Introduction to the concept of recursiveness of fuzzy functions
type: Item
instance of: scholarly article
title: Introduction to the concept of recursiveness of fuzzy functions
zbMATH Open document ID: 0639.03044
DOI: 10.1016/0165-0114(87)90131-X
author: B. George
published in: Fuzzy Sets and Systems
publication date: 1987-01-01T00:00:00Z
review text: The hypothesis that the class of recursive functions is identical with the one of functions being computable by a Turing machine is known as ``Church's soft hypothesis''. The main purpose of this article is to extend this hypothesis to the fuzzy calculus. Let \(W=([0,1],\oplus,\otimes,\leq)\) be an ordered semiring. The fuzzy functions are considered as associating an output to an input with membership degree belonging to W. For such W-functions the concepts of computability and recursiveness are extended, obtaining the so-called W- computability and W-recursiveness, respectively. Some properties of W- recursive functions are analyzed and the equivalence between W-recursive and W-computable functions is shown.
Mathematics Subject Classification ID: 03D20
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 4041896
zbMATH Keywords: fuzzy recursiveness
zbMATH Keywords: fuzzy computability
zbMATH Keywords: Church's soft hypothesis
reviewed by: Satoshi Miura
MaRDI profile type: Publication
cites work: Q4085278
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full work available at URL: 0165-0114(87)90131-x
OpenAlex ID: W1989564131
description: scientific article; zbMATH DE number 4041896