| Title of paper:
|
Divergence measures on intuitionistic fuzzy sets
|
| Author(s):
|
| Vladimír Kobza
|
| Department of Mathematics, Matej Bel University, Tajovskeho 40, 974 01 Banská Bystrica, Slovak Republic
|
| vladimir.kobza@umb.sk
|
|
| Presented at:
|
International Workshop on Intuitionistic Fuzzy Sets, founded by Prof. Beloslav Riečan, 2 December 2022, Banská Bystrica, Slovakia
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 4, pages 413–427
|
| DOI:
|
https://doi.org/10.7546/nifs.2022.28.4.413-427
|
| Download:
|
 PDF (192 Kb, File info)
|
| Abstract:
|
The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. Many authors investigated possibilities how two fuzzy sets can be compared and the most common kind of measures used in the mathematical literature are dissimilarity measures. The previous approach to the dissimilarities is too restrictive, because the third axiom in the definition of dissimilarity measure assumes the inclusion relation between fuzzy sets. While there exist many pairs of fuzzy sets, which are incomparable to each other with respect to the inclusion relation. Therefore we need some new concept for measuring a difference between fuzzy sets so that it could be applied for arbitrary fuzzy sets. We focus on the special class of so called local divergences. In the next part we discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets. In this case we define the local property modified to this object. We discuss also the relation of usual divergences between fuzzy sets to the divergences between intuitionistic fuzzy sets.
|
| Keywords:
|
Intuitionistic fuzzy set, Dissimilarity measure, Divergence measure, Local divergence, Entropy measure.
|
| AMS Classification:
|
03B52.
|
| References:
|
- Anthony, M., & Hammer, P. L. (2006). A Boolean measure of similarity. Discrete Applied Mathematics, 154(16), 2242–2246.
- Atanassov, K. T. (1983). Intuitionistic Fuzzy Sets. VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted in: Int. J. Bioautomation, 2016, 20(S1), S1–S6. (in English).
- Bouchon-Meunier, B., Rifqi, M., & Bothorel, S. (1996). Towards general measures of comparison of objects. Fuzzy Sets and Systems, 84, 143–153.
- Burillo, P., & Bustince, H. (1996). Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 78, 305–316.
- Couso, I., Garrido, L., & Sánchez, L. (2013). Similarity and dissimilarity measures between fuzzy sets: A formal relational study. Information Sciences, 229, 122–141.
- Hung, W. L., & Yang, M. S. (2006). Fuzzy Entropy on Intuitionistic Fuzzy Sets. International Journal of Intelligent Systems, 21, 443–451.
- Lui, X. (1992). Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems, 52, 305–318.
- Montes, I. M. (2014). Comparison of alternatives under uncertainty and imprecision [Doctoral Dissertation, University of Oviedo, Spain].
- Kobza, V., Janiš, V., Montes, S. (2017). Generalizated local divergence measures. Journal of Intelligent & Fuzzy Systems, 33, 337–350.
- Montes, S. (1998). Partitions and divergence measures in fuzzy models [Doctoral Dissertation, University of Oviedo, Spain].
- Montes, S., Couso, I., Gil, P., & Bertoluzza, C. (2002). Divergence measure between fuzzy sets. International Journal of Approximate Reasoning, 30, 91–105.
- Szmidt, E., & Kacprzyk, J. (2001). Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118, 467–477.
- Zadeh, L. (2014). A note on similarity-based definitions of possibility and probability. Information Sciences, 267, 334–336.
- Zhang, C., & Fu, H. (2006). Similarity measures on three kinds of fuzzy sets. Pattern Recognition Letters, 27 (2), 1307–1317
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
