Representing attribute reduction and concepts in concept lattice using graphs

Mao, Hua

doi:10.1007/s00500-016-2441-2

Cited by 15 publications

(8 citation statements)

References 20 publications

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“…We have C = {c 1 , c 2 } and N + G(O,P,I)(c1) = {b, n}. The following represents how the algorithm runs when we exactly follow exactly the steps in Mao (2017).…”

Section: Example For Algorithmmentioning

confidence: 99%

“…We use the same notions and the same notations as Mao (2017); however we need to also recall a few notions from (Ganter and Wille, 1999) to explain our case. Thus, for the reader's convenience, we provide full preliminaries.…”

Section: Preliminariesmentioning

confidence: 99%

“…1 Introduction Mao (2017) claims that she studies attribute reduction and formal concept enumeration in Formal Concept Analysis (FCA) with the aid of Graph Theory. We show, that the use of the Graph Theory is trivial.…”

mentioning

confidence: 99%

“…As an example of the latter, (Mao, 2017, Theorem 3.1) characterizes objects with full row. The theorem states that we need not check whether the object has all attributes, instead we can just check whether it has all attributes that are minimal w.r.t.…”

mentioning

confidence: 99%

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Note on representing attribute reduction and concepts in concept lattice using graphs

Konečný

2019

Soft Comput

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Mao H. (2017, Representing attribute reduction and concepts in concept lattice using graphs. Soft Computing 21(24):7293-7311) claims to make contributions to the study of reduction of attributes in concept lattices by using graph theory. We show that her results are either trivial or already well-known and all three algorithms proposed in the paper are incorrect.We use the same notions and the same notations as Mao (2017); however we need to also recall a few notions from (Ganter and Wille, 1999) to explain our case. Thus, for the reader's convenience, we provide full preliminaries.An input to FCA is a triplet (O, P, I), called a formal context, where O, P are finite non-empty sets of objects and attributes, respectively, and I is a binary relation between O and P ; (o, a) ∈ I means that the object o has the attribute a. Finite formal contexts are usually depicted as tables, in which rows represent objects, columns represent attributes, and each entry contains a cross if the corresponding object has the corresponding attribute, and is otherwise left blank (see top parts of Figures 3-5 for examples).The formal context induces the following operators:

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“…We have C = {c 1 , c 2 } and N + G(O,P,I)(c1) = {b, n}. The following represents how the algorithm runs when we exactly follow exactly the steps in Mao (2017).…”

Section: Example For Algorithmmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Note on representing attribute reduction and concepts in concept lattice using graphs

Konečný

2019

Soft Comput

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“…This attempts to formalise logic, where a fundamental step was the reduction of a concept to its 'extent' (Wille, 1982). The concept lattice is a research area for concepts and concept hierarchies in computing (Mao, 2017) and concept lattices have been used in FCA to construct a hierarchy of concepts (Butka et al, 2018). Hierarchy theory is likewise able to conceptualise complex ecological systems as composed of relatively isolated levels each operating at a distinct time and space scale (O'Neill et al, 1989).…”

Section: A Hierarchy Of Conceptsmentioning

confidence: 99%

A hierarchical framework for concepts in physical geography

Gregory

Lewin

2018

Progress in Physical Geography: Earth and Environment

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The word concept is widely used in physical geography but seldom defined. Developing from an earlier proposal of concept types in geomorphology, this paper considers a structure for categorising concepts in physical geography in the light of sciences and philosophy more generally. It reviews where our concepts derive from, and their relation to kinds, universals and categories, whilst also indicating the lack of an agreed clear distinction between them. Because an unstructured diversity of concepts has previously been proposed in physical geography by different authors, a new provisional hierarchy is constructed. This is cognisant of specific developments in a range of disciplines, including formal concept analysis, lattice theory and hierarchy theory. A ‘concept of concepts’ hierarchy of six categories is proposed in which multidisciplinary (superordinate, contextual meta-concepts) and fundamental, operational and ancillary categories provide a 6 × 5 framework. This enables attention to be focused on stimulating conceptual underpinnings that can be tested at different levels in future learning, teaching and research. This can support the formation of knowledge structures and monitoring procedures that keep in step with ways that are characterising other disciplines.

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Bipolar fuzzy concept learning using next neighbor and Euclidean distance

Singh

2018

Soft Comput

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Representing attribute reduction and concepts in concept lattice using graphs

Cited by 15 publications

References 20 publications

Note on representing attribute reduction and concepts in concept lattice using graphs

Note on representing attribute reduction and concepts in concept lattice using graphs

A hierarchical framework for concepts in physical geography

Bipolar fuzzy concept learning using next neighbor and Euclidean distance

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