NDLI: The Logical Operations on Relations, Scales and Concept Lattices

Content Provider	IEEE Xplore Digital Library
Author	Yuxia Lei Yuefei Sui Cungen Cao
Copyright Year	2009
Abstract	Object-attribute-value-relationships, which are a frequently used data structure to code real-world problems,are formalized via many-valued contexts in Formal Concept Analysis (FCA). The aim of FCA is to explore (formal) concepts from empirical data contexts. A concept of a context consists of two parts: the extent (objects the concept covers) and the intent (attributes describing the concept). From the logical point of view, the intent of each concept is a conjunction of some attributes. Similar to conjunction, negation and disjunction are also important logical operations of attributes or attribute value pairs, which are common in human language. However, the classical FCA as a mathematical theory of concepts lacks a theory of negation and disjunction. In this paper, we take negation and disjunction into consideration in the process of constructing concepts, and hence obtain the following extended concepts: negative concepts of a context (i.e., a binary relation), negative concepts of a relation with some scales, disjunctive concepts of a relation, disjunctive concepts of a relation with some scales, logical concepts of a relation, and logical concepts of a relation with some scales. Compared with concepts in the classical FCA, the extended concepts mentioned above are more pertinent and more meaningful.
Starting Page	160
Ending Page	167
File Size	356130
Page Count	8
File Format	PDF
ISBN	9780769538105
DOI	10.1109/SKG.2009.37
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-10-12
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	negation Laboratories disjunction Lattices Humans Relational databases Educational institutions Data structures concept lattices Intelligent structures relational databases Information analysis Computer science logical operations conjunction Information processing
Content Type	Text
Resource Type	Article

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