scholarly journals Attribute Extended Algorithm of Lattice-Valued Concept Lattice Based on Congener Formal Context

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Li Yang ◽  
Yang Xu
Keyword(s):  
Parallel Processing ◽  
Distributed Storage ◽  
Concept Lattice ◽  
Research Work ◽  
Sufficient Conditions ◽  
Formal Context ◽  
Concept Lattices ◽  
Lattice Implication Algebra ◽  
Implication Algebra ◽  
Necessary And Sufficient

This paper is the continuation of our research work about lattice-valued concept lattice based on lattice implication algebra. For a better application of lattice-valued concept lattice into data distributed storage and parallel processing, it is necessary to research attribute extended algorithm based on congener formal context. The definitions of attribute extended formal context and congener formal context are proposed. On condition that the extent set stays invariable when the new attribute is increased, the necessary and sufficient conditions of forming attribute values are researched. Based on these conditions, the algorithms of generating lattice-valued congener formal context and establishing concept lattice are given, by which we can provide a useful basis for union algorithm and constructing algorithm of lattice-valued concept lattices in distributed and parallel system.

CHARACTERIZING TREES IN CONCEPT LATTICES

2008 ◽  
Vol 16 (supp01) ◽  
pp. 1-15 ◽  
Author(s):  
RADIM BĚLOHLÁVEK ◽  
BERNARD DE BAETS ◽  
JAN OUTRATA ◽  
VILEM VYCHODIL
Keyword(s):  
Formal Concept Analysis ◽  
Input Data ◽  
Concept Lattice ◽  
Sufficient Conditions ◽  
Formal Concept ◽  
Clustering Methods ◽  
Concept Lattices ◽  
Classification Schemes ◽  
Formal Concepts ◽  
Necessary And Sufficient

Concept lattices are systems of conceptual clusters, called formal concepts, which are partially ordered by the subconcept/superconcept relationship. Concept lattices are basic structures used in formal concept analysis. In general, a concept lattice may contain overlapping clusters and need not be a tree. On the other hand, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output concept lattice to form a tree after one removes its least element. We present these conditions for input data with yes/no attributes as well as for input data with fuzzy attributes. In addition, we show how Lindig's algorithm for computing concept lattices gets simplified when applied to input data for which the associated concept lattice is a tree after removing the least element. The paper also contains illustrative examples.

Research of Unary Lattice Implication Algebra Equations on Interval Sets

2013 ◽  
Vol 850-851 ◽  
pp. 761-766 ◽  
Author(s):  
Hao Cui Du ◽  
Bin Sun ◽  
Ying Le Yao
Keyword(s):  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Prime Filter ◽  
Lattice Implication Algebra ◽  
Implication Algebra ◽  
Dual Atom ◽  
Necessary And Sufficient

The concepts are re-defined on the interval sets which are filter, prime filter, LI-ideal, dual atom and convex sub-lattice in the lattice implication algebra. Three basic unary lattice implication algebra equations on the interval sets are researched. The necessary and sufficient conditions for existence of solutions for the equations are presented. And some properties of equation sets also are given.

The construction of multi-granularity concept lattices

2020 ◽  
Vol 39 (3) ◽  
pp. 2783-2790
Author(s):  
Qian Hu ◽  
Ke-Yun Qin
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mutual Transformation ◽  
Concept Lattices ◽  
Construction Methods ◽  
Formal Concepts ◽  
Transformation Methods

The construction of concept lattices is an important research topic in formal concept analysis. Inspired by multi-granularity rough sets, multi-granularity formal concept analysis has become a new hot research issue. This paper mainly studies the construction methods of concept lattices in multi-granularity formal context. The relationships between concept forming operators under different granularity are discussed. The mutual transformation methods of formal concepts under different granularity are presented. In addition, the approaches of obtaining coarse-granularity concept lattice by fine-granularity concept lattice and fine-granularity concept lattice by coarse-granularity concept lattice are examined. The related algorithms for generating concept lattices are proposed. The practicability of the method is illustrated by an example.

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.

scholarly journals On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 427 ◽  
Author(s):  
Tèmítọ́pẹ́ Jaíyéọlá ◽  
Emmanuel Ilojide ◽  
Memudu Olatinwo ◽  
Florentin Smarandache
Keyword(s):  
Research Finding ◽  
Research Work ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Structures ◽  
Associative Algebras ◽  
Necessary And Sufficient

In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be associative while quasi-associativity is found to be necessary and sufficient for F 19 , F 52 , F 56 and F 59 algebras to be associative. Two pairs of the 14 non-associative algebras are found to be equivalent to associativity ( F 52 and F 55 , and F 55 and F 59 ). Every BCI-algebra is naturally an F 54 BCI-algebra. The work is concluded with recommendations based on comparison between the behaviour of identities of Bol-Moufang (Fenyves’ identities) in quasigroups and loops and their behaviour in BCI-algebra. It is concluded that results of this work are an initiation into the study of the classification of finite Fenyves’ quasi neutrosophic triplet loops (FQNTLs) just like various types of finite loops have been classified. This research work has opened a new area of research finding in BCI-algebras, vis-a-vis the emergence of 540 varieties of Bol-Moufang type quasi neutrosophic triplet loops. A ‘Cycle of Algebraic Structures’ which portrays this fact is provided.

scholarly journals Upper class of type I on coupled coincidence point results for some contractions in partially ordered JS-metric spaces

