.org/0000-0002-9112-7626
Xianlong Yang School of Science, Guiyang University, Guiyang, 550005, Guizhou, China Author https://orcid.org/0000-0003-3708-4597
Haixin Du School of Science, Guiyang University, Guiyang, 550005, Guizhou, China Author https://orcid.org/0000-0002-1297-9573
Dragan Pamucar 1) Department of Applied Mathematical Science, College of Science and Technology, Korea University, Sejong 30019, Republic of Korea; 2) Széchenyi István University, Győr, Hungary; 3) Transport and Logistics Competence Centre, Vilnius Gediminas Technical University, Vilnius, Lithuania Author https://orcid.org/0009-0001-9876-0328

Keywords:

Interval-valued intuitionistic fuzzy set, Distance measure, Decision-making

Abstract

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely employed in decision-making and pattern recognition, where distance measures serve as fundamental tools. However, many existing distance measures for IVIFSs have two limitations: one is the low discriminant ability, which usually produces the same value for different pairs; the second is the violation of the axiom of regularity, and the distance value is not within [0,1]. To overcome these shortcomings, this paper proposes a new distance measure, which integrates a non-linear transformation of endpoint differences with min/max interaction terms. In addition, it is proved that the proposed measure satisfies all four axioms of distance. Finally, comparative experiments show the effectiveness and superiority of the proposed measure. The results establish the proposed measure as a more discriminative and axiomatically sound tool for IVIFS-based analysis.

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References

Atanassov, K., & Gargov, G. (1989). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349. https://doi.org/10.1016/0165-0114(89)90205-4

Atanassov, K. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3

Kong, D., Chang, T., Pan, J., Hao, N., Xu, K., Zhang, L., & Yang, G. (2019). A decision variable-based combinatorial optimization approach for interval-valued intuitionistic fuzzy magdm. Information Sciences, 484, 197–218. https://doi.org/10.1016/j.ins.2019.01.016

Malik, M., & Gupta, S. (2024). On basic arithmetic operations for interval-valued intuitionistic fuzzy sets using the hamming distance with their application in decision making. Expert Systems with Applications, 239, 122429. https://doi.org/10.1016/j.eswa.2023.122429

Gohain, B., Chutia, R., & Dutta, P. (2023). A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications. Engineering Applications of Artificial Intelligence, 119, 105747. https://doi.org/10.1016/j.engappai.2022.105747

Suo, C., Fu, L., & Sun, S. (2026). Selection of giant panda habitat based on the overlap degree of interval-valued intuitionistic fuzzy sets. Expert Systems with Applications, 307, 131043. https://doi.org/10.1016/j.eswa.2025.131043

Chen, T.-Y. (2016). An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis. Applied Soft Computing, 42, 390–409. https://doi.org/10.1016/j.asoc.2016.02.006

Chen, Z., & Shi, L. (2024). Fmea risk assessment method based on interval valued intuitionistic fuzzy sets and cloud mode. Safety and Environmental Engineering, 31(2), 9–16.

Varshney, A. K., Muhuri, P. K., & Lohani, Q. D. (2023). Density-based ifcm along with its interval valued and probabilistic extensions, and a review of intuitionistic fuzzy clustering methods. Artificial Intelligence Review, 56(4), 3755–3795. https://doi.org/10.1007/s10462-022-10236-y

Xu, Z., & Chen, J. (2008). An overview of distance and similarity measures of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16(04), 529–555. https://doi.org/10.1142/S0218488508005406

Tiwari, P., & Gupta, P. (2018). Entropy, distance and similarity measures under interval-valued intuitionistic fuzzy environment. Informatica, 42, 617–627. https://doi.org/10.31449/inf.v42i4.1303

Rashid, T., Faizi, S., & Zafar, S. (2018). Distance based entropy measure of interval-valued intuitionistic fuzzy sets and its application in multicriteria decision making. Advances in Fuzzy Systems, 2018(1), 3637897. https://doi.org/10.1155/2018/3637897

Li, S., Yang, J., Wang, G., & Xu, T. (2021). Multi-granularity distance measure for interval-valued intuitionistic fuzzy concepts. Information Sciences, 570, 599–622. https://doi.org/10.1016/j.ins.2021.05.003

Rani, P., Mishra, A. R., Cavallaro, F., & FahadAlrasheedi, A. (2024). Location selection for offshore wind power station using interval-valued intuitionistic fuzzy distance measure-rancom-wisp method. Scientific Reports, 14, 4706. https://doi.org/10.1038/s41598-024-54929-6

Mishra, A. R., Rani, P., Alrasheedi, A. F., & Tirkolaee, E. B. (2025). Assessing the challenges of collaborative innovation systems in public higher education: Interval-valued intuitionistic fuzzy combined compromise solution approach. Group Decision and Negotiation, 34, 1035–1072. https://doi.org/10.1007/s10726-025-09941-0

Mishra, A., Rani, P., Pamucar, D., & Alrasheedi, A. (2025). Household solid waste processing plant location selection: Interval-valued intuitionistic fuzzy information-based gained and lost dominance score approach. International Journal of Environmental Science and Technology, 22, 59–78. https://doi.org/10.1007/s13762-024-06098-2