| Title of paper:
|
Difference and symmetric difference for intuitionistic fuzzy sets
|
| Author(s):
|
| Taiwo Enayon Sunday
|
| Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Hong Kong
|
| estaiwo2-c@my.cityu.edu.hk
|
| Romuald Dzati Kamga
|
| Laboratoire de Mathématiques Appliquées-UFRD MIBA, Université de Yaoundé I, B.P. 812 Yaoundé, Cameroun
|
| romualdkamga1@yahoo.fr
|
| Siméon Fotso
|
| ENS Yaoundé - Université de Yaoundé I, B.P. 47 Yaoundé, Cameroun
|
| simeonfotso@yahoo.fr
|
| Louis Aimé Fono
|
| Laboratoire de Mathématiques, Université de Douala, B.P. 24157 Douala, Cameroun
|
| lfono2000@yahoo.fr
|
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 113–140
|
| DOI:
|
https://doi.org/10.7546/nifs.2018.24.4.113-140
|
| Download:
|
 PDF (274 Kb Kb, File info)
|
| Abstract:
|
Fono et al. [10] determined some classes of difference and symmetric difference operations for fuzzy sets using fuzzy implication operators. Intuitionistic fuzzy sets are known to be generalizations of fuzzy sets. So, in this paper, we propose new difference and symmetric difference operations for intuitionistic fuzzy sets based on intuitionistic fuzzy R-implication operators and standard intuitionistic fuzzy negation operator. We establish that some common properties of the difference operations for fuzzy sets established earlier by Fono et al. in [10] and for crisp sets are preserved by the new obtained operations for intuitionistic fuzzy sets. We display a specific property satisfied by difference operation in crisp and fuzzy cases and violated in intuitionistic fuzzy case. The proposed difference and symmetric difference operations for intuitionistic fuzzy sets generalize the case for fuzzy sets. This strength provides a more dynamic perspective into the studies and applications of these operations.
|
| Keywords:
|
Intuitionistic fuzzy set, Difference operation, Symmetric difference operation, Intuitionistic fuzzy R-implication, Intuitionistic fuzzy negation.
|
| AMS Classification:
|
03F55.
|
| References:
|
- Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy sets and Systems, 20 (1), 87–96.
- Atanassov, K. T. (1999). Intuitionistic fuzzy sets: theory and applications, Physica-Verlag, New York.
- Atanassov, K. T. (2010). On intuitionistic fuzzy negations and law for excluded middle, Proceedings of 5th IEEE International Conference Intelligent Systems (IS), 7–9 July 2010, London, United Kingdom, 266–269.
- Bustince, H., Kacprzyk, J., & Mohedano, V. (2000). Intuitionistic fuzzy generators application to intuitionistic fuzzy complementation, Fuzzy sets and systems, 114 (3), 485–504.
- Cornelis, C., Deschrijver, G. & Kerre, E. E. (2004). Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application, International Journal of Approximate Reasoning, 3 (1), 55–95.
- Deschrijver, G., Cornelis, C. & Kerre, E. E. (2004). On the Representation of Intuitionistic Fuzzy t-Norms and t-Conorms, IEEE Transactions on Fuzzy Systems, 12 (1), 45–61.
- Despi, I., Opris, D. & Yalcin, E. (2013). Generalised Atanassov Intuitionistic Fuzzy Sets, Proceedings of 5th International Conference on Information, Process and Knowledge Management, 24 Feb. - 1 Mar. 2013, Nice, France, 51–52.
- Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J. & Prade, H. (2005). Terminological difficulties in fuzzy set theory—the case of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 156 (3), 485–491.
- Ejegwa, P. A., Akowe, S. O., Otene, P. M. & Ikyule, J. M. (2014). An Overview on Intuitionistic Fuzzy Sets, International Journal of Scientific & Technology Research, 3 (3), 142–145.
- Fono, L. A., Gwet, H. & Bouchon-Meunier, B. (2007). Fuzzy implication operators for difference operations for fuzzy sets and cardinality-based measures of comparison, European Journal of Operational Research, 183, 314–326.
- Fono, L. A., Gwet, H. & Fotso, S. (2008). On strict lower and upper sections of weakly complete fuzzy pre-orders based on co-implication, Fuzzy Sets and Systems, 159, 2240– 2255.
- Fono, L. A. & Gwet, H. (2003). On strict lower and upper sections of fuzzy orderings, Fuzzy Sets and Systems, 139, 583–599.
- Fono, L. A., Njanpong, G. N., Salles, M. & Gwet, H. (2009). A binary intuitionistic fuzzy relation: some new results, a general factorization and two properties of strict components, International Journal of Mathematics and Mathematical Sciences, 3–7.
- Hinde, C. & Atanassov, K. T. (2008). On intuitionistic fuzzy negations and intuitionistic fuzzy extended modal operators (Part 2), Proceedings of 4th International IEEE Conference Intelligent Systems, 6-8 Sept. 2008, Varna, Bulgaria, 3, 13–19.
- Huawen, L. (1987). Difference operation defined over the intuitionistic fuzzy sets (PhD thesis), School of Mathematics and System Sciences, Shandong University, Jinan, Shandong 250100, China.
- Lee, K. H. (2006). First course on fuzzy theory and applications, Springer Science & Business Media.
- Njanpong, G. N. & Fono, L. A. (2013). Arrow-type results under intuitionistic fuzzy preferences, New Mathematics and Natural Computation, 9 (1), 98–99.
- Reiser, R. H. S. & Bedregal, B. (2013). Interval-valued intuitionistic fuzzy implications – construction, properties and representability, Information Sciences, 248, 68–88.
- Tripathy, B. K., Jena, S. P. & Ghosh, S. K. (2013). An intuitionistic fuzzy count and cardinality of intuitionistic fuzzy sets, Malaya Journal of Matematik, 4 (1), 123–133.
- Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8 (3), 338–353.
|
| 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.
|
|
