Intuitionistic FWI-ideals of residuated lattice Wajsberg algebras

Shanmugapriya R. Shanmugapriya, Ibrahim Abdul

Abstract


The notions of intutionistic fuzzy Wajsberg implicative ideal( –ideal) and intuitionistic fuzzy lattice ideal of residuated Wajsberg algebras are introduced. Also,  we show that every intuitionistic - ideal of residuated lattice Wajsberg algebra is an intuitionistic fuzzy lattice ideal of residuated lattice Wajsberg algebra. Further, we discuss its converse part.


Keywords


Wajsberg algebra; Lattice Wajsberg algebra; Residuated lattice Wajsberg algebra; WI–ideal; FWI –ideal; Intuitionistic FWI –ideal; Intuitionistic fuzzy lattice ideal.

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References


K.T. Atanassav, Intuitionistic fuzzy sets, Fuzzy sets and systems, 20(1):87-96,1986.

K.T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems,61(2):137-142,1994.

J. M. Font, A. J. Rodriguez and A.Torrens, Wajsberg algebras, STOCHASTICA, 8 (1): 5-31,1984.

A. Ibrahim and C. Shajitha Begum, On WI-Ideals of lattice Wajsberg algebras, Global Journal of Pure and Applied Mathematics, 13(10): 7237-7254, 2017.

A. Ibrahim and C. Shajitha Begum, Fuzzy and normal fuzzy WI-ideals of lattice Wajsberg algebras, International Journal of Mathematical Archive, 8(11):122-130, 2017.

A. Ibrahim and C. Shajitha Begum, Intuitionistic fuzzy WI-ideals of lattice Wajsberg algebras, International Journal of Mathematical Archive,7-17,2018.

A. Ibrahim and R.S hanmugapriya, WI-Ideals of residuated lattice Wajsberg algebras, Journal of applied science and computations,792-798, 2018.

A. Ibrahim and R. Shanmugapriya, FWI-Ideals of residuated lattice Wajsberg algebras, Journal of Computer and Mathematical Sciences, 491-501,2019.

A. Ibrahim and R.Shanmugapriya, Anti FWI-Ideals of residuated lattice Wajsberg algebras, Advances in mathematics:Scientific Journal 8:300-306, 2019.

M. Wajsberg, Beitrage zum Metaaussagenkalkul, Monat. Mat. Phy., 42: 221-242,1935.

M. Word and R. P. Dilworth, Residuated Lattices, Transactions the American Mathematical Society 45: 335-354,1939.

Yi Liu, Ya Qin, Qin Xiaoyan and Xu Yang, Ideals and fuzzy ideals on residuated lattices, International Journal of machine Learning and Cybernetics, volume 8(1): 239-253, 2017.

L. A. Zadeh, Fuzzy Sets, Information and Control, 8(3): 338-353,1965.




DOI: http://dx.doi.org/10.23755/rm.v40i1.587

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.