In this paper, we define and investigate the generalized Pisano sequences deal with, in detail, two special cases, namely, Pisano–Lucas sequences. We present Binet’s formulas, generating functions Simson’s formulas for these Moreover, give some identities matrices associated with Furthermore, show that there are close relations between numbers modified Oresme, Oresme–Lucas Oresme numbers.

In this paper, we introduce the generalized Oresme sequence and deal with, in detail, three special cases which call them modified Oresme, Oresme-Lucas sequences. We present Binet's formulas, generating functions, Simson summation formulas for these Moreover, give some identities matrices related with

In the mathematical analysis, there are some theorems and definitions that established for both real and fuzzy numbers. In this study, we try to prove  Bernoulli's inequality in fuzzy real numbers with some of its applications. Also, we prove two other theorems in fuzzy real numbers which are proved before, for real numbers.

in applications there occur different forms of uncertainty. the twomost important types are randomness (stochastic variability) and imprecision(fuzziness). in modelling, the dominating concept to describe uncertainty isusing stochastic models which are based on probability. however, fuzzinessis not stochastic in nature and therefore it is not considered in probabilisticmodels.since many years t...

in this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. we investigate some properties of this metric, and finally presentan application. we think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.

we are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. convergence and stability of the method are also proved in detail. moreover, a specific method of order 4 is found. the numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

In highly competitive industrial market, the concept of failure analysis is an unavoidable fact in complex industrial systems. Reliability of such systems not only depends on the reliability of each element of these systems, but also depends on occurrence of sequence of failures. In this paper, a novel approach to sequential failure analysis is proposed which is based upon fuzzy logic and the c...