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.

Aswani Kumar Cherukuri

Department of Information Technology

School of Information Technology and Engineering

Vellore Campus

Singh P.K.

Fulltext

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Global Trends in Intelligent Computing Research and Development Advances in Computational Intelligence and Robotics

This paper introduces a mathematical model for precise analysis of uncertainty and its fluctuation in the given interval-valued fuzzy attributes. In this regard, a method is introduced for drawing the interval-valued complex lattice and its navigation at user required complex granules with demonstration. © 2019, Springer Nature Singapore Pte Ltd.

Advances in Intelligent Systems and Computing Recent Developments in Machine Learning and Data Analytics

Interval-Valued Complex Fuzzy Concept Lattice and Its Granular Decomposition

Role based access control (RBAC) is one of the popular access control models. On representing the policy behind RBAC, the literatures investigate the use of various knowledge representation techniques such as Descriptive logics, Formal Concept Analysis (FCA), Ontology etc. Based on the input of binary access control table, the existing knowledge representation techniques on RBAC derives two-way decisions whether to permit the access request or not. It works well when single element in the set of elements of a constituent of RBAC initiates the access request. Consider the scenario of multiple distinct elements in the set of elements of a constituent of RBAC initiate the collective access request to a set of elements in other constituent of RBAC. In many cases of this scenario, some elements possess but not all of the elements possess the permission to access all elements in other subset of a constituent of RBAC. On this situation, the collective access decision to those multiple distinct elements in the set of elements of a RBAC constituent appears in three forms such as permit, deny and non-commitment. Three-way formal concept analysis (3WCA) is an emerging knowledge representation technique which provides two types of three-way concepts and their lattices to enable three-way decisions from the binary information table. At this juncture, it is more suitable to apply 3WCA on representing the RBAC policy to enable three-way decisions instead of existing two-way decisions in classical FCA and triadic FCA. The main objective of this paper is to propose a methodology for modelling RBAC using 3WCA and attain its distinctive merits. Our discussion is on two lines of inquiry. We present on how 3WCA can provide suitable representation of RBAC policy and whether this representation follows role hierarchy and constraints of RBAC.

International Journal of Machine Learning and Cybernetics

Role based access control design using three-way formal concept analysis

This paper describes an efficient algorithm for formal concepts generation in large formal contexts. While many algorithms exist for concept generation, they are not suitable for generating concepts efficiently on larger contexts. We propose an algorithm named as HaLoopUNCG algorithm based on MapReduce framework that uses a lightweight runtime environment called HaLoop. HaLoop, a modified version of Hadoop MapReduce, suits better for iterative algorithms over large datasets. Our approach uses the features of HaLoop efficiently to generate concepts in an iterative manner. First, we describe the theoretical concepts of formal concept analysis and HaLoop. Second, we provide a detailed representation of our work based on Lindig’s fast concept analysis algorithm using HaLoop and MapReduce framework. The experimental evaluations demonstrate that HaLoopUNCG algorithm is performing better than Hadoop version of upper neighbour concept generation (MRUNCG) algorithm, MapReduce implementation of Ganter’s next closure algorithm and other distributed implementations of concept generation algorithms.

Journal of Information & Knowledge Management

HaLoop Approach for Concept Generation in Formal Concept Analysis

Granular Computing

Concept lattice reduction using different subset of attributes as information granules

Formal concept analysis (FCA) is a mathematical model for data analysis and processing tasks. Recently, FCA has received significant attention for the analysis of data with fuzzy attributes by representing them as a matter of degree in the formal context. In this paper, we concentrated on the analysis of fuzzy contexts (X, Y, R1) and (Z, Y, R2) which share same attribute set (Y). We can observe that, these two contexts can be connected through composition as (X, Z, R3 = R1 ∗ R2), which contains objects set from one context and attribute set from another. In this case, the problem is how to analyse the composed contexts with regard to its object and attribute set with less number of formal concepts using FCA. For this purpose, a method is proposed in this study which provides one context with regard to its object set and another with regard to its attribute set. © 2016 Inderscience Enterprises Ltd.

Journal	Global Trends in Intelligent Computing Research and Development Advances in Computational Intelligence and Robotics
Publisher	IGI Global
ISSN	2327-0411
Open Access	No