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
A. H. Ansari ◽  
A. Khemphet ◽  
N. Phudolsitthiphat ◽  
A. Wiriyapongsanon
Keyword(s):  
Metric Spaces ◽  
Coincidence Point ◽  
Research Work ◽  
Sufficient Conditions ◽  
Coupled Coincidence Point ◽  
Upper Class ◽  
Type I ◽  
System Of Integral Equations ◽  
Necessary And Sufficient ◽  
Coupled Coincidence

AbstractIn this research work, the necessary and sufficient conditions of a coupled coincidence point of certain type of generalized contractions are explored. These results are considered under JS-metric spaces equipped with a partial order. Moreover, examples satisfying theorems are given. Finally, an application to a system of integral equations is obtained using our results. In addition, an example of the system is provided.

scholarly journals A Novel Incorporate Algorithm of Concept Lattice

2013 ◽  
Vol 756-759 ◽  
pp. 2803-2807
Author(s):  
Xi Gong
Keyword(s):  
Direct Product ◽  
Concept Lattice ◽  
Research Field ◽  
Formal Context ◽  
Concept Lattices ◽  
Product Operation ◽  
Single Attribute ◽  
Bottom To Top

With the expansion of the research field, the research object of some original seemingly unrelated properties have been studied together. At this time, the number of attribute in formal context has changed. For the increased attributes, we need to construct a new concept lattice. The existing incremental building algorithms of concept lattice need the original formal context as the basis, with single attribute or a set of attribute of the object to rebuild the concept lattice. They can't effectively utilize these existing concept lattice that have not relation in attributes. Here, the paper presents one new algorithm for incorporating concept lattice based on the existed concept lattices. We can directly build the together lattice from bottom to top by direct product operation on the existed concept lattices and the mapping relation between the direct product lattice of two existed concept lattices and the together lattice. Formal contexts that attribute sets have no intersection are fit for this algorithm.

Using Formal Concept Analysis and Rough Set Constructing the System of Semantic Web

2011 ◽  
Vol 58-60 ◽  
pp. 1664-1670
Author(s):  
Hong Sheng Xu ◽  
Rui Ling Zhang
Keyword(s):  
Semantic Web ◽  
Rough Set ◽  
Formal Concept Analysis ◽  
Rough Set Theory ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Great Promise ◽  
Formal Concept ◽  
Concept Lattices

Formal concept analysis (FCA) is based on a formalization of the philosophical understanding of a concept as a unit of thought constituted by its extent and intent. The rough set philosophy is founded on the assumption that with every object of the universe of discourse we associate some information. This paper deals with approaches to knowledge reduction in generalized consistent decision formal context. Finally, a new system model of semantic web based on FCA and rough set is proposed, which preserve more structural and featural information of concept lattice. In order to obtain the concept lattices with relatively less attributes and objects, we study the reduction of the concept lattices based on FCA and rough set theory. The experimental results indicate that this method has great promise.

Research on Web Dynamic Ontology Construction Based on Concept Lattice

2013 ◽  
Vol 411-414 ◽  
pp. 589-592
Author(s):  
Hua Zhu Song ◽  
Xiao Xue Wang ◽  
Lu Xu ◽  
Fan Zhou
Keyword(s):  
Information System ◽  
Concept Lattice ◽  
Formal Context ◽  
The Novel ◽  
Concept Lattices ◽  
Ontology Construction ◽  
Similarity Calculation ◽  
Novel Method ◽  
Stock Information ◽  
The Web

Ontology and semantic are very popular in Web, and the construction of Web dynamic ontology has been the problem urgent to be solved. Firstly, the basic framework for constructing Web dynamic ontology is shown. Next, the concept lattice is introduced, based on which the novel method of building Web dynamic ontology is given. It includes constructing the initial ontology, extracting web knowledge, generating the formal contexts, merging formal context, merging concept lattices with ontology-based similarity calculation, transforming the concept lattice to the ontology. At last, the stock information system is employed to verify the methods proposed. The results showed the stock ontology could be dynamically updated with the change from the Web, and we can get new inferred knowledge from the updated stock ontology by Racer; the method proposed is valid and feasible.

scholarly journals Dynamic Horizontal Union Algorithm for Multiple Interval Concept Lattices

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 159 ◽  
Author(s):  
Yafeng Yang ◽  
Ru Zhang ◽  
Baoxiang Liu
Keyword(s):  
Big Data ◽  
Real Time ◽  
Association Rules ◽  
Lattice Structure ◽  
Concept Lattice ◽  
Concept Lattices ◽  
Generation Algorithm ◽  
Mining Association Rules ◽  
Necessary And Sufficient

In the era of big data, the data is updating in real-time. How to prepare the data accurately and efficiently is the key to mining association rules. In view of the above questions, this paper proposes a dynamic horizontal union algorithm of multiple interval concept lattices under the same background of the different attribute set and object set. First, in order to ensure the integrity of the lattice structure, the interval concept lattice incremental generation algorithm was improved, and then interval concept was divided into existing concept, redundancy concept and empty concept. Secondly, combining the characteristics of the interval concept lattice, the concept of consistency of interval concept lattice was defined and it is necessary and sufficient for the horizontal union of the lattice structure. Further, the interval concepts united were discussed, and the principle of horizontal unions was given. Finally, the sequence was scanned by the traversal method. This method increased the efficiency of horizontal union. A case study shows the feasibility and efficiency of the proposed algorithm.

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