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Abstract

Using the notions of a soft set and a fuzzy set, Jun’s introduced a new type of notion called a hybrid structure, which is a generalization of soft set and fuzzy set. In this paper, we apply hybrid structure in hemirings and introduce the concept of hybrid h-ideals of hemirings and the related properties are investigated. Some operational properties of hybrid structures are first investigated. The concepts of a hybrid h-sum and a hybrid h-product are discussed and the related properties are investigated. The notions of hybrid h-ideals, hybrid h-bi-ideals and hybrid h-quasi-ideals are introduced and several properties are provided. The notion of a hybrid level set is introduced and the basic properties of hybrid h-ideals, hybrid h-bi-ideals and hybrid h-quasi-ideals are studied in detail. The characterizations of h-hemiregular hemirings are discussed and several important results of a h-hemiregular hemirings are provided.

Keywords

Hybrid structure hybrid structures operations

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References

Aktas and

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

M.I.

Ali ,

Feng ,

Liu ,

W.K.

Min and

Shabir , On some new operations in soft set theory, Comput Math Appl 57 (2009), 1547–1553.

M.I.

Ali ,

Shabir and

Naz , Algebraic structure of soft sets associated with new operations, Comput Math Appl 61 (2011), 2647–2654.

Cagman ,

Citak and

Aktas , Soft-int group and its applications to group theory, Neural Comput Applic 21 (Suppl1) (2012), 151–158.

Cagman and

Enginoglu , Soft set theory and uni-int decision making, Eur J Oper Res 207 (2010), 848–855.

Feng ,

Y.B.

Jun and

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

Henriksen , Ideals in semirings with commutative addition, Am Math Soc Not 6 (1958), 321.

Iizuka , On the Jacobson radical of a semiring, Tohoku Math J 11 (1959), 409–421.

D.R.

LaTorre , On h-ideals and k-ideals in hemirings, Publ Math (Debrecen) 12 (1965), 219–226.

10.

Y.B.

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

11.

Y.B.

Jun ,

M.A.

Ozturk and

S.Z.

Song , On fuzzy h-ideals in hemirings, Inform Sci 162 (2004), 211–226.

12.

Y.B.

Jun ,

S.Z.

Song and

Muhiuddin , Hybrid structures and applications, (in press) 2017.

13.

Anis ,

Khan and

Y.B.

Jun , Hybrid ideals in semigroups, Cogent Mathematics 4 (2017), 1352117.

14.

Ma ,

Yin and

Zhan , Characterizations of h-intra-and hquasi-hemiregular hemirings, Comput Math Appl 63 (2012), 783–793.

15.

Ma and

Zhan , Applications of soft intersection set theory to h-hemiregular and h-semisimple hemirings, J Mult-Valued Logic Soft Comput 25 (2015), 105–124.

16.

Ma and

Zhan , Generalized fuzzy h-bi-ideals and h-quasiideals of hemirings, Inform. Sci 179 (2009), 1249–1268.

17.

Ma and

Zhan , New fuzzy h-ideals in hemirings, Politehn Univ Bucharest Sci Bull Ser A Appl Math Phys 74 (2012), 11–24.

18.

P.K.

Maji ,

Biswas and

A.R.

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

19.

P.K.

Maji ,

A.R.

Roy and

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

20.

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

21.

Sezgin and

A.O.

Atagun , On operations of soft sets, Comput Math Appl 61 (2011), 1457–1467.

22.

Zhan and

W.A.

Dudek , Fuzzy h-ideals of hemirings, Inform Sci 177 (2007), 876–886.

23.

Yin and

Li , The characterizations of h-hemiregular hemirings and h-intra-hemiregular hemirings, Inform Sci 178 (2008), 3451–3464.

24.

X.H.

Zhang , Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras, J Intell Fuzzy Syst 33 (2017), 1767–1774.

25.

X.H.

Zhang and

S.P.

Choonkil Park , Wu, Soft set theoretical approach to pseudo-BCI algebras, J Intell Fuzzy Syst 34 (2018), 559–568.

26.

X.H.

Zhang ,

C.X.

Bo ,

Smarandache and

Park , New operations of totally dependent-neutrosophic sets and totally dependent-neutrosophic soft sets, Symmetry 10 (6) (2018), 187; https://doi.org/10.3390/sym10060187.

27.

X.H.

Zhang ,

Smarandache and

X.L.

Liang , Neutrosophic duplet semi-group and cancellable neutrosophic triplet groups, Symmetry 9 (2017), 275. doi: 10.3390/sym9110275

Hybrid structures applied to hemirings

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