Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory I

Liu, Xiaodong; Chai, Tianyou; Wang, Wei; Liu, Wanquan

doi:10.1016/j.ins.2006.07.011

Cited by 65 publications

(28 citation statements)

References 11 publications

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“…Distance functions play a major role in pattern recognition and data analysis [1]- [4]. When each object is described with respect to quantitative feature variables, Minkowski metrics are often used as convenient dissimilarity measures in classification methods.…”

Section: Similarity Measurementioning

confidence: 99%

“…Another category is based on a relation matrix such as correlation coefficient, equivalence relation, similarity relation and fuzzy relations, etc, agglomerative hierarchical clustering method belongs to the second type, it is simple and useful in application system. The investigate in this paper focus on this type of clustering, we cluster the objects in concept lattice into groups, thus we avoid the heavy burden computing of every subsets of feature sets with a definite subset of objects, this builds a bridge between concept analysis with clustering.Fuzzy clustering and concept analysis have been explored [1]- [5], this paper explores the connection further.…”

Section: Introductionmentioning

confidence: 99%

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Computing Concept Lattices with Clustering Approaches

Zhang¹,

Wang²,

Liu³

2007

Proceedings on Intelligent Systems and Knowledge Engineering (ISKE2007)

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Finding the concepts in formal concept context is time-consuming, which is a NP problem. In this paper, hierarching conceptual clustering analysis based on distance function is investigated, under this clustering, we only check the some subset of feature set instead of all of them, which largely reduces the computing steps in finding the concepts, we pave a way to explore concept lattice with clustering approaches.

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Section: Similarity Measurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computing Concept Lattices with Clustering Approaches

Zhang¹,

Wang²,

Liu³

2007

Proceedings on Intelligent Systems and Knowledge Engineering (ISKE2007)

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“…Formal concept analysis (FCA) has been extended with ideas from fuzzy set theory [1,2,3], fuzzy logic reasoning [4,5,6], rough set theory [7,8,9], some integrated approaches such as fuzzy and rough [10], or rough and domain theory [11].…”

Section: Introductionmentioning

confidence: 99%

Building multi-adjoint concept lattices

Díaz¹,

Garcia²,

Medina³

et al. 2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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In Formal Concept Analysis it is very important to study fast algorithms to compute concept lattices. This paper introduces an algorithm on the multiadjoint concept lattice framework, in order to compute the whole concept lattice. This fuzzy framework is very general and provides more flexibility in relational systems. This has been theoretically studied and, now, we need an algorithm to compute the concept lattice for each frame and context.

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“…In part I of this paper [28], various kinds of representations and logic operations of fuzzy concepts have been extensively investigated in the framework of AFS theory (refer to [16][17][18][19][20][21][22][23][24][25][26][27][28]47,48]). We have proposed the E # I n algebras and studied the norms of the AFS algebras.…”

Section: Introductionmentioning

confidence: 99%

“…In order to show that the framework of determining membership functions proposed in [28] can mimic human intuition to some extent and are feasible for applications, we propose a new fuzzy description and clustering algorithm based on AFS theory in Section 4. In this method, the attributes of objects can be various data types described by simple concepts and they are still valid without the assumptions of X & R p·n .…”

Section: Introductionmentioning

confidence: 99%

Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory II

Liu

Wang

Chai

et al. 2007

Information Sciences

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In part II of this paper, firstly, we study the relationship between the AFS (Axiomatic Fuzzy Zet) and FCA (Formal Concept Analysis, which has become a powerful theory for data analysis, information retrieval, and Knowledge discovery) and some algebraic homomorphisms between the AFS algebras and the concept lattices are established. Then, the numerical approaches to determining membership functions proposed in part I of this paper are used to study the fuzzy description and data clustering problems by mimicking human reasoning process. Finally, illustrative examples show that the framework of AFS theory offers a far more flexible and effective approach to artificial intelligence system analysis and design with applications to knowledge acquisition and representations in practice.

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Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory I

Cited by 65 publications

References 11 publications

Computing Concept Lattices with Clustering Approaches

Computing Concept Lattices with Clustering Approaches

Building multi-adjoint concept lattices

Approaches to the representations and logic operations of fuzzy concepts in the framework of axiomatic fuzzy set theory II

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