Soft semirings
Computers & Mathematics with ApplicationsPublished 10 August 2008
Feng Feng, Young Bae Jun, Xianzhong Zhao
Citations574
SJR quartileQ1
SJR score0.95
SNIP1.31
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
This paper initiates the study of soft semirings by using the soft set theory, and the notions of soft Semirings, soft subsemirings,soft ideals, idealistic softSemirings and soft semiring homomorphisms are introduced, and several related properties are investigated.
Abstract
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.
Keywords
Computer ScienceDecision Sciences
International Journal of Parallel ProgrammingRough sets
12,138 Citations1982Zdzis aw Pawlak
The presented approach may be considered as an alternative to fuzzy sets theory and tolerance theory and some applications are outlined.
Computers & Mathematics with ApplicationsSoft set theory—First results
4,633 Citations1999D.A. Molodtsov
The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the the theory, and to discuss some problems of the future.
Computers & Mathematics with ApplicationsSoft set theory
2,252 Citations2003Pabitra Kumar Maji, Ranjit Biswas +1 more
The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.
Information SciencesRudiments of rough sets
2,036 Citations2006Zdzisław Pawlak, Andrzej Skowron
The basic concepts of rough set theory are presented and some rough set-based research directions and applications are pointed out, indicating that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences.
Computers & Mathematics with ApplicationsAn application of soft sets in a decision making problem
1,700 Citations2002Pabitra Kumar Maji, Arijit Roy +1 more
IEEE Transactions on Systems Man and CyberneticsVague sets
1,649 Citations1993Wen-Bing Gau, Daniel J. Buehrer
A vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of according to the inequality of the following type:
Information SciencesSoft sets and soft groups
1,095 Citations2007Hacı Aktaş, Naim Çağman
The basic properties of soft sets are introduced, and compare soft sets to the related concepts of fuzzy sets and rough sets, and a definition of soft groups is given.
Fuzzy Sets and SystemsA method of inference in approximate reasoning based on interval-valued fuzzy sets
1,071 Citations1987Marian B. Gorzałczany
This method allows a formal, fuzzy representation to be built for verbal decision algorithms and can have an effective computer representation.
Information SciencesToward a generalized theory of uncertainty (GTU)––an outline
1,059 Citations2005Lotfi A. Zadeh
The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a much broader perspective and represents a significant change both in perspective and direction in dealing with uncertainty and information.
Computers & Mathematics with ApplicationsThe parameterization reduction of soft sets and its applications
651 Citations2005Degang Chen, Eric C.C. Tsang +2 more
This paper proposes a reasonable definition of parameterization reduction of soft sets and compares it with the concept of attributes reduction in rough sets theory and improves the application of a soft set in a decision making problem found in [1].
Computers & Mathematics with ApplicationsSoft BCK/BCI-algebras
415 Citations2008Young Bae Jun
This paper applies the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras and soft subalgeBRas, and their basic properties are derived.
Information SciencesApplications of soft sets in ideal theory of BCK/BCI-algebras
388 Citations2008Y JUN, Chul Hwan Park
The intersection, union, ''AND'' operation, and ''OR'' operation of soft ideals and idealistic soft BCK/BCI-algebras are established.
Semirings and Affine Equations over Them: Theory and Applications
177 Citations2003Jonathan S. Golan
A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences
107 Citations2002Kazimierz Głazek
The author presents a short guide to the Literature on Semirings and discusses some of the applications of the algebraic theory ofSemirings.
Information SciencesOn fuzzy h-ideals in hemirings
85 Citations2003Young Bae Jun, Mehmet Ali̇ Öztürk +1 more
The fuzzy setting of a left h-ideal in a hemiring is constructed, and basic properties are investigated.
Fuzzy Sets and SystemsFuzzy k-ideals of semirings
60 Citations1998Shamik Ghosh
The aim of this paper is to characterize prime fuzzy k-ideals, semiregular semirings, NoetherianSemirings and Artinian Semirings by fuzzy k -ideals.
Czechoslovak Mathematical JournalOn L-fuzzy Ideals in Semirings I
31 Citations1998Young Bae Jun, J. Neggers +1 more
It is shown that each level left (resp. right) ideal of a ring to a semiring R is characteristic iff μ is L-fuzzy characteristic.
Czechoslovak Mathematical JournalOn L-fuzzy ideals in semirings II
26 Citations1999J. Neggers, Young Bae Jun +1 more
Fuzzy Sets and SystemsIsomorphism theorems and fuzzy -ideals of -semirings
21 Citations2000Chang Bum Kim
The fuzzy maximal k-ideal of a k-semiring is defined and study and some isomorphism theorems in commutative k-semirings are studied.
Fuzzy Sets and SystemsNormal L-fuzzy ideals in semirings
20 Citations1996Young Bae Jun, J. Neggers +1 more
The notion of a normal L-fuzzy left (resp. right) ideal in a semiring, and some properties of this ideal are investigated.
Korean Journal of MathematicsON FUZZY κ-IDEALS IN SEMIRINGS
9 Citations2000Seung Il Baik, Hee Sik Kim
Studies in fuzziness and soft computingFuzzy k-Ideals of Semirings
7 Citations2012Ahsan Javed, John N. Mordeson +1 more
Kyungpook mathematical journalExtensions of L-fuzzy Ideals in Semirings
5 Citations1998J. Neggers, Young-Bae Jun +1 more