Strong Robust Similarity Measures: A Detailed Analysis and Application

Document Type : Research Paper

Authors

1 Department of Statistics and Operational Research and Mathematics Didactics, University of Oviedo, Spain

2 Department of Computer Science. University of Oviedo, Spain

3 Department of Computer Science, University of Oviedo, Spain

4 Department of Statistics and Operational Research and Mathematics Didactics, University of Oviedo Oviedo, Spain

Abstract

Similarity measures are fundamental tools for comparing and evaluating data across various domains. Robust similarity measures extend classical similarities. However, when dealing with interval data, robust measures are often insufficient due to the intrinsic properties of intervals. In this study, we introduce the concept of strong robust similarity measures, which incorporate three additional axioms specifically considered to manage uncertainty represented by intervals. Furthermore, we characterize these measures through a novel class of functions, referred to as preinclusions. We also provide a comprehensive analysis of the proposed measures, examining their behaviour with respect to different axioms. Finally, we illustrate the applicability of our approach through a real-world case study using meteorological data collected by AEMET (the Spanish National Weather Service) in 2021.

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References

[1] M. Allahdadi, S. Soradi-Zeid, H. Torabi, E. Hosseini, Solving optimal control problems under interval uncertainty
using robust model predictive control, Iranian Journal of Fuzzy Systems, 22(6) (2025), 147-165. https://doi.org/
10.22111/ijfs.2025.52170.9204
[2] M. Arefi, S. M. Taheri, Weighted similarity measure on interval-valued fuzzy sets and its application to pattern
recognition, Iranian Journal of Fuzzy Systems, 11(5) (2014), 67-79. https://doi.org/10.22111/ijfs.2014.1723
[3] B. Bedregal, H. Bustince, J. Fernandez, G. Deschrijver, R. Mesiar, Interval-valued contractive fuzzy negations,
Proceedings of the International Conference on Fuzzy Systems, Barcelona, (2010), 1-6. https://doi.org/10.
1109/FUZZY.2010.5584635
[4] G. Beliakov, H. Bustince, T. Calvo, A practical guide to averaging functions, Springer, (2016). https://doi.org/
10.1007/978-3-319-24753-3
[5] G. Beliakov, A. Pradera, T. Calvo, Aggregation functions: A guide for practitioners, Springer Berlin, Heidelberg,
(2007). https://doi.org/10.1007/978-3-540-73721-6
[6] A. Bouchet, M. Sesma-Sara, G. Ochoa, H. Bustince, S. Montes, I. D´ıaz, Measures of embedding for interval-valued
fuzzy sets, Fuzzy Sets and Systems, 467 (2023), 108505. https://doi.org/10.1016/j.fss.2023.03.008
[7] H. Cheng, A novel similarity measure based on the centre of nine-point circle of the isosceles triangular fuzzy
numbers and their applications, Iranian Journal of Fuzzy Systems, 21(2) (2024), 87-104. https://doi.org/10.
22111/ijfs.2024.43959.7742
[8] I. Couso, D. Dubois, Statistical reasoning with set-valued information: Ontic vs. epistemic views, International
Journal of Approximate Reasoning, 55(7) (2014), 1502-1518. https://doi.org/10.1016/j.ijar.2013.07.002
[9] L. R. Dice, Measures of the amount of ecologic association between species, Ecology, 26(3) (1945), 297-302. https:
//doi.org/10.2307/1932409
[10] D. S. Guru, B. B. Kiranagi, P. Nagabhushan, Multivalued type proximity measure and concept of mutual similarity
value useful for clustering symbolic patterns, Pattern Recognition Letters, 25(10) (2004), 1203-1213. https://doi.
org/10.1016/j.patrec.2004.03.016
[11] P. Huidobro, N. Rico, A. Bouchet, S. Montes, I. D´ıaz, A new similarity measure for real intervals to solve the aliasing
problem, Proceedings of the International Conference on Information Processing and Management of Uncertainty
in Knowledge-Based Systems, Springer, (2022), 542-554. https://doi.org/10.1007/978-3-031-08971-8_45
