Product Family Representation and Redesign: Increasing Commonality Using Formal Concept Analysis

2005 ◽  
Author(s):  
Jyotirmaya Nanda ◽  
Henri J. Thevenot ◽  
Timothy W. Simpson
Keyword(s):  
Time Use ◽  
Complete Lattice ◽  
Formal Concept Analysis ◽  
Lattice Structure ◽  
Product Family ◽  
Concept Analysis ◽  
Single Component ◽  
Hasse Diagram ◽  
Formal Concept ◽  
Multiple Products

In this paper we propose a framework based on Formal Concept Analysis (FCA) that can be applied systematically to (1) visualize a product family (PF) and (2) improve commonality in the product family. Within this framework, the components of a PF are represented as a complete lattice structure using FCA. A Hasse diagram composed of the lattice structure graphically represents all the products, components, and the relationships between products and components in the PF. The lattice structure is then analyzed to identify prospective components to redesign to improve commonality. We propose two approaches as part of this PF redesign methodology: (1) Component-Based approach, and (2) Product-Based approach. In the Component-Based approach, emphasis is given to a single component that could be shared among the products in a PF to increase commonality. In the Product-Based approach, multiple products from a PF are selected, and commonality is improved among the selected products. Various commonality indices are used to assess the degree of commonality within a PF during its redesign. In this paper, we apply the framework to represent and redesign a family of one-time-use cameras. Besides increasing the understanding of the interaction between components in a PF, the framework explicitly captures the redesign process for improving commonality using FCA.

Browsing Large Concept Lattices through Tree Extraction and Reduction Methods

2013 ◽  
Vol 9 (4) ◽  
pp. 16-34 ◽  
Author(s):  
Cassio Melo ◽  
Bénédicte Le-Grand ◽  
Marie-Aude Aufaure
Keyword(s):  
Fault Tolerance ◽  
Formal Concept Analysis ◽  
Concept Analysis ◽  
Hasse Diagram ◽  
Formal Concept ◽  
Concept Lattices ◽  
Direct Graph ◽  
Concept Clustering ◽  
Reduction Methods ◽  
Tree Extraction

Browsing concept lattices from Formal Concept Analysis (FCA) becomes a problem as the number of concepts can grow significantly with the number of objects and attributes. Interpreting the lattice through direct graph-based visualisation of the Hasse diagram rapidly becomes difficult and more synthetic representations are needed. In this work the authors propose an approach to simplify concept lattices by extracting and visualising trees derived from them. The authors further simplify the browse-able trees with two reduction methods: fault-tolerance and concept clustering.

Representing and Processing Medical Knowledge Using Formal Concept Analysis

2002 ◽  
Vol 41 (02) ◽  
pp. 160-167 ◽  
Author(s):  
M. Schnabel
Keyword(s):  
Complete Lattice ◽  
Formal Concept Analysis ◽  
Medical Knowledge ◽  
Mathematical Structure ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Inference Process ◽  
Therapeutic Decisions ◽  
Analyze Data

Summary Objectives: The aim is to show the flexibility, adequateness, and generality of formal concept analysis (FCA) applied to expert systems in medicine. Methods: The basic idea of formal concept analysis is to look at a set of objects together with their attributes (formal context) under a definite mathematical view. This view leads to a mathematical structure, a complete lattice, which can be represented graphically. Results: Some examples show that this method is very general and can be used to describe diseases, relationships between diseases and findings, the inference process, and, among others, types of uncertainty. For many applications, the adequateness of this method, concerning the underlying semantics, can easily be made plausible. Conclusions: FCA can be used to analyze data that can be described by objects and attributes of any kind. The selected examples (diseases, patient cases, therapeutic decisions, rules) show the usefulness of this method. Although it is not difficult to transform the relevant semantics into a formal context in many cases, much more experience is necessary.

