Generalized interval valued fuzzy ideals of KU-algebra

Downloads

DOI:

https://doi.org/10.26637/MJM0703/0020

Abstract

In this paper, we introduced the concept of "belongs to" relation $\left(\epsilon_{\hat{a}}\right)$ between interval valued fuzzy point to an interval valued fuzzy set with respect to an interval $\hat{a}$ and "quasi-coincident with " relation $\left(q_{(\hat{a}, \hat{b})}\right)$ between interval valued fuzzy point to an interval valued fuzzy set with respect to intervals $\hat{a}, \hat{b}$ and combining both the concepts we define $\left(\hat{a}, \hat{b} ; \epsilon_{\hat{a}}, \epsilon_{\hat{a}} \vee q_{(\hat{a}, \hat{b})}\right)$-interval valued fuzzy KU-ideals in KU-algebras and investigated some of their related properties. Some characterizations of these generalized interval valued fuzzy KU-ideal are derived.

Keywords:

KU -algebra, Fuzzy ideal, (∈,∈∨q) -fuzzy ideal, Homomorphism

Mathematics Subject Classification:

Mathematics
  • S. R. Barbhuiya Department of Mathematics, Srikishan Sarda College, Hailakandi-788151, Assam, India.
  • A. K. Dutta Department of Mathematics, D.H.S.K. College, Dibrugarh, Assam- 786001, India.
  • Pages: 486-496
  • Date Published: 01-07-2019
  • Vol. 7 No. 03 (2019): Malaya Journal of Matematik (MJM)

M. Akram, N. Yaqoob and J. Kavikumar, Interval valued $(tilde{theta}, tilde{delta})$-fuzzy KU-ideals of KU-algebras, Int. J. Pure Appl. Math. 92(3) (2014), 335-349.

S. K. Bhakat and P. Das, $(in, in vee q)$-fuzzy subgroup, Fuzzy sets and systems, 80 (1996), 359-368.

S. K. Bhakat and P. Das, $(in vee q)$-level subset,Fuzzy sets and systems, 103(3)(1999), 529-533.

R. Biswas, Rosenfels fuzzy subgroups with interval valued membership functions,Fuzzy Sets and Systems, 63 (1994) 87-90.

P. Das, Products of $left(a, b ; in_a, in_a vee q_{(a, b)}right)$-Fuzzy subgroups, J. Fuzzy Math. 4(4) (1996), 871-878.

P. Das, Fuzzy subalgebras redefined,J. Fuzzy Math, 3(3) (1995), 517-527.

T. K. Dutta, S. Kar, and S. Purkait, Interval-valued fuzzy prime and semiprime ideals of a hyper semiring,Annals of Fuzzy Mathematics and Informatics, 9(2), (2015), 261278.

Y. Imai and K. Iseki, On Axiom systems of Propositional calculi XIV,Proc, Japan Academy, 42 (1966), 19-22.

K. Iseki, An algebra related with a propositional calculus, Proc. Japan Academy, 42 (1966), 26-29.

K. Iseki, On some ideals in BCK-algebras,Math.Seminar Notes, 3 (1975), 65-70.

D. S. Lee, and C. H. Park, Interval valued $left(in vee q_kright)-$ Fuzzy Ideals Rings, International Mathematical Forum, 4(13),(2009) 623-630.

P. P. Ming and L. Y. Ming, Fuzzy topology I, Neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Maths. Anal. Appl, 76(1980), 571-599.

V. Murali, Fuzzy points of equivalent fuzzy subsets, inform Sci, 158 (2004), 277-288.

G. Muhiuddin, Bipolar fuzzy KU-subalgebras and ideals of KU-algebras, Ann. Fuzzy Math. Inform. 8(3) (2014), $409-418$.

J. Neggers and H. S. Kim, On B-algebras,Math. Vensik, 54 (2002), 21-29. 54 (2002), 21-29.

C. Prabpayak and U. Leerawat,On ideals and congruence in KU-algebras,scientia Magna, international book series, Vol. 5(2009), No.1, 54-57.

${ }^{[17]}$ C. Prabpayak and U. Leerawat, On isomorphisms of KU-algebras, scientia Magna,international book series, 5(2009), no .3, 25-31.

S. M. Mostafa, M. A. Abd-Elnaby and M.M.M. Yousef, Fuzzy ideals of KU-Algebras,Int. Math. Forum, 6(63) (2011) 3139-3149.

Mostafa, S.M., Abd-Elnaby, M.A., Elgendy, O.R. Interval-valued fuzzy KU-ideals in KU-algebras, Int. Math. Forum, 6(64),(2011), 3151-3159.

S. M. Mostafa and F. F. Kareem, N-fold commutative KU-Algebras,Int. J. Algebra, 8(6) (2014), 267-275.

S. M. Mostafa and F. F. Kareem, Fuzzy n-fold KU-ideals KU-Algebras,Ann. Fuzzy Math.

M. Gulistan, M. Shahzad and S. Ahmed, On $(alpha, beta)$-fuzzy KU-ideals of KUalgebras,Afr. Mat., (2014), 1-11, doi: 10.1007/s13370-014-0234-2.

O. G. Xi, Fuzzy BCK algebras, Math Japonica, 36,(1991) 935-942.

Y. B. Yun, On $(alpha, beta)$-Fuzzy ideals of BCK/BCI-Algebras, Scientiae Mathematicae Japonicae, online, e-2004, 101105.

Y. B. Yun, Interval-valued fuzzy subalgebras/ideals in BCK-algebras, Scientiae Mathematicae, $3(3)$ (2000) 435444.

Y. B. Jun and K.H. Kim, Interval-valued fuzzy rsubgroups of near-rings, Indian Journal of Pure and Applied Mathematics, 33(1) (2002) 71-80.

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

L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Inf Science., $8,(1975) 199-249$.

J. Zhan, Y. B. Jun and B. Davvaz, On $(in vee q)$-Fuzzy Ideals of BCI-algebras, Iranian Journal of Fuzzy Systems, $6(1),(2009) 81-94$.

X. Ma,J. Zhan, B. Davvaz and Y. B. Jun, Some kinds of $left(in vee q_kright)$-interval-valued fuzzy ideals of $B C I$-algebras, Information Sciences, 178,(2008)3738-3754.

  • NA

Metrics

Metrics Loading ...

Published

01-07-2019

How to Cite

S. R. Barbhuiya, and A. K. Dutta. “Generalized Interval Valued Fuzzy Ideals of KU-Algebra”. Malaya Journal of Matematik, vol. 7, no. 03, July 2019, pp. 486-9, doi:10.26637/MJM0703/0020.