[12] P. Jaccard, Nouvelles recherches sur la distribution florale, Bulletin de la Soci´et´e Vaudoise des Sciences Naturelles,
44 (1908), 223-270. https://doi.org/10.5169/seals-268384
[13] S. Kabir, C. Wagner, T. C. Havens, D. T. Anderson, A similarity measure based on bidirectional subsethood for
intervals, IEEE Transactions on Fuzzy Systems, 28(11) (2020), 2890-2904. https://doi.org/10.1109/TFUZZ.
2019.2945249
[14] S. Kabir, C. Wagner, T. C. Havens, D. T. Anderson, U. Aickelin, Novel similarity measure for interval-valued
data based on overlapping ratio, Proceedings of the 2017 IEEE International Conference on Fuzzy Systems (FUZZIEEE),
(2017). https://doi.org/10.1109/FUZZ-IEEE.2017.8015623
[15] Y. S. Lin, J. Y. Jiang, S. J. Lee, A similarity measure for text classification and clustering, IEEE Transactions on
Knowledge and Data Engineering, 26(7) (2013), 1575-1590. https://doi.org/10.1109/TKDE.2013.19
[16] G. Mayor, E. Trillas, On the representation of some aggregation functions, Proceedings of the IEEE International
Symposium on Multiple-Valued Logic, (1986), 111-114.
[17] A. R. Mishra, P. Rani, Information measures based TOPSIS method for multicriteria decision making problem in
intuitionistic fuzzy environment, Iranian Journal of Fuzzy Systems, 14(6) (2017), 41-63. https://doi.org/10.
22111/ijfs.2017.3497
[18] H. T. Nguyen, V. Kreinovich, Computing degrees of subsethood and similarity for interval-valued fuzzy sets: Fast
algorithms, Proceedings of the 9th International Conference on Intelligent Technologies, (2008), 47-55.
[19] S. Onta˜n´on, An overview of distance and similarity functions for structured data, Artificial Intelligence Review, 53
(2020), 5309-5351. https://doi.org/10.1007/s10462-020-09821-w
[20] A. Pradera, G. Beliakov, H. Bustince, B. De Baets, A review of the relationships between implication, negation and
aggregation functions from the point of view of material implication, Information Sciences, 329 (2016), 357-380.
https://doi.org/10.1016/j.ins.2015.09.033
[21] Y. Ren, Y. H. Liu, J. Rong, R. Dew, Clustering interval-valued data using an overlapped interval divergence,
Proceedings of the Eighth Australasian Data Mining Conference (AusDM), 101 (2009), 35-42.
[22] N. Rico, P. Huidobro, A. Bouchet, I. D´ıaz, Similarity measures for interval-valued fuzzy sets based on average
embeddings and its application to hierarchical clustering, Information Sciences, 615 (2022), 794-812. https://
doi.org/10.1016/j.ins.2022.10.028
[23] R. E. Tulloss, Assessment of similarity indices for undesirable properties and a new tripartite similarity index
based on cost functions, Mycology in Sustainable Development: Expanding Concepts, Vanishing Borders, (1997),
122-143.
[24] A. Tversky, Features of similarity, Psychological Review, 84 (1977), 327-352. https://psycnet.apa.org/doi/
10.1037/0033-295X.84.4.327
[25] C. Wagner, S. Miller, J. M. Garibaldi, D. T. Anderson, T. C. Havens, From interval-valued data to general type-2
fuzzy sets, IEEE Transactions on Fuzzy Systems, 23(2) (2014), 248-269. https://doi.org/10.1109/TFUZZ.2014.
2310734
[26] Z. Xu, Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision
making, Fuzzy Optimization and Decision Making, 6(2) (2007), 109-121. https://doi.org/10.1007/
s10700-007-9004-z
[27] L. Xuecheng, Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and
Systems, 52(3) (1992), 305-318. https://doi.org/10.1016/0165-0114(92)90239-Z
[28] W. Zeng, P. Guo, Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy
sets and their relationship, Information Sciences, 178(5) (2008), 1334-1342. https://doi.org/10.1016/j.ins.
2007.10.007
[29] R. R. Zhao, M. X. Luo, S. G. Li, L. N. Ma, A parametric similarity measure between picture fuzzy sets and its
applications in multi-attribute decision-making, Iranian Journal of Fuzzy Systems, 20(1) (2023), 87-102. https:
//doi.org/10.22111/ijfs.2023.7348
Iranian Journal of Fuzzy Systems
Volume 23, Issue 1
January and February 2026
Pages 75-94

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