Interval-Valued Fuzzy Galois Connections: Algebraic Requirements and Concept Lattice Construction

2010 ◽  
Vol 99 (2) ◽  
pp. 169-186 ◽  
Author(s):  
Yassine Djouadi ◽  
Henri Prade
Keyword(s):  
Concept Lattice ◽  
Galois Connections ◽  
Lattice Construction ◽  
Interval Valued

scholarly journals G. Czédli’s tolerance factor lattice construction and weak ordered relations

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Sándor Radeleczki
Keyword(s):  
Concept Lattice ◽  
Tolerance Factor ◽  
Macneille Completion ◽  
Lattice Construction

AbstractG. Czédli proved that the blocks of any compatible tolerance T of a lattice L can be ordered in such a way that they form a lattice L/T called the factor lattice of L modulo T. Here we show that the Dedekind–MacNeille completion of the lattice L/T is isomorphic to the concept lattice of the context (L, L, R), where R stands for the reflexive weak ordered relation $$ \mathord {\le } \circ T$$ ≤ ∘ T . Weak ordered relations constitute the generalization of the ordered relations introduced by S. Valentini. Reflexive weak ordered relations can be characterized as compatible reflexive relations $$R\subseteq L^{2}$$ R ⊆ L 2 satisfying $$R=\ \mathord {\le } \circ R\circ \mathord {\le } $$ R = ≤ ∘ R ∘ ≤ .

scholarly journals A New Rapid Incremental Algorithm for Constructing Concept Lattices

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 78 ◽  
Author(s):  
Jingpu Zhang ◽  
Ronghui Liu ◽  
Ligeng Zou ◽  
Licheng Zeng
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Incremental Algorithm ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices ◽  
Covering Relation ◽  
Canonical Generator ◽  
Lattice Construction ◽  
Time And Space Complexity

Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.

The Research of Constructing Rough Concept Lattices Model

2011 ◽  
Vol 63-64 ◽  
pp. 664-667
Author(s):  
Hong Sheng Xu ◽  
Ting Zhong Wang
Keyword(s):  
Rough Set ◽  
Rough Set Theory ◽  
Concept Lattice ◽  
Attribute Reduction ◽  
Formal Concept ◽  
Concept Lattices ◽  
Variable Precision ◽  
Whole Process ◽  
Variable Precision Rough Set ◽  
Lattice Construction

Formal concept lattices and rough set theory are two kinds of complementary mathematical tools for data analysis and data processing. The algorithm of concept lattice reduction based on variable precision rough set is proposed by combining the algorithms of β-upper and lower distribution reduction in variable precision rough set. The traditional algorithms aboutβvalue select algorithm, attribute reduction based on discernibility matrix and extraction rule in VPRS are discussed, there are defects in these traditional algorithms which are improved. Finally, the generation system of concept lattice based on variable precision rough set is designed to verify the validity of the improved algorithm and a case demonstrates the whole process of concept lattice construction.

scholarly journals Representation of Fuzzy Concept Lattices in the Framework of Classical FCA

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Peter Butka ◽  
Jozef Pócs ◽  
Jana Pócsová
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Concept ◽  
Concept Lattices ◽  
Fuzzy Concept Lattice ◽  
Galois Connections ◽  
Fuzzy Concept ◽  
Needed Information

We describe a representation of the fuzzy concept lattices, defined via antitone Galois connections, within the framework of classical Formal Concept Analysis. As it is shown, all needed information is explicitly contained in a given formal fuzzy context and the proposed representation can be obtained without a creation of the corresponding fuzzy concept lattice.

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