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Averaging operators on the unit interval
Author(s) -
Gehrke Mai,
Walker Carol,
Walker Elbert
Publication year - 1999
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/(sici)1098-111x(199909)14:9<883::aid-int2>3.0.co;2-u
Subject(s) - unit interval , negation , interval (graph theory) , lattice (music) , operator (biology) , mathematics , unit (ring theory) , bounded function , discrete mathematics , scaling , arithmetic , algebra over a field , computer science , pure mathematics , combinatorics , mathematical analysis , mathematics education , physics , biochemistry , chemistry , geometry , repressor , acoustics , transcription factor , gene , programming language
In working with negations and t‐norms, it is not uncommon to call upon the arithmetic of the real numbers even though that is not part of the structure of the unit interval as a bounded lattice. To develop a self‐contained system, we incorporate an averaging operator, which provides a (continuous) scaling of the unit interval that is not available from the lattice structure. The interest here is in the relations among averaging operators and t‐norms, t‐conorms, negations, and their generators. ©1999 John Wiley & Sons, Inc.