Sage Journals: Discover world-class research

Abstract

In this paper, the concept of quasi-coincidence of a bipolar fuzzy point within a bipolar fuzzy set is introduced. The notion of ∈-bipolar fuzzy soft set and q-bipolar fuzzy soft set is introduced based on a bipolar fuzzy set and characterizations for an ∈-bipolar fuzzy soft set and a q-bipolar fuzzy soft set to be bipolar fuzzy soft BCK/BCI-algebras are given. Also, the notion of (∈ , ∈ ∨ q)-bipolar fuzzy subalgebras and ideals are introduced and characterizes for an ∈-bipolar fuzzy soft set and q-bipolar fuzzy soft set to be a bipolar fuzzy soft BCK/BCI-algebras are established. Some characterization theorems of these (∈ , ∈ ∨ q)-bipolar fuzzy soft subalgebras and ideals are derived. The relationship among these (∈ , ∈ ∨ q)-bipolar fuzzy soft subalgebras and ideals are also considered.

Keywords

soft set ∈-bipolar fuzzy soft set

Get full access to this article

View all access options for this article.

References

Molodtsov

, Soft set theory-first results, Comput Math Appl 37 (1999), 19–31.

Molodtsov

, The Theory of Soft Sets (in Russian), URSS Publishers, Moscow, 2004.

Maji

P.K.

, Biswas

and Roy

A.R.

, Soft set theory, Comput Math Appl 45 (2003), 555–562.

Maji

P.K.

, Roy

A.R.

and Biswas

, An application of soft sets in a decision making problem, Comput Math Appl 44 (2002), 1077–1083.

Dubois

, Kaci

and Prade

, Bipolarity in Reasoning and Decision, an Introduction, Int Con on Inf Pro Man Unc IPMU’04, 2004, pp.959–966.

Zhang

W.R.

, Bipolar fuzzy sets and relations: A computational framework for cognitive and modeling and multiagent decision analysis, Proc of IEEE conf (1994), 305–309.

Zhang

W.R.

, Bipolar fuzzy sets, Proc of FUZZ-IEEE (1998), 835–840.

Zhang

W.R.

and Zhang

, YinYang bipolar logic and bipolar fuzzy logic, Inform Sci 165 (2004), 265–287.

Zadeh

L.A.

, Fuzzy sets, Inform Control 8 (1965), 338–353.

10.

Lee

K.M.

, Bipolar-valued fuzzy sets and their basic operations, Proc Int Conf, Bangkok, Thailand, 2000, pp.307–317.

11.

Lee

K.M.

, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets, and bipolar-valued fuzzy sets, J Fuzzy Logic Intell Sys 14 (2004), 125–129.

12.

Imai

and Iseki

, On axiom system of propositional calculi, XIV Proc Japan Academy 42 (1966), 19–22.

13.

Iseki

, An algebra related with a propositional calculus, Proceedings of the Japan Academy 42 (1966), 26–29.

14.

Jun

Y.B.

and Shim

W.H.

, Fuzzy strong implicative hyper BCK-ideals of hyper BCK-algebras, Inform Sci 170 (2005), 351–361.

15.

Jun

Y.B.

and Xin

X.L.

, Involutory and invertible fuzzy BCK-algebras, Fuzzy Sets and Systems 117 (2001), 463–469.

16.

Liu

Y.L.

, Xu

and Meng

, BCI-implicative ideals of BCIalgebras, Inform Sci 177 (2007), 4987–4996.

17.

Lee

K.J.

and Jun

Y.B.

, Bipolar fuzzy a-ideals of BCIalgebras, Commun Korean Math Soc 26(4) (2011), 531–542.

18.

Meng

and Jun

Y.B.

, BCK-algebras, Kyungmoon Sa Co, Seoul, 1994.

19.

Meng

and Guo

, On fuzzy ideals inBCK/BCI-algebras, Fuzzy Sets and Systems 149(3) (2005), 509–525.

20.

Muhiuddin

, Kim

H.S.

, Song

S.Z.

and Jun

Y.B.

, Hesitant fuzzy translations and extensions of subalgebras and ideals in BCK/BCI-algebras, J Int Fuzzy syst 32(1) (2017), 43–48.

21.

Jana

and Pal

, On (α, β)-Union-soft sets in BCK/BCIalgebras, Mathematics 7 (2019), 252.

22.

Senapati

and Shum

K.P.

, Atanassov’s intuitionistic fuzzy binormed KU-subalgebras of a KU-algebra, Missouri J Math Sci 29 (2017), 92–112.

23.

, Zhan

and Jun

Y.B.

, Some kinds of (∈_γ, ∈ _γ ∨ qδ)-fuzzy ideals of BCI-algebras, Comput Math Appl 61(4) (2011), 1005–1015.

24.

, Zhan

and Jun

Y.B.

, New types of fuzzy ideals of BCI-algebras, Neural Comput Applic 21 (2012), S19–S27.

25.

Jana

, Senapati

, Bhowmik

and Pal

, On intuitionistic fuzzy G-subalgebras of G-algebras, Fuzzy Inf Eng 7(2) (2015), 195–209.

26.

Jana

, Pal

, Senapati

and Bhowmik

, Atanassov’s intutionistic L-fuzzy G-subalgebras of G-algebras, J Fuzzy Math 23(2) (2015), 195–209.

27.

