# Soft semirings

##### Citations

1,223 citations

### Cites background from "Soft semirings"

...1 Note that restricted intersection is also known as bi-intersection in [5]....

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832 citations

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### Cites methods from "Soft semirings"

...[6] initiated the study of soft semirings by using the soft set theory and investigated several related properties....

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607 citations

494 citations

### Cites background from "Soft semirings"

...Soft semirings and several related notions are defined in [7] in order to establish a connection between soft sets and semirings....

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##### References

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52,705 citations

3,759 citations

### "Soft semirings" refers background in this paper

...Molodtsov [7] defined the notion of a soft set in the following way: Let U be an initial universe set and E be a set of parameters....

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...For illustration,Molodtsov considered several examples in [7]....

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...In 1992, Molodtsov [7] introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainties....

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...Contents lists available at ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa Soft semirings Feng Feng a,∗, Young Bae Jun b, Xianzhong Zhao c a Department of Applied Mathematics and Applied Physics, Xi’an Institute of Posts and Telecommunications, Xi’an 710061, PR China b Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Republic of Korea c Department of Mathematics, Northwest University, Xi’an 710069, PR China a r t i c l e i n f o Article history: Received 20 February 2008 Received in revised form 4 May 2008 Accepted 23 May 2008 Keywords: Soft sets Soft semirings Soft subsemirings Soft ideals Idealistic soft semirings Soft semiring homomorphisms Fuzzy sets a b s t r a c t Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty....

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...Molodtsov introduced the concept of soft sets,which can be seen as a newmathematical tool for dealingwith uncertainty....

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2,114 citations

### "Soft semirings" refers background in this paper

...[10] introduced and investigated several binary operations such as intersection, union, AND-operation, and OR-operation of soft sets....

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...[10] defined and studied several operations on soft sets....

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...Thus a null soft set in [10] is indeed a soft set with an empty support, and we say that a soft set (η, A) is non-null if Supp (η, A) 6= ∅....

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...These examples were also discussed in [11,10]....

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2,004 citations

### "Soft semirings" refers background in this paper

...Alternatively, mathematical theories such as probability theory, fuzzy set theory [1,2], rough set theory [3,4], vague set theory [5] and the interval mathematics [6] were established by researchers to modelling uncertainties appearing in the above fields....

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1,567 citations

### "Soft semirings" refers background in this paper

...Alternatively, mathematical theories such as probability theory, fuzzy set theory [1,2], rough set theory [3,4], vague set theory [5] and the interval mathematics [6] were established by researchers to modelling uncertainties appearing in the above fields....

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