Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

We extend the taming techniques for explicit Euler approximations of stochastic differential equations (SDEs) driven by Lévy noise with super-linearly growing drift coefficients. Strong convergence results are presented for the case of locally Lipschitz coefficients. Moreover, rate of convergence results are obtained in agreement with classical literature when the local Lipschitz continuity ass...

We present an algorithm that enables one to perform locally adaptive block thresholding, while maintaining image continuity. Images are divided into sub-images based some standard image attributes and thresholding technique is employed over the sub-images. The present algorithm makes use of the thresholds of neighboring sub-images to calculate a range of values. The image continuity is taken ca...

The focus of this paper is to propose a new notion of neutrosophic crisp sets via neutrosophic crisp ideals and to study some basic operations and results in neutrosophic crisp topological spaces. Also, neutrosophic crisp L-openness and neutrosophic crisp Lcontinuity are considered as a generalizations for a crisp and fuzzy concepts. Relationships between the above new neutrosophic crisp notion...

In this paper, we introduce several concepts of tightness for a sequence of random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in Rp and give some characterizations of their concepts. Also, counter-examples for the relationships between the concepts of tightness are given.

We show here some of our results on intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set [1]. Some basic results on intuitionistic fuzzy sets were publised in [2,3], and the book [4] provides a comprehensive coverage of virtually all results until 1999 in the area of the theory and applicat...

A method for incorporating uncertainty in terrain modelling by expressing elevations as fuzzy numbers is proposed. Given a finite set of fuzzy elevations representative of the topographic surface in a certain region, we develop methods to construct surfaces that incorporate the uncertainty. The smoothness and continuity conditions of the surface generating method are maintained. Using this appr...

LoA) and τ is a subalgebra of A . Morphisms (X,A, τ) (f,φ) −−−→ (Y,B, σ) are Set × LoA-morphisms (X,A) (f,φ) −−−→ (Y,B) such that φ ◦ p ◦ f ∈ τ for every p ∈ σ (the so-called continuity). Our definition subsumes the traditional latticevalued approach of [2]. The motivation for the new concept was provided by the problem of doing fuzzy mathematics without order. In [1] the authors consider a rel...

In this paper, we introduce the concept of free abstract fuzzy economy and, using Wu’s existence theorem of maximal elements for lower semicontinuous correspondences [26] and Kim and Lee’s existence theorems of best proximity pairs [14], we prove the existence of fuzzy equilibrium pairs for free abstract fuzzy economies first with upper semicontinuous and then with lower semicontinuous constrai...

In this paper, we establish some results on strong convergence for weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in Rp.