Attribute dependencies for data with grades I.

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F16%3A33161530" target="_blank" >RIV/61989592:15310/16:33161530 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1080/03081079.2016.1205711" target="_blank" >http://dx.doi.org/10.1080/03081079.2016.1205711</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/03081079.2016.1205711" target="_blank" >10.1080/03081079.2016.1205711</a>

Result language

angličtina

Original language name

Attribute dependencies for data with grades I.

Original language description

This paper examines attribute dependencies in data that involve grades, such as a grade to which an object is red or a grade to which two objects are similar. We thus extend the classical agenda by allowing graded, or "fuzzy", attributes instead of Boolean, yes-or-no attributes in case of attribute implications, and allowing approximate match based on degrees of similarity instead of exact match based on equality in case of functional dependencies. In a sense, we move from bivalence, inherently present in the now-available theories of dependencies, to a more flexible setting that involves grades. Such a shift has far-reaching consequences. We argue that a reasonable theory of dependencies may be developed by making use of mathematical fuzzy logic, a recently developed many-valued logic. Namely, the theory of dependencies is then based on a solid logic calculus the same way classical dependencies are based on classical logic. For instance, rather than handling degrees of similarity in an ad hoc manner, we consistently treat them as truth values, the same way as true (match) and false (mismatch) are treated in classical theories. In addition, several notions intuitively embraced in the presence of grades, such as a degree of validity of a particular dependence or a degree of entailment, naturally emerge and receive a conceptually clean treatment in the presented approach. In the first part of this two-part paper, we discuss motivations, provide basic notions of syntax and semantics and develop basic results which include entailment of dependencies, associated closure structures and a logic of dependencies with two versions of completeness theorem.

Czech name

—

Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

IN - Informatics

OECD FORD branch

—

Project

<a href="/en/project/GAP202%2F10%2F0262" target="_blank" >GAP202/10/0262: Decompositions of matrices with binary and ordinal data: theory, algorithms, and complexity</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

International Journal of General Systems

ISSN

0308-1079

e-ISSN

—

Volume of the periodical

45

Issue of the periodical within the volume

7-8

Country of publishing house

GB - UNITED KINGDOM

Number of pages

25

Pages from-to

864-888

UT code for WoS article

000393213500010

EID of the result in the Scopus database

2-s2.0-85007016052