Scalar and fuzzy cardinalities of crisp and fuzzy multisets

Scalar and fuzzy cardinalities of crisp and fuzzy multisets

We define in an axiomatic way scalar and fuzzy cardinalities of finite multisetsover ]0, 1], and we obtain explicit descriptions for them. We show that, for multisetsover ]0, 1] associated to finite fuzzy sets, the cardinalities defined in this paper areequivalent to the cardinalities of the corresponding fuzzy sets previously introducedin the literature. Finally, we also de...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Scalar cardinalities for divisors of a fuzzy cardinality

In this paper, we investigate the value of the scalar cardinality for the finite fuzzy sets, whose fuzzy cardinality is known as a rational part of the cardinality of another finite fuzzy set, which is defined as generalized natural numbers and their division.

Fuzzy Multisets and Their Generalizations

Fuzzymultisets with infinitemembership sequences and their generalization using set-valued memberships are considered. Two metric spaces of the infinite fuzzy multisets are defined in terms of cardinality. One is the completion of fuzzy multisets of finite membership sequences; the other is derived from operations among fuzzy multisets and realvalued multisets. Theoretical properties of these i...

Cardinalities of Fuzzy Sets and Fuzzy Quantifiers over Residuated Lattices