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INTUITIONISTIC FUZZY BI-IMPLICATOR AND PROPERTIES OF LUKASIEWICZ INTUITIONISTIC FUZZY BI-IMPLICATOR

Yıl 2019, Cilt: 9 Sayı: 2, 315 - 326, 01.06.2019

Öz

This paper presents axiomatic as well as constructive de nitions of intu- itionistic fuzzy bi-implicators based on intuitionistic fuzzy t-norms and their intuition- istic fuzzy residual implicators. The inter-relationship among di erent proposed classes is presented along with a detailed study of the properties of one of these intuitionistic fuzzy bi-implicators called the intuitionistic fuzzy bi-implicator operator constructed using Lukasiewicz intuitionistic fuzzy t-norm and its R-implicator.

Kaynakça

  • [1] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and Systems, 20(1), 87-96.
  • [2] Atanassov, K. T. (1999). Applications of Intuitionistic Fuzzy Sets. In Intuitionistic Fuzzy Sets Physica-Verlag HD, 237-288.
  • [3] Atanassov, K. T. (2001). Remarks on the conjunctions, disjunctions and implications of the intuitionistic fuzzy logic. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(01), 55-65.
  • [4] Ashraf, S., Kerre, E.E., & Qayyum, M. (2017). The intuitionistic fuzzy multicriteria decision making based on inclusion degree. Comptes Rendus Del’ Academie Bulgare Des Sciences, 70(7), 925-934.
  • [5] Baczynski, M. (2003). On some properties of intuitionistic fuzzy implications. In EUSFLAT Conf, 168-171.
  • [6] Bedregal, B. C. and Cruz, A. P. (2008). A characterization of classic-like fuzzy semantics. Logic Journal of IGPL, 16(4), 357-370.
  • [7] Bustince, H., and Burillo, P. (1996). Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems, 79(3), 403-405.
  • [8] Bustince, H., Barrenechea, E. and Pagola, M. (2006). Restricted equivalence functions. Fuzzy Sets and Systems, 157(17), 2333-2346.
  • [9] Cornelis, C., Deschrijver, G. and Kerre, E. (2004). Implication in Intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. International Journal of Approximate Reasoning, 35(1), 55-95.
  • [10] Cornelis, C., Deschrijver, G. and Kerre, E. (2002). Classification Of Intuitionistic Fuzzy Implicators: An Algebraic Approach. In JCIS,105-108.
  • [11] Deschrijver, G. and Kerre, E. (2003). On the relationship between some extensions of fuzzy set theory. Fuzzy sets and systems, 133(2), 227-235.
  • [12] Deschrijver, G., Cornelis, C. and Kerre, E. (2004). On the representation of intuitionistic fuzzy t-norms and t-conorms. Fuzzy Systems, IEEE Transactions on, 12(1), 45-61.
  • [13] Deschrijver, G. and Kerre, E. (2003). Classes of intuitionistic fuzzy t-norms satisfying the residuation principle. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11(06), 691-709.
  • [14] Fodor, J. C. and Roubens, M. R. (2013). Fuzzy preference modelling and multicriteria decision support. Springer Science & Business Media 14(1).
  • [15] Gau, W. L., and Buehrer, D. J. (1993). Vague sets. IEEE Transactions on Systems, Man, and Cybernetics, 23(2), 610-614.
  • [16] H´ajek, P. (1998). Metamathematics of fuzzy logic. Springer Science & Business Media, 4(1).
  • [17] Moser, B. (2006). On the T-transitivity of kernels. Fuzzy Sets and Systems, 157(13), 1787-1796.
  • [18] Murugadas, P., and Lalitha, K. (2014). Bi-implication Operator on Intuitionistic Fuzzy Set. International Journal of Computer Applications, 89(1).
  • [19] Nov´ak, V. and De Baets, B. (2009). EQ-algebras. Fuzzy Sets and Systems, 160(20), 2956-2978.
  • 20] Qayyum, M., S. Ashraf, E. E. Kerre (2016). Measure of intuitionistic fuzzy inclusion. Comptes Rendus Del’ Academie Bulgare Des Sciences, 69(8), 971-980.
Yıl 2019, Cilt: 9 Sayı: 2, 315 - 326, 01.06.2019

