Computability theorists have introduced multiple hierarchies to measure the complexity of sets natural numbers. The Kleene Hierarchy classifies according first-order their defining formulas. Ershov $\Delta^0_2$ with respect number mistakes that are needed approximate them. Biacino and Gerla extended realm fuzzy sets, whose membership functions range in a complete lattice $L$ (e.g., real interva...

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...

This work substantiates novel perspectives and tools for analysis and design of Fuzzy Inference Systems (FIS). It is shown rigorously that the cardinality of the set F of fuzzy numbers equals א1, hence a FIS can implement “in principle” א2 functions, where א2 = 2א1>א1 and א1 is the cardinality of the set R of real numbers; furthermore a FIS is endowed with a capacity for local generalization. A...

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.

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

We consider the internal rate of return (IRR) decision rule in capital budgeting problems with fuzzy cash flows. The possibility distribution of the IRR at any r ≥ 0, is defined to be the degree of possibility that the (fuzzy) net present value of the project with discount factor r equals to zero. Generalizing our earlier results on fuzzy capital budegeting problems [5] we show that the possibi...