The purpose of this paper is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of sequences of fuzzy numbers. We give some relations related to these concepts. We establish some connections between strongly almost lacunary convergence and almost lacunary statistical convergence of sequences of fuzzy numbers. It is also shown that if a ...

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...

The objective of this work is to describe a numerical technique to identify parameters of a fuzzy model. When this model and the membership functions of the input variables are continuously differentiable, we show that the estimation of parameters can be performed with a two-levels hierarchical algorithm, comprising the estimation of the model parameters and the estimation of the membership fun...

The paper proposes and develops new globally convergent algorithms of the generalized damped Newton type for solving important classes nonsmooth optimization problems. These are based on theory calculations second-order subdifferentials functions with employing machinery variational analysis differentiation. First we develop a superlinearly Newton-type algorithm class continuously differentiabl...

Convergent product is an assembly shape concept integrating functions and sub-functions to form a final product. To conceptualize the convergent product problem, a web-based network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is considered to be a link between two nodes. The aim is to find an optimal tree of functionali...

and Applied Analysis 3 Definition 1.3 see 25 . Let X, μ, ν, ∗, be a intuitionistic fuzzy metric space. Let A be any subset of X. Define φ t inf { μ ( x, y, t ) : x, y ∈ A}, ψ t sup{ν(x, y, t) : x, y ∈ A}, 1.2 i A is said to be q-bounded if limt→∞φ t 1 and limt→∞ψ t 0, ii A is said to be semibounded if limt→∞φ t k and limt→∞ψ t 1 − k, 0 < k < 1 iii A is said to be unbounded if limt→∞φ t 0 and li...

A modification of Watson's lemma for Laplace transforms ∫0∞f(t)e−ztdt was introduced in [Nielsen, 1906], deriving a new asymptotic expansion large |z| with the extra property being convergent as well. Inspired that idea, this paper we derive expansions two-dimensional F(x,y):=∫0∞∫0∞f(t,s)e−xt−ysdtds |x| and |y| are also convergent. The F(x,y) accompanied by error bounds. Asymptotic some special...

Let E be a closed set in C, normally with empty interior, and let us consider continuously-differentiable functions on E in the sense of Whitney, in which the differential of the function is automatically included. This means a continuous complex-valued function f(z) on E together with a real-linear mapping dfz : C n → C defined and continuous for z ∈ E, with properties like those of an ordinar...

In this paper, we introduce the concept of λ-statistically Cauchy sequence of fuzzy numbers and show that it is equivalent to λ-statistically convergent sequence of fuzzy numbers. AMS Subject Classification: 40A05, 40C05, 40D05