Generalized interval valued fuzzy ideals of \(KU\)-algebra
Downloads
DOI:
https://doi.org/10.26637/MJM0704/0018Abstract
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 $\left(\hat{a}, \hat{b} ; \in_{\hat{a}}, \in_{\hat{a}} \vee q_{(\hat{a}, \hat{b})}\right)$-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, fuzzy ideal, HomomorphismMathematics Subject Classification:
Mathematics- Pages: 735-745
- Date Published: 01-10-2019
- Vol. 7 No. 04 (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.
$mathrm{S}$. 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, $(in vee V q)$-level subset, Fuzzy Sets and Systems, 103(3)(1999), 529-533.
$mathrm{R}$. Biswas, Rosenfels fuzzy subgroups with interval valued membership functions, Fuzzy Sets and Systems, 63(1994), 87-90.
P. Das, Products of $left(a, b ; epsilon_a, epsilon_a vee q_{(a, b)}right)$-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 $left(in V q_kright)$ 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 $S c i, 158$ (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, $54(2002), 21-29$
C. Prabpayak and U. Leerawat,On ideals and congruence in KU-algebras,scientia Magna, international book series, $5(1)(2009), 54-57$
C. Prabpayak and U. Leerawat, On Isomorphisms of $K U$-algebras, Scientia Magna, International Book Series, $5(3)(2009), 25-31$.
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., 4(3)(2014), 12-23.
M. Gulistan, M. Shahzad and S. Ahmed, On $(alpha, beta)$-fuzzy KU-ideals of KUalgebras, Afr. Mat., (2014), 1-11.
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, 101-105.
Y. B. Yun, Interval-valued fuzzy subalgebras/ideals in BCK-algebras, Scientiae Mathematicae, 3(3)(2000), $435-$ 444.
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, $$
(1965), 338-353 text {. }
$$
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 ( $in mathcal{V})$-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
Similar Articles
- Arif Mehmood Khattak, Fawad Nadeem, Muhammad Zamir, Giorgio Nordo, Choonkil Park, Mehak Gul, Other separation axioms in soft bi-topological spaces , Malaya Journal of Matematik: Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 MJM
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.