Interval sets and interval-set algebras

Yao, Yiyu

doi:10.1109/coginf.2009.5250723

Cited by 37 publications

(35 citation statements)

References 46 publications

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“…For interval sets, operations and satisfy commutativity, associativity, idempotent and absorption (see 20,24 ). Using these properties, we can get following results.…”

Section: For All E ∈ C H(e) = F(e) G(e)mentioning

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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“…For interval sets, operations and satisfy commutativity, associativity, idempotent and absorption (see 20,24 ). Using these properties, we can get following results.…”

Section: For All E ∈ C H(e) = F(e) G(e)mentioning

confidence: 99%

“…For representing qualitative information, Yao 20 proposed the notion of interval set, and the relationship among interval sets, rough sets and fuzzy sets are investigated in 21,22,23,24 . As a generalization of interval set, Zhang et al 25 introduced lattice-valued interval set and discussed its algebra operations.…”

Section: Introductionmentioning

confidence: 99%

On Interval Soft Sets with Applications

Zhang¹

2014

IJCIS

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“…The most important partial order relation we are going to introduce has received attention in several fields, and it is known as knowledge ordering (Belnap 1977;Yao 2009a) or semantic precision (Lawry and Dubois 2012) or sharpening relation (Shapiro 2006). We will use the symbol " I to denote it, the I standing for information:…”

Section: Partial Orderingsmentioning

confidence: 99%

“…In , we reviewed some works made in the '60s by Fadini, Andreoli and Gentilhomme (some of their results will also be reported in this paper). More recently, Yao investigated pairs of nested sets under the name interval sets, as a tool to represent imprecise or partial knowledge (Yao 1993(Yao , 2009a. In this sense, they are strictly related to orthopairs and all the considerations put forward here could apply also to interval sets and to interval set applications such as clustering ), at least from a purely theoretical standpoint.…”

Section: Introductionmentioning

confidence: 99%

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Orthopairs and granular computing

Ciucci

2016

Granul. Comput.

101

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Pairs of disjoint sets (orthopairs) naturally arise or have points in common with many tools to manage uncertainty: rough sets, shadowed sets, version spaces, three-valued logics, etc. Indeed, they can be used to model partial knowledge, borderline cases, consensus, examples and counter-examples pairs. Moreover, generalized versions of orthopairs are the well known theories of Atanassov intuitionistic fuzzy sets and possibility theory and the newly established three-way decision theory. Thus, it is worth studying them on an abstract level in order to outline general properties that can then be casted to the different paradigms they are in connection with. In this paper, we will review how to define orthopairs and a hierarchy on them in the light of granular computing. Aggregation operators will also be discussed as well as possible generalizations and connections with different paradigms. This will permit us to point out new facets of these paradigms and outline some possible future developments.

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Equivalent Structures of Interval Sets and Fuzzy Interval Sets

Wong

Yiu

2017

Int. J. Intell. Syst.

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Ideas of interval sets come from the lower and upper approximations of rough sets to study a unified structure of rough sets and their generalizations. Starting from the interval sets and their operations, this paper summarizes and analyzes other sets that have similarities with the interval sets or fuzzy interval sets. Our conclusions are that interval sets are mathematically equivalent to shadowed sets and flou sets, respectively, and fuzzy interval sets are mathematically equivalent to interval-valued fuzzy sets and intuitionistic fuzzy sets, respectively. C 2017 Wiley Periodicals, Inc.

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Interval sets and interval-set algebras

Cited by 37 publications

References 46 publications

On Interval Soft Sets with Applications

On Interval Soft Sets with Applications

Orthopairs and granular computing

Equivalent Structures of Interval Sets and Fuzzy Interval Sets

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