Three-Way Formal Concept Analysis

Qi, Jianjun; Ling, Wei; Yao, Yiyu

doi:10.1007/978-3-319-11740-9_67

Cited by 106 publications

(57 citation statements)

References 17 publications

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“…Indeed, besides the already mentioned possibility to define a hexagon of opposition on FCA, there are several other links with the paradigms presented here. Indeed, version spaces can be described in terms of formal concept analysis (Ganter and Kuznetsov 2003), FCA has been generalized by ideas from possibility theory (Dubois and Prade 2012b) and, recently, orthopairs have been explicitly used to generalize FCA (Qi et al 2014). -As anticipated in Remark 2 and in Sect.…”

Section: Open Problems Related To Other Paradigmsmentioning

confidence: 99%

“…Thanks to their simplicity in representing bipolar information, orthopairs can be found at work in several contexts such as, to make some recent example, trust and distrust statement expressed by experts in Social Network Analysis (Wu et al 2015), representing partial knowledge (Aguirre et al 2014) or vague knowledge (Crosscombe and Lawry 2015;Vetterlein 2015), formal concept analysis (Qi et al 2014). …”

Section: Introductionmentioning

confidence: 99%

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Orthopairs and granular computing

Ciucci

2016

Granul. Comput.

103

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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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Section: Open Problems Related To Other Paradigmsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Orthopairs and granular computing

Ciucci

2016

Granul. Comput.

103

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“…Applying the idea of three-way decision into formal concept analysis, Qi et al [23] recently proposed three-way concept analysis. Firstly, based on the formal concept in Definition 2 and the operators defined on it, called positive operators here, another pair of two-way operators are given, named negative operators, as follows:…”

Section: Three-way Concept Analysismentioning

confidence: 99%

“…In relation to the above three-way operators, their inverse can be defined as follows [23] : for X, Y ⊆ G and A, B ⊆ M ,…”

Section: Three-way Concept Analysismentioning

confidence: 99%

“…Actually, the formal context also offers us the information about whether an object (attribute) does not possesses (is not shared by) any attribute (object), which is called exclusion method, but this cannot be reflected in the formal concept. Since this kind of exclusion method is commonly used in our daily life, Qi et al [23] applied 3WD to FCA and proposed three-way concept analysis (3WCA). Two key components in 3WCA are three-way concepts and three-way concept lattices.…”

Section: Introductionmentioning

confidence: 99%

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The attribute reductions of three-way concept lattices

Ren

Ling

2016

Knowledge-Based Systems

Self Cite

124

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Object-induced three-way object concept Attribute-induced three-way attribute concept Discernibility attribute set a b s t r a c t Three-way concept analysis is a newly proposed area of formal concept analysis from which one can obtain both the inclusion decision and the exclusion decision. In general, given a context, some attributes may not be essential in three-way concept analysis, such as forming three-way concept lattice. So in this paper, we study the attribute reductions of three-way concept lattices in order to make the data easily be understood. Firstly, based on different criteria generated from object-induced three-way concept (OEconcept), four kinds of attribute reductions are proposed. The four reductions together embody different characteristics of a formal context and can be used in different occasions. Secondly, we discuss their relationships, including their advantages and disadvantages and the relationships among consistent sets and among the cores. Thirdly, based on attribute-induced three-way concept (AE-concept), we also give four attribute-induced three-way attribute reductions and discuss their relationships. Finally, the approaches to computing these attribute reductions are presented and the obtained results are demonstrated and verified by an empirical case. In this paper, we systematically investigate the attribute reductions of threeway concept lattices which enriches the study of formal concept analysis.

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The Prototype View of Concepts

Ren

Ling

2019

Rough Sets

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Three-Way Formal Concept Analysis

Cited by 106 publications

References 17 publications

Orthopairs and granular computing

Orthopairs and granular computing

The attribute reductions of three-way concept lattices

The Prototype View of Concepts

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