Soft semirings

By Feng Feng, Young Bae Jun, Xianzhong Zhao. Computers and Mathematics with Applications, 2008

720 citations recorded by the source corpus.

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft semirings by using the soft set theory. The notions of soft semirings, soft subsemirings, soft ideals, idealistic soft semirings and soft semiring homomorphisms are introduced, and several related properties are investigated.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/09f78eda3ea97220ffe0a3ee4e0f2236befbd264

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In Computational Theory and Mathematics

In Management Science and Operations Research

Citations in the corpus

Soft Regular Generalized Closed Sets in Soft Topological Spaces (2014, background): “[14] The intersection (H,C) of (F,A) and (G,B) over X, denoted (F,A) (G,B), is defined as C = A∩B, and H(e) = F (e)∩G(e) for all e ∈ C.”
On some new operations in soft set theory (2009, background): “1 Note that restricted intersection is also known as bi-intersection in [5].”
On soft linear spaces and soft normed linear spaces (2013, background): “8 [8] The intersection of two soft sets (F,A) and (G,B) over the common universe U is the soft set (H,C) , where C = A ∩ B and for all e ∈ C, H (e) = F (e) ∩G(e).”
On Continuity of Soft Mappings (2015, background): “Keywords: Soft set, soft continuity, soft mapping, soft separation axiom”
Soft matrix theory and its decision making (2010, methodology): “[19] initiated the study of soft semirings by using the soft set theory and investigated several related properties.”
Soft sets and soft rough sets (2011, background): “Soft semirings and several related notions are defined in [7] in order to establish a connection between soft sets and semirings.”
Soft set theory and uni-int decision making (2010, methodology): “[6] initiated the study of soft semirings by using the soft set theory and investigated several related properties.”
Soft set theory and topology (2014, background): “The soft set theory has been applied to many different fields (see, for example, [1], [2], [4], [5], [7], [8], [10], [12], [13], [14], [15], [21], [23], [25]).”
A NOTE ON SOFT NEAR-RINGS AND IDEALISTIC SOFT NEAR-RINGS (2011, background): “A similar notion for soft sets is defined in [8].”
FUZZY SOFT SET THEORY AND ITS APPLICATIONS (2011, neutral): “In [8], Feng et al.”
Interval-valued intuitionistic fuzzy soft sets and their properties (2010, background): “[20] defined soft semirings and several related notions to establish a connection between soft sets and semirings.”