A Unified View of Different Axiomatic Measures Defined on $L$-Fuzzy Sets

Fuzzy sets form A meta-system-theoretic point of view

A kind of fuzzy upper topology on L-preordered sets

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

Supplementarity measures on fuzzy sets

In this paper, we tackle the study of so-called supplementarity measures. They are introduced axiomatically and are then related to incompatibility measures by antonyms. To do this, we have to establish what we mean by antonymous measure. We then prove that, under certain conditions, supplementarity and incompatibility measures are antonymous. Besides, with the aim of constructing antonymous me...

Measures of Fuzziness under Different Uses of Fuzzy Sets

In this paper we discuss on the relationship between fuzziness and its measuring on the one side, and the possible uses of fuzzy sets on the other side. We conclude that the usual axioms and measures of fuzziness disregard the commensurability assumption and view the fuzzy set as a collection of fuzzy singletons. We propose new axioms and a relation “less fuzzy than” for a conjunctive view of f...

Fuzzy universal algebras on $L$-sets

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...