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Titlebook: Goguen Categories; A Categorical Approa Michael Winter Book 2007 Springer Science+Business Media B.V. 2007 Allegories.Categories.Computer s

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发表于 2025-3-21 17:35:38 | 显示全部楼层 |阅读模式
书目名称Goguen Categories
副标题A Categorical Approa
编辑Michael Winter
视频video
概述Rigorous application of formal logics to fuzzy concepts.A mathematical introduction to fuzzy concepts for researchers in formal logics.Unique approach to formal semantics of fuzzy controllers
丛书名称Trends in Logic
图书封面Titlebook: Goguen Categories; A Categorical Approa Michael Winter Book 2007 Springer Science+Business Media B.V. 2007 Allegories.Categories.Computer s
描述.Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations. The book then introduces Goguen categories and provides a comprehensive study of these structures including their representation theory, and the definability of norm-based operations...The power of the theory is demonstrated by a comprehensive example. A certain Goguen category is used to specify and to develop a fuzzy controller. Based on its abstract description as well as certain desirable properties and their formal proofs, a verified controller is derived without compromising the - sometimes - intuitive choice of norm-based operations by fuzzy engineers..
出版日期Book 2007
关键词Allegories; Categories; Computer science; Fuzzy relations; Goguen; Relation algebras; proof
版次1
doihttps://doi.org/10.1007/978-1-4020-6164-6
isbn_softcover978-90-481-7554-3
isbn_ebook978-1-4020-6164-6Series ISSN 1572-6126 Series E-ISSN 2212-7313
issn_series 1572-6126
copyrightSpringer Science+Business Media B.V. 2007
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https://doi.org/10.1007/978-3-319-96589-5[18], i.e., the Zermelo-Fraenkel axioms of set theory. As usual, we denote the fact that “. is an element of a set .” by .. The set with no elements is called the ., and is denoted by .. If every element of a set . is also an element of the set ., we say . is a . of . denoted by ..
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Sets, Relations, And Functions,[18], i.e., the Zermelo-Fraenkel axioms of set theory. As usual, we denote the fact that “. is an element of a set .” by .. The set with no elements is called the ., and is denoted by .. If every element of a set . is also an element of the set ., we say . is a . of . denoted by ..
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978-90-481-7554-3Springer Science+Business Media B.V. 2007
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https://doi.org/10.1007/978-1-4020-6164-6Allegories; Categories; Computer science; Fuzzy relations; Goguen; Relation algebras; proof
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Categories Of L-Fuzzy Relations,y. We have shown that there are some notions of crispness within Dedekind categories, which grasp the notion of 0–1 crispness under an assumption on the underlying lattice. Unfortunately, a general notion, which coincides with 0–1 crispness has not yet been given.
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