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{{issue/title
{{issue/title
  | title          = Comparison study based on the divergence measures between intuitionistic fuzzy sets and some applications
  | title          = Comparison study based on the divergence measures between intuitionistic fuzzy sets and some applications
  | shortcut        = nifs/30/4/323-332
  | shortcut        = nifs/30/4/333-348
}}
}}
{{issue/author
{{issue/author
  | author          = Michaela Bruteničová
  | author          = Vladimír Kobza
  | institution    = Department of Mathematics, University of Matej Bel   
  | institution    = Department of Mathematics, Matej Bel University  
  | address        = Tajovského 40, Banská Bystrica, Slovakia
  | address        = Tajovského 40, Banská Bystrica, Slovakia
| email-before-at = michaela.brutenicova
  | email-before-at = vladimir.kobza
| email-after-at  = umb.sk
}}
{{issue/author
| author          = Vladimír Janiš
| institution    = Department of Mathematics, University of Matej Bel 
| address        = Tajovského 40, Banská Bystrica, Slovakia
  | email-before-at = vladimir.janis
  | email-after-at  = umb.sk
  | email-after-at  = umb.sk
}}
}}


{{issue/data
{{issue/data
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/30/4|Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 4]], pages 323–332
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/30/4|Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 4]], pages 333–348
  | doi            = https://doi.org/10.7546/nifs.2024.30.4.323-332
  | doi            = https://doi.org/10.7546/nifs.2024.30.4.333-348
  | file            = NIFS-30-4-323-332.pdf
  | file            = NIFS-30-4-333-348.pdf
  | format          = PDF
  | format          = PDF
  | size            = 292
  | size            = 229
  | abstract        = Comparison of measuring the degree of inclusion for two intuitionistic fuzzy sets (IF-sets) and measuring the degree of embedding of two intervals is considered. Embedding is understood as the classical inclusion of intervals. Inclusion of IF-sets is based on a specific order. In case that the nonmebership function does not exceed the membership function in an IF set, and we replace formally the IF-set by an interval-valued fuzzy set, then the inclusion of IF-sets corresponds to an embedding of interval-valued sets. The embedding measure for interval-valued fuzzy sets was defined previously and we compare the concept of embedding with the inclusion of IF-sets.
  | abstract        = Many authors investigated possibilities how two fuzzy sets can be compared. The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. The previous approach to the dissimilarities is too restrictive, because it assumes the inclusion relation between fuzzy sets and many pairs of fuzzy sets are incomparable to each other with respect to this relation. Therefore we need new concept for measuring - divergence measures. We discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets (IFSs). We have focused on some applications of this concept to pattern recognition and to decision making. In both cases, we present an illustrative example.
  | keywords        = Inclusion measure, Embedding measure, Intuitionistic fuzzy sets.
 
  | ams            = 03E72.
  | keywords        = Intuitionistic fuzzy set, Divergence measure, Applications, Pattern recognition, Decision making.
  | ams            = 03B52.
  | references      =  
  | references      =  
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# Anthony, M., & Hammer, P. L. (2006). A Boolean measure of similarity. In: Discrete Applied Mathematics, 154(16), 2242–2246.
# Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets Theory. Studies in Fuzziness and Soft Computing 283, Springer-Verlag Berlin Heidelberg, 2012.
# 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).
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  | citations      =  
  | citations      =  
  | see-also        =  
  | see-also        =  
}}
}}

Latest revision as of 23:25, 13 December 2024

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http://ifigenia.org/wiki/issue:nifs/30/4/333-348
Title of paper: Comparison study based on the divergence measures between intuitionistic fuzzy sets and some applications
Author(s):
Vladimír Kobza
Department of Mathematics, Matej Bel University, Tajovského 40, Banská Bystrica, Slovakia
vladimir.kobza@umb.sk
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 30 (2024), Number 4, pages 333–348
DOI: https://doi.org/10.7546/nifs.2024.30.4.333-348
Download:  PDF (229  Kb, File info)
Abstract: Many authors investigated possibilities how two fuzzy sets can be compared. The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. The previous approach to the dissimilarities is too restrictive, because it assumes the inclusion relation between fuzzy sets and many pairs of fuzzy sets are incomparable to each other with respect to this relation. Therefore we need new concept for measuring - divergence measures. We discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets (IFSs). We have focused on some applications of this concept to pattern recognition and to decision making. In both cases, we present an illustrative example.
Keywords: Intuitionistic fuzzy set, Divergence measure, Applications, Pattern recognition, Decision making.
AMS Classification: 03B52.
References:
  1. Anthony, M., & Hammer, P. L. (2006). A Boolean measure of similarity. In: Discrete Applied Mathematics, 154(16), 2242–2246.
  2. 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).
  3. Bouchon-Meunier, B., Rifqi, M., & Bothorel, S. (1996). Towards general measures of comparison of objects. Fuzzy Sets and Systems, 84, 143–153.
  4. Couso, I., Garrido, L., & Sanchez, L. (2013). Similarity and dissimilarity measures between fuzzy sets: A formal relational study. Information Sciences, 229, 122–141.
  5. Kobza, V. (2022). Divergence measures on intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 28(4), 413–427.
  6. Kobza, V., Janis, V., & Montes, S. (2017). Generalizated local divergence measures. ˇ Journal of Intelligent & Fuzzy Systems, 33, 337–350.
  7. Lui, X. (1992). Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems, 52, 305–318.
  8. Montes, S. (1998). Partitions and divergence measures in fuzzy models. [Doctoral Dissertation, University of Oviedo, Spain].
  9. Montes, S., Couso, I., Gil, P., & Bertoluzza, C. (2002). Divergence measure between fuzzy sets. International Journal of Approximate Reasoning, 30, 91–105.
  10. Papakostas, G. A., Hatzimichailidis, A. G., & Kaburlasos, V. G. (2013). Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view. Pattern Recognition Letters, 34(14), 1609–1622.
  11. Szmidt, E. (2014). Distances and Similarities in Intuitionistic Fuzzy Sets. “Studies in Fuzziness and Soft Computing”, Vol. 307, Springer.
  12. Wang, W., & Xin, X. (2005). Distance measure between intuitionistic fuzzy sets. In: Pattern Recognition Letters, 26, 2063–2069.
  13. Xu, Z., & Xia, M. (2011). Distance and similarity measures for hesitant fuzzy sets. Information Sciences, 181, 2128–2138.
  14. Zadeh, L. (2014). A note on similarity-based definitions of possibility and probability. Information Sciences, 267, 334–336.
  15. Zhang, C., & Fu, H. (2006). Similarity measures on three kinds of fuzzy sets. Pattern Recognition Letters, 27(2), 1307–1317.
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