𝔖 Bobbio Scriptorium
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T-partitions of the real line generated by idempotent shapes

✍ Scribed by B. De Baets; M. Mareš; R. Mesiar

Book ID
104292484
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
535 KB
Volume
91
Category
Article
ISSN
0165-0114

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✦ Synopsis

The idea of generating fuzzy numbers as equivalence classes of particular J-equivalences on the real line R is fully exploited. Scales (or generators) are used to define certain (pseudo-)metrics on R. By means of a shape (function), these (pseudo-)metrics are then transformed into binary fuzzy relations on R. Shapes leading to 3--equivalences, and hence to a class of fuzzy numbers forming a o~--partition of ~, are completely characterized in the case of a continuous generator. This characterization problem is shown to be closely related to determining the idempotents w.r.t, the 3--addition of fuzzy numbers. (~)

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