Combination of interval-valued fuzzy set and soft set

Yang, Xibei; Lin, Tsau Young; Yang, Jingyu; Li, Yan; Yu, Dong‐Jun

doi:10.1016/j.camwa.2009.04.019

Cited by 418 publications

(251 citation statements)

References 13 publications

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“…Every mathematical tool always has its limitations, and the integration of a variety of tools often can obtain the desired result of unexpected, therefore, the new theories by integrating different uncertainty mathematical tools become a hot of academic research (for example, probabilistic soft sets 29 , fuzzy soft sets 7,17,19 and rough soft sets 4 ). recently, we introduced the new notion of interval soft set by combining interval set theory and soft set theory in 27 (It is differing from interval-valued fuzzy soft set 19 ).…”

Section: Introductionmentioning

confidence: 99%

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On Interval Soft Sets with Applications

Zhang¹

2014

IJCIS

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Interval set theory and soft set theory are mathematical tools for dealing with uncertainty information. As a combination of interval set and soft set, recently, we introduced the new notion of interval soft sets. In this paper we further research interval soft sets and its application. We investigate the tabular representation of interval soft sets, introduce the new concepts of interval choice values, and apply the theory of interval soft sets to solve a decision making problem by using two methods. We discuss some operations of interval soft sets, and construct some lattice structures. Moreover, we introduce the notion of soft equality in interval soft set theory, establish quotient algebra by soft equality relation, and discuss the application of soft equality relations in preconditioning of decision making.

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Section: Introductionmentioning

confidence: 99%

“…recently, we introduced the new notion of interval soft set by combining interval set theory and soft set theory in 27 (It is differing from interval-valued fuzzy soft set 19 ).…”

Section: Introductionmentioning

confidence: 99%

On Interval Soft Sets with Applications

Zhang¹

2014

IJCIS

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“…The proof is straightforward. Note that example 3.6 [18] show that the converse of proposition 4.3 is not true in general. …”

Section: Then ( ) = ( ) ⊲ ( ) Thus ( ) ⊲ ( ) For All ∈ and So ( mentioning

confidence: 95%

“…Therefore, there has been a great deal of alternative research and applications in the literature concerning some special tools such as probability theory, fuzzy set theory [18,19,20], rough set theory [14,15], vague set theory [3], and interval mathematics [4]. Although they are all useful approaches to describe uncertainty, each of these theories has its inherent difficulties, as mentioned by Molodtsov [13].Consequently, Molodtsov [13] proposed a completely new approach, called soft set theory, for modeling vagueness and uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Ideals And Fuzzy Soft Ideals Of Bch-algebras

Moradian¹,

Hamidi²,

Radfar³

2015

J. Math. Computer Sci.

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“…Thereafter many researchers have applied this concept on di erent algebraic structures in mathematics (see, [5, 6, 8-11, 14, 15, 17, 20, 23, 25]). The concept of interval-valued fuzzy soft sets was introduced by Yang et al [24].…”

Section: Introductionmentioning

confidence: 99%