Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory

Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory

In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included...

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Main Author: Vilém Novák
Format: Article
Language:English
Published: MDPI AG 2020-03-01
Series:Mathematics
Subjects:
higher-order fuzzy logic
fuzzy type theory
alternative set theory
rough sets
indiscernibility relation
fuzzy equality
Online Access:https://www.mdpi.com/2227-7390/8/3/432
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spelling doaj-936df70ac42042a3abe6e63c36fe472b2020-11-25T02:25:05ZengMDPI AGMathematics2227-73902020-03-018343210.3390/math8030432math8030432Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type TheoryVilém Novák0Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech RepublicIn this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.https://www.mdpi.com/2227-7390/8/3/432higher-order fuzzy logicfuzzy type theoryalternative set theoryrough setsindiscernibility relationfuzzy equality
collection DOAJ
language English
format Article
sources DOAJ
author Vilém Novák
spellingShingle Vilém Novák
Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory
Mathematics
higher-order fuzzy logic
fuzzy type theory
alternative set theory
rough sets
indiscernibility relation
fuzzy equality
author_facet Vilém Novák
author_sort Vilém Novák
title Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory
title_short Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory
title_full Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory
title_fullStr Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory
title_full_unstemmed Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory
title_sort topology in the alternative set theory and rough sets via fuzzy type theory
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2020-03-01
description In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.
topic higher-order fuzzy logic
fuzzy type theory
alternative set theory
rough sets
indiscernibility relation
fuzzy equality
url https://www.mdpi.com/2227-7390/8/3/432
work_keys_str_mv AT vilemnovak topologyinthealternativesettheoryandroughsetsviafuzzytypetheory
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