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t‐Operators and uninorms on a finite totally ordered set
Author(s) -
Mas M.,
Mayor, G.,
Torrens J.
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<909::aid-int4>3.0.co;2-b
Subject(s) - mathematics , negation , set (abstract data type) , algebra over a field , duality (order theory) , operator theory , pure mathematics , discrete mathematics , computer science , programming language
This paper presents a detailed study of two classes of operators on a finite totally ordered set of labels L : t‐operators and uninorms. Both kinds of operators (on [0, 1]) are introduced as generalizations of t‐norms and t‐conorms. We characterize these operators on L as special combinations of operators of directed algebras in a similar way as they are characterized in the case of [0, 1] as special combinations of t‐norms and t‐conorms. We also study duality of these operators with respect to the only negation N on L , and we give the number of different t‐operators and uninorms that exist on L , related to the number of elements in L . ©1999 John Wiley & Sons, Inc.