Intuitionistic Fuzzy Congruence Relations on Intuitionistic Fuzzy Abstract Algebras

Yıl 2019, Cilt: 32 Sayı: 2, 649 - 658, 01.06.2019

Sinem Tarsuslu Yılmaz Mehmet Cıtıl

Öz

In
this study, the intuitionistic fuzzy congruence relations on intuitionistic
fuzzy abstract algebras were examined using Zadeh extension principle. Some
basic properties of intuitionistic fuzzy congruence relations on n-ary
operations were obtained.

Anahtar Kelimeler

Intuitionistic fuzzy sets, intuitionistic fuzzy universal algebra, intuitionistic fuzzy equivalence relations, intuitionistic fuzzy congruence relations

Kaynakça

• [1] Atanassov K.T., Intuitionistic Fuzzy Sets, VII ITKR.s Session, SoÖa, June 1983.
• [2] K. T. Atanassov, Studies in fuzziness and soft computing-on intuitionistic fuzzy sets theory, ISBN 978-3-642-29126-5, Springer 2012.
• [3] Birkho§ G., LatticeTheory, American Mathematical Society, United States of America, 418 p., (1940).
• [4] Burillo P., Bustince H., Intuitionistic fuzzy relations (Part I) Mathware Soft Comput., 2 (1995), 5-38.
• [5] Bustince H., Burillo P., Structures on intuitionistic fuzzy relations, Fuzzy Sets and Systems, 78 (1996), 293-303.
• [6] Cohn P.M., Universal Algebra, D. Reidel Publishing Company, Dordrecht: Holland/ Boston: U.S.A/ London: England, 412 p., (1981).
• [7] Çuvalcıoglu, G.; Yılmaz, S. Some properties of intuitionistic Fuzzy equivalence relations º and class trees w.r.t. intuitionistic Fuzzy equivalence relations. ADV. STUDIES CONTEMP. · MATH, 2014, 1(24), 1-9.
• [8] Çuvalcıoglu G., Tarsuslu(Yılmaz) S., Universal Algebra in Intuitionistic Fuzzy Set Theory, º Notes on Intuitionistic Fuzzy Sets, 23 (1), 2017, 1-5.
• [9] Çuvalcıoglu G., Tarsuslu(Yılmaz) S., Isomorphism theorems on Intuitionistic Fuzzy Universal º Algebras, Hacettepe Journal of Mathematics and Statistics, under review.
• [10] Deschrijver G., Kerre E.E., On the composition of intuitionistic fuzzy relations, Fuzzy Sets and systems, 2003, 136, 333ñ361.
• [11] Hur K, Su Y. J., Hee W. K., The lattice of intuitionistic fuzzy congruences, Int. Math. Forum, 5(1), 2006, 211-236.
• [12] Hur K., Jang S. Y. and Ahn Y. S., Intuitionistic fuzzy equivalence relations, Honam Math. J. 27(2), 2005, 163-181.
• [13] Li M., Cut sets of intuitionistic fuzzy sets (in Chinese), Journal of Liaoning Normal university, 30(2) (2007) 152-154.
• [14] Mural¨V., A Study of Universal Algebra in Fuzzy Set Theory, Rhodes University, Department of Mathematics, PhD. Thesis, 1987, 104p.
• [15] Mural¨V., Fuzzy congruence relations, Fuzzy Sets and Systems, 41(3), 1991, 359-369.
• [16] Palaniappan N., Naganathan S. and Arjunan K., A study on Intuitionistic L-Fuzzy Subgroups, App. Math. Sciences, 3(53), 2009, 2619-2624.
• [17] Zadeh L.A., Fuzzy Sets, Information and Control, 8, 1965, 338-353.
• [18] Zadeh L.A., The concept of linguistic variable and its application to approximate reasoning. Inform. Sci., 8 (1975). 133-139.