As of August 2024, International Journal "Notes on Intuitionistic Fuzzy Sets" is being indexed in Scopus.
Please check our Instructions to Authors and send your manuscripts to nifs.journal@gmail.com. Next issue: March 2025.

Issue:Non-conjunctive and non-disjunctive uninorms in Atanassov's intuitionistic fuzzy set theory

From Ifigenia, the wiki for intuitionistic fuzzy sets and generalized nets
Jump to navigation Jump to search
shortcut
http://ifigenia.org/wiki/issue:eusflat-2009-184-188
Title of paper: Non-conjunctive and non-disjunctive uninorms in Atanassov's intuitionistic fuzzy set theory
Author(s):
Glad Deschrijver
Fuzziness and Uncertainty Modelling Research Unit, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B–9000 Gent, Belgium
Glad.Deschrijver@UGent.be
Presented at: Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society for Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009
Published in: Conference proceedings, pages 184—188
Download:  PDF (118  Kb, File info)
Abstract: Uninorms are a generalization of t-norms and t-conorms for which the neutral element is an element of [0,1] which is not necessarily equal to 0 (as for t-norms) or 1 (as for t-conorms). Uninorms on the unit interval are either conjunctive or disjunctive, i.e. they aggregate the pair (0,1) to either 0 or 1. In real life applications, this kind of aggregation may be counter-intuitive. Atanassov's intuitionistic fuzzy set theory is an extension of fuzzy set theory which allows to model uncertainty about the membership degrees. In Atanassov's intuitionistic fuzzy set theory there exist uninorms which are neither conjunctive nor disjunctive. In this paper we study such uninorms more deeply and we investigate the structure of these uninorms. We also give several examples of uninorms which are neither conjunctive nor disjunctive.
Keywords: Conjunctive, disjunctive, interval-valued fuzzy set, intuitionistic fuzzy set, uninorm.
References:
  1. M. B. Gorzałczany. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets and Systems, 21(1):1–17, Jan 1987.
  2. R. Sambuc. Fonctions Φ-floues. Application à l'aide au diagnostic en pathologie thyroidienne. PhD thesis, Universit´e de Marseille, France, 1975.
  3. D. Dubois. On ignorance and contradiction considered as truthvalues. Logic Journal of the IGPL, 16(2):195–216, 2008.
  4. K. T. Atanassov. Intuitionistic fuzzy sets. Physica-Verlag, Heidelberg, New York, 1999.
  5. G. Deschrijver and E. E. Kerre. On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, 133(2):227–235, 2003.
  6. J. A. Goguen. L-fuzzy sets. Journal of Mathematical Analysis and Applications, 18(1):145–174, Apr 1967.
  7. R. R. Yager and A. Rybalov. Uninorm aggregation operators. Fuzzy Sets and Systems, 80(1):111–120, May 1996.
  8. G. Deschrijver and E. E. Kerre. Uninorms in L*-fuzzy set theory. Fuzzy Sets and Systems, 148(2):243–262, 2004.
  9. A. H. Clifford. Naturally totally ordered commutative semigroups. Amer. J. Math., 76:631–646, 1954.
  10. S. Jenei. A note on the ordinal sum theorem and its consequence for the construction of triangular norms. Fuzzy Sets and Systems, 126(2):199–205, Mar 2002.
  11. C.-H. Ling. Representation of associative functions. Publ. Math. Debrecen, 12:189–212, 1965.
  12. S. Saminger. On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets and Systems, 157(10):1403–1416, May 2006.
  13. B. Schweizer and A. Sklar. Associative functions and abstract semigroups. Publ. Math. Debrecen, 10:69–81, 1963.
  14. J. C. Fodor, R. R. Yager, and A. Rybalov. Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 5(4):411–427, Aug 1997.
  15. M. Eisenberg. Axiomatic theory of sets and classes. Holt, Rinehart and Winston, Inc., New York, 1971.
  16. B. Depaire, K. Vanhoof, and G. Wets. The application of uninorms in importance-performance analysis. In FS’06: Proceedings of the 7th WSEAS International Conference on Fuzzy Systems, pages 1–7, Stevens Point, Wisconsin, USA, 2006. World Scientific and Engineering Academy and Society (WSEAS).
  17. K. Vanhoof, P. Pauwels, J. Dombi, T. Brijs, and G. Wets. Penalty-reward analysis with uninorms: A study of customer (dis)satisfaction. In D. Ruan, C. Chen, E. E. Kerre, and G.Wets, editors, Intelligent Data Mining: Techniques and Applications, volume 5, pages 237–252. 2005.
  18. B. Depaire, K. Vanhoof, and G.Wets. Managerial opportunities of uninorm-based importance-performance analysis. WSEAS Transactions on Business and Economics, 3(3):101–108, 2007.
  19. B. Depaire, K. Vanhoof, and G.Wets. Expectation-performance compatibility in a customer satisfaction context modelled by means of aggregation operators. In B. De Baets, K. Maes, and R. Mesiar, editors, Proceedings of the 4th International Summer School on Aggregation Operators, pages 45–50. Academia Press, 2007.
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.

Retrieved from "https://ifigenia.org/index.php?title=Issue:Non-conjunctive_and_non-disjunctive_uninorms_in_Atanassov%27s_intuitionistic_fuzzy_set_theory&oldid=5238"