✦ LIBER ✦

Lattice fuzzy logics

✍ Scribed by Ernest A. Edmonds

Publisher: Elsevier Science
Year: 1980
Weight: 448 KB
Volume: 13
Category: Article
ISSN: 0020-7373
DOI: 10.1016/s0020-7373(80)80006-x

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✦ Synopsis

Although the characterizing membership functions of fuzzy sets normally have as their range the interval [0, 1], it is possible for the range to be a partially ordered set. The use of lattices for this set is explored. Various forms of restricted infinite lattice are considered. Rose's logical operator for logics whose truth values form lattices are reviewed. A basis for lattice fuzzy logics, using Rose's operators, is discussed and a particular infinite lattice is proposed for use in characterizing lattice fuzzy sets. Some of the concepts are used to extend edge detection techniques in image processing from grey scale to colour images.

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## Abstract It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w. r. t. the class of all finite MTL‐chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since