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

Autor:	Vilém Novák
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	higher-order fuzzy logic fuzzy type theory alternative set theory rough sets indiscernibility relation fuzzy equality Mathematics QA1-939
Zdroj:	Mathematics, Vol 8, Iss 3, p 432 (2020)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math8030432
Popis:	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.
Databáze:	Directory of Open Access Journals
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