| Title of paper:
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Intuitionistic L-fuzzy congruence on a ring
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| Author(s):
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| K. Meena
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| P. G. Research Centre in Mathematics, Bharata Mata College, Kochi–682 021, Kerala, India
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| meena_k11@yahoo.co.in
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| K. V. Thomas
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| P. G. Research Centre in Mathematics, Bharata Mata College, Kochi–682 021, Kerala, India
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| Published in:
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"Notes on IFS", Volume 19, 2013, Number 1, pages 7—20
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| Download:
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 PDF (169 Kb, Info)
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| Abstract:
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In this paper we discuss and study some properties of intuitionistic L-fuzzy equivalence relation on a ring. We introduce the concept of intuitionistic L-fuzzy transitive closure of an intuitionistic L-fuzzy relation on a ring. Further the definition of intuitionistic L-fuzzy congruence relation on a ring is introduced and proved that the set of intuitionistic L-fuzzy congruences forms a modular lattice.
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| Keywords:
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Lattice, Intuitionistic L-fuzzy set, Intuitionistic L-fuzzy relation, Intuitionistic L-fuzzy equivalence relation, Intuitionistic L-fuzzy congruence relation.
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| AMS Classification:
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06B10.
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| References:
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- Atanassov, K. T. Intuitionistic Fuzzy Sets. VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
- Atanassov, K. T., S. Stoeva. Intuitionistic L-fuzzy sets, In:- R. Trappl(Ed.), Cybernetics and Systems Research, Vol. 2, Elsevier Sci. Publ., Amsterdam, 1984, 539–540.
- Atanassova, L. On intuitionistic fuzzy versions of L. Zadeh's extension principle, Notes on Intuitionistic Fuzzy Sets, Vol. 13, 2007, No. 3, 33–36.
- Atanassov, K. T. Intuitionistic Fuzzy Sets, Springer, Heidelberg, 1999.
- Atanassov, K. T. On Intuitionistic Fuzzy Sets Theory, Springer, Berlin, 2012.
- Banerjee, B., D. K. Basnet. Intuitionistic Fuzzy Subrings and ideals, J. Fuzzy Math., Vol. 2, 2003, No. 1, 139–155.
- Biswas, R. Intuitionistic Fuzzy Subgroups, Math Forum, Vol. 10, 1989, 39–44.
- Bustince, H., P. Burillo. Intuitionistic Fuzzy Relations (Part I), Mathware and Soft Computing, Vol. 2, 1995, 5–38.
- Khatibi, V., G. A. Montazer. Intuitionistic Fuzzy Set vs Fuzzy Set Application in Medical Pattern Recognition, J. Artificial Intelligence in Medicine, Elsevier, Vol. 47, 2009, No. 1, 43–52.
- Kumar De, S., R. Biswas, A. R. Roy. Some Operations on Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, Vol. 114, 2000, No. 4, 477–484.
- Kumar De, S., R. Biswas, A. R. Roy. An Application of Intuitionistic Fuzzy Sets in Medical Diagnosis, Fuzzy Sets and Systems, Vol. 117, 16 January 2001, Issue 2, 209–213.
- Kul Hur, Su Youn Jang, Hee Won Kang. Intuitionistic Fuzzy Congruences on a lattice, J. Appl. Math and Computing, Vol. 18, 2005, No. 1–2, 465–486.
- Kul Hur, Su Youn Jang, Young Bae Jun. Intuitionistic Fuzzy Congruences, Far East J. Math. Sci. (FJMS), Vol. 17, 2005, No. 1, 1–29.
- Kul Hur, Su Youn Jang, Young Sin Ahn. Intuitionistic Fuzzy Equivalence Relation, Honam Mathematical Journal, Vol. 27, 2005, No. 2, 163–181.
- Kul Hur, Su Youn Jang. The Lattice of Intuitionistic Fuzzy Congruences, IMF, Vol. 1, 2006, No. 5, 211–236.
- Renčová, M. An example of Applications of Intuitionistic Fuzzy Sets to Sociometry, Cybernetics and Technologies, Vol. 9, 2009, No. 2, 43–45.
- Meena, K., K. V. Thomas. Intuitionistic L-Fuzzy Subrings, IMF, Vol. 6, 2011, No. 52, 2561–2572.
- Meena, K., K. V. Thomas. Intuitionistic L-Fuzzy Rings, GJSFR(F), Vol. 12, 2012, No. 14-F, Art. 2.
- Rosenfeld, A. Fuzzy Groups, J. Math. Anal. Appl., Vol. 35, 1971, 512–517.
- Zadeh, L. A. Fuzzy Sets, Information and Control, Vol. 8, 1965, 338–353.
- Zeshui Xu, Jian Chen, Junjie Wu, Clustering Algorithm for Intuitionistic Fuzzy Sets, Information Sciences, Vol. 178, Issue 19, October 2008, 3775–3790.
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| Citations:
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- VEERAMMAL, P., and G. VELAMMAL. "INTUITIONISTIC L-FUZZY ALMOST IDEALS." International Journal of Mathematical Archive EISSN 2229-5046 9.1 (2018), pp. 197-203.
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