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.

Ciucci, D. (2016). Orthopairs and granular computing. GRANULAR COMPUTING, 1(3), 159-170 [10.1007/s41066-015-0013-y].

Orthopairs and granular computing

CIUCCI, DAVIDE ELIO
Primo
2016

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.
No
Articolo in rivista - Articolo scientifico
Scientifica
Orthopair; Partial knowledge; Rough sets
English
159
170
12
Ciucci, D. (2016). Orthopairs and granular computing. GRANULAR COMPUTING, 1(3), 159-170 [10.1007/s41066-015-0013-y].
Ciucci, D
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/136742
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