This paper extends the author’s earlier work on the Law of Large Numbers for fuzzy numbers [2] to the case where the fuzzy numbers are of type L-R. Namely, we shall define a class of Archimedean triangular norms in which the equality lim n→∞ Nes(mn − ≤ ηn ≤ mn + = 1, for any > 0, holds for all sequences of fuzzy numbers, ξi = (Mi, α, β)LR, i ∈ N, with twice differentiable and concave shape func...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

In this paper, we de ne generalized concepts of cardinality of a fuzzy-valued function and obtained some properties of these new concepts. Also, we investigate examples for the calculation of two generalized cardinality of fuzzy-valued functions and compared with concepts of cardinality of a fuzzy set and a fuzzy-valued function. c © 2001 Elsevier Science B.V. All rights reserved.

In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using established identity, offer some Simpson?s type inequalities co-ordinated convex functions in a rectangle from plane R2.

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 authors discover a general k-fractional integral identity with multi-parameters for twice differentiable functions. By using this integral equation, the authors derive some new bounds on Hermite–Hadamard’s and Simpson’s inequalities for generalized (m,h)-preinvex functions through k-fractional integrals. By taking the special parameter values for various suitable choices of function h, some...

in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...