Interactive Data Mining for Large-Scale Image Databases Based on Formal Concept Analysis

2010 ◽  
Vol 14 (3) ◽  
pp. 303-308 ◽  
Author(s):  
Takanari Tanabata ◽  
◽  
Kazuhito Sawase ◽  
Hajime Nobuhara ◽  
Barnabas Bede ◽  
...  
Keyword(s):  
Data Mining ◽  
Formal Concept Analysis ◽  
Large Scale ◽  
Lattice Structure ◽  
Concept Analysis ◽  
Image Features ◽  
Image Databases ◽  
Formal Concept ◽  
Interactive Data Mining ◽  
Interactive Data

In order to perform an interactive data-mining for huge image databases efficiently, a visualization interface based on Formal Concept Analysis (FCA) is proposed. The proposed interface system provides an intuitive lattice structure enabling users freely and easily to select FCA attributes and to view different aspects of the Hasse diagram of the lattice of a given image database. The investigation environment is implemented using C++ and the OpenCV library on a personal computer (CPU = 2.13 GHz, MM = 2 GB). In visualization experiments using 1,000 Corel Image Gallery images, we test image features such as color, edge, and face detectors as FCA attributes. Experimental analysis confirms the effectiveness of the proposed interface and its potential as an efficient datamining tool.

m-Algebraic lattices in formal concept analysis

2019 ◽  
Vol 29 (10) ◽  
pp. 1556-1574
Author(s):  
Zhongxi Zhang ◽  
Qingguo Li ◽  
Nan Zhang
Keyword(s):  
Complete Lattice ◽  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Continuous Functions ◽  
Algebraic Lattice ◽  
Formal Concept ◽  
Algebraic Lattices ◽  
Special Cases ◽  
Cartesian Closed

AbstractThe notion of an m-algebraic lattice, where m stands for a cardinal number, includes numerous special cases, such as complete lattice, algebraic lattice, and prime algebraic lattice. In formal concept analysis, one fundamental result states that every concept lattice is complete, and conversely, each complete lattice is isomorphic to a concept lattice. In this paper, we introduce the notion of an m-approximable concept on each context. The m-approximable concept lattice derived from the notion is an m-algebraic lattice, and conversely, every m-algebraic lattice is isomorphic to an m-approximable concept lattice of some context. Morphisms on m-algebraic lattices and those on contexts are provided, called m-continuous functions and m-approximable morphisms, respectively. We establish a categorical equivalence between LATm, the category of m-algebraic lattices and m-continuous functions, and CXTm, the category of contexts and mapproximable morphisms.We prove that LATm is cartesian closed whenevermis regular and m > 2. By the equivalence of LATm and CXTm, we obtain that CXTm is also cartesian closed under same circumstances. The notions of a concept, an approximable concept, and a weak approximable concept are showed to be special cases of that of an m-approximable concept.

Knowledge Representation Using Formal Concept Analysis

2014 ◽  
pp. 306-336 ◽  
Author(s):  
Ch. Aswani Kumar ◽  
Prem Kumar Singh
Keyword(s):  
Formal Concept Analysis ◽  
Lattice Structure ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Formal Context ◽  
Formal Concept ◽  
Mathematical Framework ◽  
Formal Concepts ◽  
Conceptual Data ◽  
The Relationship

Introduced by Rudolf Wille in the mid-80s, Formal Concept Analysis (FCA) is a mathematical framework that offers conceptual data analysis and knowledge discovery. FCA analyzes the data, which is represented in the form of a formal context, that describe the relationship between a particular set of objects and a particular set of attributes. From the formal context, FCA produces hierarchically ordered clusters called formal concepts and the basis of attribute dependencies, called attribute implications. All the concepts of a formal context form a hierarchical complete lattice structure called concept lattice that reflects the relationship of generalization and specialization among concepts. Several algorithms are proposed in the literature to extract the formal concepts from a given context. The objective of this chapter is to analyze, demonstrate, and compare a few standard algorithms that extract the formal concepts. For each algorithm, the analysis considers the functionality, output, complexity, delay time, exploration type, and data structures involved.

