scholarly journals Yoneda Philosophy in Engineering

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Lambrini Seremeti ◽  
Ioannis Kougias
Keyword(s):  
Mathematical Models ◽  
Conceptual Framework ◽  
Category Theory ◽  
Formal Concept Analysis ◽  
Building Blocks ◽  
Ontology Engineering ◽  
Formal Concept ◽  
Physical Systems ◽  
Formal Concepts ◽  
Engineering Models

Mathematical models, such as sets of equations, are used in engineering to represent and analyze the behaviour of physical systems. The conventional notations in formulating engineering models do not clearly provide all the details required in order to fully understand the equations, and, thus, artifacts such as ontologies, which are the building blocks of knowledge representation models, are used to fulfil this gap. Since ontologies are the outcome of an intersubjective agreement among a group of individuals about the same fragment of the objective world, their development and use are questions in debate with regard to their competencies and limitations to univocally conceptualize a domain of interest. This is related to the following question: “What is the criterion for delimiting the specification of the main identifiable entities in order to consistently build the conceptual framework of the domain in question?” This query motivates us to view the Yoneda philosophy as a fundamental concern of understanding the conceptualization phase of each ontology engineering methodology. In this way, we exploit the link between the notion of formal concepts of formal concept analysis and a concluding remark resulting from the Yoneda embedding lemma of category theory in order to establish a formal process.

scholarly journals A Novel Concept Acquisition Approach Based on Formal Contexts

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ting Qian ◽  
Ling Wei
Keyword(s):  
Data Analysis ◽  
Formal Concept Analysis ◽  
Real Life ◽  
Experimental Results ◽  
New Method ◽  
Concept Acquisition ◽  
Formal Concept ◽  
Knowledge Processing ◽  
Formal Concepts ◽  
Novel Concept

As an important tool for data analysis and knowledge processing, formal concept analysis (FCA) has been applied to many fields. In this paper, we introduce a new method to find all formal concepts based on formal contexts. The amount of intents calculation is reduced by the method. And the corresponding algorithm of our approach is proposed. The main theorems and the corresponding algorithm are examined by examples, respectively. At last, several real-life databases are analyzed to demonstrate the application of the proposed approach. Experimental results show that the proposed approach is simple and effective.

scholarly journals Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2694
Author(s):  
Amira Mouakher ◽  
Axel Ragobert ◽  
Sébastien Gerin ◽  
Andrea Ko
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Order Structure ◽  
Formal Concept ◽  
Massive Datasets ◽  
Interestingness Measures ◽  
Galois Lattice ◽  
Formal Concepts ◽  
Representation Method

Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes the concepts in a partial order structure or concept (Galois) lattice. Unfortunately, the total number of concepts in this structure tends to grow exponentially as the size of the data increases. Therefore, there are numerous approaches for selecting a subset of concepts to provide full or partial coverage. In this paper, we rely on the battery of mathematical models offered by FCA to introduce a new greedy algorithm, called Concise, to compute minimal and meaningful subsets of concepts. Thanks to its theoretical properties, the Concise algorithm is shown to avoid the sluggishness of its competitors while offering the ability to mine both partial and full conceptual coverage of formal contexts. Furthermore, experiments on massive datasets also underscore the preservation of the quality of the mined formal concepts through interestingness measures agreed upon by the community.

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 Deep First Formal Concept Search

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Tao Zhang ◽  
Hui Li ◽  
Wenxue Hong ◽  
Xiamei Yuan ◽  
Xinyu Wei
Keyword(s):  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
End Points ◽  
Depth First Search ◽  
Visualization Analysis ◽  
Main Challenge ◽  
Formal Concepts ◽  
Exponential Complexity

The calculation of formal concepts is a very important part in the theory of formal concept analysis (FCA); however, within the framework of FCA, computing all formal concepts is the main challenge because of its exponential complexity and difficulty in visualizing the calculating process. With the basic idea of Depth First Search, this paper presents a visualization algorithm by the attribute topology of formal context. Limited by the constraints and calculation rules, all concepts are achieved by the visualization global formal concepts searching, based on the topology degenerated with the fixed start and end points, without repetition and omission. This method makes the calculation of formal concepts precise and easy to operate and reflects the integrity of the algorithm, which enables it to be suitable for visualization analysis.

scholarly journals Finding Music Formal Concepts Consistent with Acoustic Similarity

2020 ◽  
Author(s):  
Yoshiaki Okubo
Keyword(s):  
Efficient Algorithm ◽  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Point Of View ◽  
Experimental Results ◽  
Formal Concept ◽  
Acoustic Similarity ◽  
Formal Concepts

