NDLI: Universal representation of fuzzy sets' membership functions

Content Provider	IEEE Xplore Digital Library
Author	Hovanov, N.V. Kornikov, V.V. Seregin, I.A.
Copyright Year	1999
Description	Author affiliation: Fac. of Economics, St. Petersburg State Univ., Russia (Hovanov, N.V.)
Abstract	A generalized membership function of a fuzzy set A in a fixed set Z={z} is established as a mapping m(z;A):Z/spl rarr/X into a mathematical system S=(X;R), which is structured by a set R={R/sub i/,i/spl epsiv/I} of polyadic relations R/sub i//spl sube/X/sup r(i)/. The mathematical system S=(X;R) being interpreted as a "quality measurement scale" (QMS), a value m(z/sub 0/,;A)/spl epsiv/ X may be treated as a measure for the quality "membership in the fuzzy set A". For the generalized membership function a universal form is found, namely the form of the universal membership function u(z;A):Z/spl rarr/)X', which maps the fixed set Z into mathematical system S'=(X';R/sub /spl ges//), the mathematical system S' being a universal representation for the initial system S=(X;R). The structure R/sub /spl ges// of the universal mathematical system is formed from so-called chain-dominance r(i)-adic relations R/sub /spl ges///sup r(i)/(R/sub 2//sup i/), which are induced by corresponding order relations R/sub 2//sup i/. Measurement theoretical interpretation for the universal representation S' of an arbitrary mathematical system S is given and the fundamental role of ordinal measurement scales in fuzzy sets theory is discussed.
Starting Page	169
Ending Page	172
File Size	313677
Page Count	4
File Format	PDF
ISBN	0780354060
ISSN	10987584
DOI	10.1109/FUZZY.1999.793229
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1999-08-22
Publisher Place	South Korea
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy sets Fuzzy systems Fuzzy set theory Mathematics Current measurement
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Theoretical Computer Science Software

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