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On locally internal monotonic operations

✍ Scribed by J. Martı́n; G. Mayor; J. Torrens

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
246 KB
Volume
137
Category
Article
ISSN
0165-0114

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✦ Synopsis

This paper deals with monotonic binary operations F : [0; 1] 2 → [0; 1] with the property (called locally internal property) that the value at any point (x; y) is always one of its arguments x; y. After stating a theorem that characterizes this kind of operations, some special cases are studied in detail by considering additional properties of the operation: commutativity, existence of a neutral element and associativity. In case of locally internal, associative monotonic operations with neutral element, a characterization theorem gives an improvement of a well-known theorem of Czogala and Drewniak on idempotent, associative and increasing operations with neutral element, as well as an improvement of a characterization theorem for left (and right) continuous, idempotent uninorms.

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