In this paper, we present a method of finding conceptual clusters of music objects based on Formal Concept Analysis. A formal concept (FC) is defined as a pair of extent and intent which are sets of objects and terminological attributes commonly associated with the objects, respectively. Thus, an FC can be regarded as a conceptual cluster of similar objects for which its similarity can clearly be stated in terms of the intent. We especially discuss FCs in case of music objects, called music FCs. Since a music FC is based solely on terminological information, we often find extracted FCs would not always be satisfiable from acoustic point of view. In order to improve their quality, we additionally require our FCs to be consistent with acoustic similarity. We design an efficient algorithm for extracting desirable music FCs. Our experimental results for The MagnaTagATune Dataset shows usefulness of the proposed method.

scholarly journals Three-Way Concept Analysis for Incomplete Formal Contexts

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Huilai Zhi ◽  
Hao Chao
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Binary Relations ◽  
Formal Concepts ◽  
Target Set ◽  
The Relationship ◽  
Negative Attributes

Recently, incomplete formal contexts have received more and more attention from the communities of formal concept analysis. Different from a complete context where the binary relations between all the objects and attribute are known, an incomplete formal context has at least a pair of object and attribute with a completely unknown binary relation. Partially known formal concepts use interval sets to indicate the incompleteness. Three-way formal concept analysis is capable of characterizing a target set by combining positive and negative attributes. However, how to describe target set, by pointing out what attributes it has with certainty and what attributes it has with possibility and what attributes it does not has with certainty and what attributes it does not has with possibility, is still an open problem. This paper combines the ideas of three-way formal concept analysis and partially known formal concepts and presents a framework of approximate three-way concept analysis. At first, approximate object-induced and attribute-induced three-way concept lattices are introduced, respectively. And then, the relationship between approximate three-way concept lattice and classical three-way concept lattice are investigated. Finally, examples are presented to demonstrate and verify the obtained results.

Semantic Web Ontology Integration Based on Formal Concept Analysis

2013 ◽  
Vol 373-375 ◽  
pp. 1714-1718
Author(s):  
Hong Xia
Keyword(s):  
Web Services ◽  
Semantic Web ◽  
Formal Concept Analysis ◽  
Service Discovery ◽  
Concept Analysis ◽  
Domain Ontology ◽  
Ontology Engineering ◽  
Formal Concept ◽  
Modeling Concept

Matchmaking is the basis of doing service discovery and composition. Using ontology semantically express the service of capabilities, correctly match service. Domain ontology and Formal Concept Analysis aim at modeling concept. The role of FCA in ontology engineering is supporting reusing independently developed domain ontology. Evaluating concept similarity identifies the different concepts that are semantically close. In this paper, using concept and attribute of web services to construct the ontology. Also, an ontology based method for assessing similarity between FCA concepts is proposed.

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.

scholarly journals Rough Set Approximation as Formal Concept

2006 ◽  
Vol 10 (5) ◽  
pp. 606-611 ◽  
Author(s):  
Nozomi Ytow ◽  
◽  
David R. Morse ◽  
David McL. Roberts ◽  
◽  
...  
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Formal Concept Analysis ◽  
Rough Set Theory ◽  
The Other ◽  
Formal Concept ◽  
Object Based ◽  
Formal Concepts ◽  
Set Approximation

Formal Concept Analysis (FCA) defines a formal concept as a pair of sets: objects and attributes, called extent and intent respectively. A rough set, on the other hand, approximates a concept using sets of objects only (in terms of FCA). We show that 1) a formal concept can be composed using a set of objects and its complement, 2) such object-based formal concepts are isomorphic to formal concepts based on objects and attributes, 3) upper and lower approximations of rough sets give generalization of formal concept, and 4) the pair of positive and negative sets (sensu rough set theory) are isomorphic to complemental formal concepts when the equivalence of the rough set gives positive and negative sets unique to each of the formal concepts. Implications of this are discussed.

Lower and Upper Concept Lattices

2014 ◽  
Vol 60 (2) ◽  
pp. 337-352
Author(s):  
Cristian Vaideanu
Keyword(s):  
Formal Concept Analysis ◽  
Mathematical Theory ◽  
Concept Analysis ◽  
Galois Connection ◽  
Knowledge Systems ◽  
Domain Theory ◽  
Formal Concept ◽  
Concept Lattices ◽  
New Models ◽  
Formal Concepts

Abstract Formal Concept Analysis is a mathematical theory of data analysis using formal contexts and concept lattices. In this paper, two new types of concept lattices are introduced by using notions from domain theory (in particular, Hoare and Smyth powerdomains). Based on a Galois connection, we prove the fundamental theorem of the Formal Concept Analysis, as well as other properties of lower and upper formal concepts. In this way, we provide new models to represent and retrieve the information in data and knowledge systems.

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