USING FORMAL CONCEPT ANALYSIS FOR MICROARRAY DATA COMPARISON

2008 ◽  
Vol 06 (01) ◽  
pp. 65-75 ◽  
Author(s):  
V. CHOI ◽  
Y. HUANG ◽  
V. LAM ◽  
D. POTTER ◽  
R. LAUBENBACHER ◽  
...  
Keyword(s):  
Data Analysis ◽  
Microarray Data ◽  
Formal Concept Analysis ◽  
Lattice Structure ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Biological Information ◽  
Microarray Data Analysis ◽  
Mouse Lung ◽  
Formal Concept

Microarray technologies, which can measure tens of thousands of gene expression values simultaneously in a single experiment, have become a common research method for biomedical researchers. Computational tools to analyze microarray data for biological discovery are needed. In this paper, we investigate the feasibility of using formal concept analysis (FCA) as a tool for microarray data analysis. The method of FCA builds a (concept) lattice from the experimental data together with additional biological information. For microarray data, each vertex of the lattice corresponds to a subset of genes that are grouped together according to their expression values and some biological information related to gene function. The lattice structure of these gene sets might reflect biological relationships in the dataset. Similarities and differences between experiments can then be investigated by comparing their corresponding lattices according to various graph measures. We apply our method to microarray data derived from influenza-infected mouse lung tissue and healthy controls. Our preliminary results show the promise of our method as a tool for microarray data analysis.

A Methodology for Product Family Ontology Development Using Formal Concept Analysis and Web Ontology Language

2005 ◽  
Vol 6 (2) ◽  
pp. 103-113 ◽  
Author(s):  
Jyotirmaya Nanda ◽  
Timothy W. Simpson ◽  
Soundar R. T. Kumara ◽  
Steven B. Shooter
Keyword(s):  
Formal Concept Analysis ◽  
Product Family ◽  
Concept Analysis ◽  
Ontology Development ◽  
Formal Concept ◽  
Web Ontology Language ◽  
Product Family Design ◽  
Ontology Language ◽  
Development Costs ◽  
Finite Set

The use of ontologies for information sharing is well documented in the literature, but the lack of a comprehensive and systematic methodology for constructing product ontologies has limited the process of developing ontologies for design artifacts. In this paper we introduce the Product Family Ontology Development Methodology (PFODM), a novel methodology to develop formal product ontologies using the Semantic Web paradigm. Within PFODM, Formal Concept Analysis (FCA) is used first to identify similarities among a finite set of design artifacts based on their properties and then to develop and refine a product family ontology using Web Ontology Language (OWL). A family of seven one-time-use cameras is used to demonstrate the steps of the PFODM to construct such an ontology. The benefit of PFODM lies in providing a systematic and consistent methodology for constructing ontologies to support product family design. The resulting ontologies provide a hierarchical conceptual clustering of related design artifacts, which is particularly advantageous for product family design where parts, processes, and most important, information is intentionally shared and reused to reduce complexity, lead-time, and development costs. Potential uses of the resulting ontologies and FCA representations within product family design are also discussed.

An Approach Using Concept Lattice Structure for Data Mining and Information Retrieval

2015 ◽  
Vol 1 ◽  
pp. 1
Author(s):  
Tran Lam Quan ◽  
Vu Tat Thang
Keyword(s):  
Data Mining ◽  
Information Retrieval ◽  
Text Mining ◽  
Formal Concept Analysis ◽  
Mathematical Theory ◽  
Lattice Structure ◽  
Concept Lattice ◽  
Concept Analysis ◽  
Frequent Itemset ◽  
Formal Concept

Since the 1980s, the concept lattice was studied and applied to the problems of text mining, frequent itemset, classification, etc. The formal concept analysis - FCA is one of the main techniques applied in the concept lattice. FCA is a mathematical theory which is applied to the data mining by setting a table with rows describing objects and columns describing attributes, with relationships between them, and then sets up the concept lattice structure. In the area of information retrieval, FCA considers the correlation of objects-attributes the same as those of documents-terms. In the process of setting up the lattice, FCA defines each node in the lattice as a concept. The algorithm for the construction of concept lattice will install a couple on each node, including a set of documents with common terms, and a set of terms which co-occurs in documents. In a larger scale, each concept in the lattice could be recognized as a couple of questions - answers. In the lattice, the action of browsing up or down of nodes will allow approaching more general concepts or more detail concepts, respectively.

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