Fuzzy weak hyper deductive systems of hyper equality algebras and their measures

Abstract

The concepts of fuzzy weak hyper deductive systems and fuzzy sup-weak hyper deductive systems of hyper equality algebras as generalizations of fuzzy deductive systems are initiated in the paper. Moreover, several related properties and characterizations of fuzzy weak hyper deductive systems and fuzzy sup-weak hyper deductive systems are investigated, and the relationships between fuzzy sup-weak hyper deductive systems of homomorphic hyper equality algebras are also presented based on the introduced homomorphism in hyper equality algebras. It is known that a fuzzy weak hyper deductive system is a fuzzy set, while the converse is not true in general. In order to measure the degree of a fuzzy set becoming a fuzzy weak hyper deductive system, we introduce the notion of fuzzy weak hyper deductive system degrees, and put forward some equivalent characterizations of the fuzzy weak hyper deductive system.

Keywords

Hyper equality algebra fuzzy weak hyper deductive system fuzzy weak hyper deductive system degree

Get full access to this article

View all access options for this article.

References

Borzooei

R.A.

, Zarean

and Zahiri

, Involutive equality algebras, Soft Computing 22(22) (2018), 7505–7517.

Borzooei

R.A.

, Zebardast

and Kologani

M.A.

, Some types of filters in equality algebras, Categories and General Algebraic Structures with Applications 7 (2017), 33–55.

Borzooei

R.A.

, Bakhshi

and Zahiri

, Filter theory on hyper residuated lattices, Quasigroups and Related Systems 22 (2014), 33–50.

Borzooei

R.A.

, Saffar

B.G.

and Ameri

, On hyper EQ-algebras, Italian Journal of Pure and Applied Mathematics 31 (2013), 77–96.

Borzooei

R.A.

, Varasteh

H.R.

and Borna

, Quotient hyper hoop-algebras, Italian Journal of Pure and Applied Mathematics 36 (2016), 87–100.

Ciungu

L.C.

, Internal states on equality algebras, Soft Computing 19(4) (2015), 939–953.

Ciungu

L.C.

, On pseudo-equality algebras, Archive for Mathematical Logic 53(5-6) (2014), 561–570.

Corsini

and Leoreanu-Fotea

, Applications of hyperstructure theory, Kluwer, Dordrecht, 2003.

Cheng

, Xin

and He

, Generalized state maps and states on pseudo equality algebras, Open Mathematics 28(6) (2018), 133–148.

10.

Cheng

, Xin

and Jun

Y.B.

, Hyper equality algebras, Quantitative Logic and Soft Computing 2016 (2017), 415–428.

11.

Dvurečenskij

and Zahiri

, Pseudo equality algebras: revision, Soft Computing 20 (2016), 2091–2101.

12.

Dvurečenskij

and HyčKo

, Hyper effect algebras, Fuzzy Sets and Systems 326 (2017), 34–51.

13.

Ghorbani

, Hasankhani

and Eslami

, Hyper MV-algebras, Set-Valued Mathematics and Applications 2 (2008), 205–222.

14.

Hájek

, Metamathematics of fuzzy logic, Kluwer, Dordrecht, 1998.

15.

, Xin

and Zhan

, (Fuzzy) hyperlattices and fuzzy preordered lattices, Journal of Intelligent & Fuzzy Systems 26 (2014), 2369–2381.

16.

Jenei

, Equality algebras, Studia Logica 100(6) (2012), 1201–1209.

17.

Jenei

and Kóródi

, Pseudo equality algebras, Archive for Mathematical Logic 52(5-6) (2013), 469–481.

18.

Jun

Y.B.

, Zahedi

M.M.

and Xin

, et al., On hyper BCK-algebras, Italian Journal of Pure and Applied Mathematics 8(8) (2000), 127–136.

19.

Marty

, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm, 1934, 45–49.

20.

Novák

, On fuzzy type theory, Fuzzy Sets and Systems 149 (2005), 235–273.

21.

Novák

and De Baets

, EQ-algebras, Fuzzy Sets and Systems 160(20) (2009), 2956–2978.

22.

Shi

, Measures of fuzzy subgroups, Proyecciones Journal of Mathematics 29(1) (2010), 41–48.

23.

Varasteh

H.R.

and Borzooei

R.A.

, Fuzzy regular relation on hyper hoop-algebras, Journal of Intelligent & Fuzzy Systems 30 (2016), 1275–1282.

24.

Xin

, He

and Fu

, States on hyper MV-algebras, Journal of Intelligent & Fuzzy Systems 31(3) (2016), 1299–1309.

25.

, Xin

and Wang

, Fuzzy filters on equality algebras with applications, Journal of Intelligent & Fuzzy Systems 35(3) (2018), 3709–3719.

26.

Zebardast

, Borzooei

R.A.

and Kologani

M.A.

, Results on equality algebras, Information Sciences 381 (2017), 270–282.

27.

Zahiri

, Borzooei

R.A.

and Bakhshi

, (Quotient) hyper residuated lattices, Quasigroups and Related Systems 20 (2012), 125–138.

28.

Zhang

X.H.

, Park

and Wu

S.P.

, Soft set theoretical approach to pseudo-BCI algebras, Journal of Intelligent & Fuzzy Systems 34 (2018), 559–568.