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Granular Computing
Erschienen in: Granular Computing 3/2016

01.09.2016 | Original Paper

Orthopairs and granular computing

verfasst von: Davide Ciucci

Erschienen in: Granular Computing | Ausgabe 3/2016

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Abstract

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.
Nächster Artikel Solving equations (and systems of equations) under uncertainty: how different practical problems lead to different mathematical and computational formulations

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Fußnoten
1
A relation is serial iff any element is in relation through \({\mathcal R}\) with at least one other element. Formally, \( \forall x\in X, \, \exists y\in X: x{\mathcal R}y\).
 
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Metadaten
Titel
Orthopairs and granular computing
verfasst von
Davide Ciucci
Publikationsdatum
01.09.2016
Verlag
Springer International Publishing
Erschienen in
Granular Computing / Ausgabe 3/2016
Print ISSN: 2364-4966
Elektronische ISSN: 2364-4974
DOI
https://doi.org/10.1007/s41066-015-0013-y