Öz

Kaynakça

  • [1] Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy sets and Systems, 20(1), 87-96.
  • [2] Atanassov, K. T. (1999). Applications of Intuitionistic Fuzzy Sets. In Intuitionistic Fuzzy Sets Physica-Verlag HD, 237-288.
  • [3] Atanassov, K. T. (2001). Remarks on the conjunctions, disjunctions and implications of the intuitionistic fuzzy logic. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(01), 55-65.
  • [4] Ashraf, S., Kerre, E.E., & Qayyum, M. (2017). The intuitionistic fuzzy multicriteria decision making based on inclusion degree. Comptes Rendus Del’ Academie Bulgare Des Sciences, 70(7), 925-934.
  • [5] Baczynski, M. (2003). On some properties of intuitionistic fuzzy implications. In EUSFLAT Conf, 168-171.
  • [6] Bedregal, B. C. and Cruz, A. P. (2008). A characterization of classic-like fuzzy semantics. Logic Journal of IGPL, 16(4), 357-370.
  • [7] Bustince, H., and Burillo, P. (1996). Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems, 79(3), 403-405.
  • [8] Bustince, H., Barrenechea, E. and Pagola, M. (2006). Restricted equivalence functions. Fuzzy Sets and Systems, 157(17), 2333-2346.
  • [9] Cornelis, C., Deschrijver, G. and Kerre, E. (2004). Implication in Intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. International Journal of Approximate Reasoning, 35(1), 55-95.
  • [10] Cornelis, C., Deschrijver, G. and Kerre, E. (2002). Classification Of Intuitionistic Fuzzy Implicators: An Algebraic Approach. In JCIS,105-108.
  • [11] Deschrijver, G. and Kerre, E. (2003). On the relationship between some extensions of fuzzy set theory. Fuzzy sets and systems, 133(2), 227-235.
  • [12] Deschrijver, G., Cornelis, C. and Kerre, E. (2004). On the representation of intuitionistic fuzzy t-norms and t-conorms. Fuzzy Systems, IEEE Transactions on, 12(1), 45-61.
  • [13] Deschrijver, G. and Kerre, E. (2003). Classes of intuitionistic fuzzy t-norms satisfying the residuation principle. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 11(06), 691-709.
  • [14] Fodor, J. C. and Roubens, M. R. (2013). Fuzzy preference modelling and multicriteria decision support. Springer Science & Business Media 14(1).
  • [15] Gau, W. L., and Buehrer, D. J. (1993). Vague sets. IEEE Transactions on Systems, Man, and Cybernetics, 23(2), 610-614.
  • [16] H´ajek, P. (1998). Metamathematics of fuzzy logic. Springer Science & Business Media, 4(1).
  • [17] Moser, B. (2006). On the T-transitivity of kernels. Fuzzy Sets and Systems, 157(13), 1787-1796.
  • [18] Murugadas, P., and Lalitha, K. (2014). Bi-implication Operator on Intuitionistic Fuzzy Set. International Journal of Computer Applications, 89(1).
  • [19] Nov´ak, V. and De Baets, B. (2009). EQ-algebras. Fuzzy Sets and Systems, 160(20), 2956-2978.
  • 20] Qayyum, M., S. Ashraf, E. E. Kerre (2016). Measure of intuitionistic fuzzy inclusion. Comptes Rendus Del’ Academie Bulgare Des Sciences, 69(8), 971-980.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S. Ashraf Bu kişi benim

M. Qayyum Bu kişi benim

E. E. Kerr Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 2

Kaynak Göster