Jana

and Senapati

, Cubic G-subalgebras of G-algebras, Annals of Pure and Applied Mathematics 10(1) (2015), 105–115.

28.

Jana

and Pal

, Generalized intuitionistic fuzzy ideals of BCK/BCI-algebras based on 3-valued logic and its computational study, Fuzzy Inf Eng 9 (2017), 455–478.

29.

Jana

, Senapati

and Pal

, Derivation, f-derivation and generalized derivation of KUS-algebras, Cogent Mathematics 2 (2015), 1–12.

30.

Jana

and Pal

, Applications of new soft intersection set on groups, Ann Fuzzy Math Inform 11(6) (2016), 923–944.

31.

Jana

, Senapati

and Pal

, (∈, ∈ ∨ q)-intuitionistic fuzzy BCI-subalgebras of BCI-algebra, J Int Fuzzy Syst 31 (2016), 613–621.

32.

Jana

and Pal

, Applications of (α, β)-soft intersectional sets on BCK/BCI-algebras, Int J of Intelligent Systems Technologies and Applications 16(3) (2017), 269–288.

33.

Jana

, Senapati

and Pal

, On t-Derivations of complicaated subtraction algebraas, Journal of Discrete Mathematical Sciences and Cryptography 20(8) (2018), 1583–1595.

34.

Jana

, Pal

and Saied

A.B.

, (∈, ∈ ∨ q)-bipolar fuzzy BCK/BCI-algebras, Missouri J of Math Sci 29(2) (2017), 139–160.

35.

Jana

and Pal

On (∈_α, ∈ _β ∨ q_β)-fuzzy soft BCI algebras, Missouri J of Math Sci 29(2) (2017), 197–215.

36.

Bej

and Pal

, Doubt Atanassovs intuitionistic fuzzy Subimplicative ideals in BCI-algebras, Int J Comput Int Sys 8(2) (2015), 240–249.

37.

Murali

, Fuzzy points of equivalent fuzzy subsets, Inform Sci 158 (2004), 277–288.

38.

P.M.

and Liu

Y.M.

, Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J Math Anal Appl 76 (1980), 571–599.

39.

Bhakat

S.K.

and Das

, On the definition of a fuzzy subgroup, Fuzzy Sets and Systems 51 (1992), 235–241.

40.

Bhakat

S.K.

and Das

, (∈, ∈ ∨ q)-fuzzy subgroup, Fuzzy Sets and Systems 80 (1996), 359–368.

41.

Rosenfeld

, Fuzzy groups, J Math Anal Appl 35 (1971)512–517.

42.

Chen

, Tsang

E.C.C.

, Yeung

D.S.

and Wang

, The parametrization reduction of soft sets and its applications, Comput Math Appl 49 (2005), 757–763.

43.

Feng

, Jun

Y.B.

and Zhao

, Soft semirings, Comput Math Appl 56 (2008), 2621–2628.

44.

Jiang

, Tang

, Chen

, Liu

and Tang

, Intervalvalued intuitionistic fuzzy soft sets and their properties, Comput Math Appl 60 (2010), 906–918.

45.

Jun

Y.B.

, Öztürk

M.A.

and Muhiuddin

, A generalization of (∈, ∈ ∨ q)-fuzzy subgroups, International Journal of Algebra and Statistics 5(1) (2016), 7–18.

46.

Zhan

, Jun

Y.B.

and Davvaz

, On (∈, ∈ ∨ q)-fuzzy ideals of BCI-algebras, Iran J Fuzzy Syst 6 (2009), 81–94.

47.

Zhang

, Zhang

, Liu

and Gang

, New kinds of fuzzy ideals in BCI-algebras, Fuzzy Optim Decis Mak 5 (2006), 177–186.

48.

Jun

Y.B.

, On (α, β)-fuzzy subalgebras of BCK/BCIalgebras, Bull Korean Math Soc 42(4) (2005), 703–711.

49.

Jun

Y.B.

, On (α, β)-fuzzy ideals of BCK/BCI-algebrs, Sci Math Jpn (2004), 101–105.

50.

, Zhan

J.M.

, Davvaz

and Jun

Y.B.

, Some kinds of (∈, ∈ ∨ q)-interval-valued fuzzy ideals of BCI-algebras, Inform Sci 178 (2008), 3738–3754.

51.

Lee

K.J.

, Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras, Bull Malays Math Sci Soc 32(3) (2009), 361–373.

52.

Jun

Y.B.

, Soft BCK/BCI-algebras, Comput Math Appl 56 (2008), 1408–1413.

53.

Jun

Y.B.

and Park

C.H.

, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform Sci 178 (2008), 2466–2475.

54.

Jun

Y.B.

, Lee

K.J.

and Park

C.H.

, Soft set theory applied to ideals in d-algebras, Comput Math Appl 57 (2009), 367–378.

55.

Jun

Y.B.

, Lee

K.J.

and Zhan

, Soft p-ideals of soft BCIalgerbas, Comput Math Appl 58 (2009), 2060–2068.

56.

Aktas

and Cagman

, Soft sets and soft groups, Inform Sci 177 (2007), 2726–2735.

57.

Huang

Y.S.

, BCI-algebra, Science Press, Beijing, 2006.

Bipolar fuzzy soft subalgebras and ideals of BCK / BCI -algebras based on bipolar fuzzy points

Abstract

Keywords

Get full access to this article

References