On heterogeneous formal contexts

doi:10.1016/j.fss.2013.04.008

Fuzzy Sets and Systems

Volume 234, 1 January 2014, Pages 22-33

https://doi.org/10.1016/j.fss.2013.04.008 Get rights and content

Abstract

We propose a new type of fuzzification for formal concept analysis that works with heterogeneous values in a context and illustrate this with an example. We formulate and prove an appropriate counterpart to the so-called basic theorem of a concept lattice. We show that this is a generalization of the previous approaches: it covers the so-called generalized concept lattice and multi-adjoint t-concept lattices.

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Citation Excerpt :
The following theorem, which is proved in [1], shows the properties of heterogeneous concept forming operators. In this section, we modify and extend our running example from [1] in order to model the group preferences and group recommendation for a type of accommodation in a more general way, whereby the heterogeneous preferences and recommendations are still covered by a heterogeneous formal context and its heterogeneous concept lattice. The same application domain will be also applied for the results obtained in the following sections.
Fuzzy relations are the mappings which are intensively studied in decision, reasoning, or data analysis. We propose a method for decomposition of heterogeneous formal context by heterogeneous fuzzy subsets, which allows representing the heterogeneous structure of truth degrees for each object, heterogeneous structure of truth degrees for each attribute and heterogeneous structure of truth degrees for relationship between each pair of object and attribute. We formulate and prove the properties of decomposition in heterogeneous extension of Formal concept analysis. We put emphasis on the role of special heterogeneous formal concepts which are generated from heterogeneous singleton fuzzy subsets. We illustrate our novel results in our running example of personal requirements for accommodation as the natural continuation of our previous studies.
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Three-way concept analysis is a research hotspot. Inspired by multi-scale information system, some scholars put forward and researched multi-granularity formal context. Most of the existing algorithms for constructing three-way concept lattice take care of the static formal contexts and can not deal with the multi-granularity formal context. To address this problem, this paper primarily focuses on a constructing approach to object-induced three-way concept (OE-concept) lattices for multi-granularity formal contexts. Firstly, transformation relationships between OE-concepts based on different granularities are researched. Secondly, the mutual transformation between OE-concept lattices under different granularities is proposed via these relationships, and then corresponding algorithms are proposed. Finally, several groups of datasets are selected from UCI for comparative experiments. Experimental results exhibit that our algorithms are more effective and advantageous than the latest construction algorithms.

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On heterogeneous formal contexts

Abstract

Ann. Pure Appl. Logic

Fuzzy Sets Syst.

Inf. Sci.

Fuzzy Sets Syst.

Fuzzy Sets Syst.

Fuzzy Set Syst.

Inf. Sci.

Inf. Sci.

Crisply generated fuzzy concepts

Lect. Notes Comput. Sci.

Formal concept analysis and linguistic hedges

Int. J. Gen. Syst.