and Applied Analysis 3 Definition 1.4 see 18, 20–23 . 1 The intersection of all fuzzy α-closed resp., semiclosed, preclosed, γ-closed, semi-preclosed, β-closed sets containing a fuzzy set A is called a fuzzy α-closure resp., semiclosure, preclosure, γ-closure, semi-preclosure, β-closure of A. 2 The union of all fuzzy α-open resp., semiopen, preopen, γ-open, semi-preopen, β-open sets contained i...

In this paper, a  fuzzy numerical procedure for solving fuzzy linear Volterra integro-differential equations of the second kind under strong  generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method  and other numerical methods.Error ana...

We deepen the study of two known neighborhood structures, which here will be called f · k-neighborhood structures and f · q-neighborhood structures, in the context of Šostak fuzzy topological spaces. In particular, we characterize fuzzy topologies by f · k-neighborhood structures. Moreover we introduce and discuss the notions of f · kneighborhood prestructure and f ·m-neighborhood structure in ...

Moving target tracking in wireless sensor networks is of paramount importance. This paper considers the problem of state estimation for L-sensor linear dynamic systems. Firstly, the paper establishes the fuzzy model for measurement condition estimation. Then, Generalized Kalman Filter design is performed to incorporate the novel neighborhood function and the target motion information, improving...

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

Very recently, a (fuzzy modal) logic to reason about coherent conditional probability, in the sense of de Finetti, has been introduced by the authors. Under this approach, a conditional probability ð j Þ is taken as a primitive notion defined over conditional events of the form ‘‘’ given ’’, ’j for short, where is not the impossible event. The logic, called FCP(L ), exploits an idea already use...

The theory of fuzzy measures and fuzzy integrals was introduced by S u g e n o [16] and intensively studied. Monographs [15] and [18] are dedicated to this topic. Recently, several classical inequalities were generalized to fuzzy integral. F l o r e sF r a n u l i č and R o m á n-F l o r e s [11] provided a Chebyshev type inequality for fuzzy integral of continuous and strictly monotone functio...

This paper introduces a new approach to the theory of Ω-categories enriched by a frame. The approach combines ideas from various areas such as generalized ultrametric domains, Ω-categories, constructive analysis, and fuzzy mathematics. As the basic framework, we use the Wagner’s Ω-category [18,19] with a frame instead of a quantale with unit. The objects and morphisms in the category will be ca...