Most of the researches in the domain of fuzzy number comparisons serve the fuzzy number ordering purpose. For making a comparison between two fuzzy numbers, beyond the determination of their order, it is needed to derive the magnitude of their order. In line with this idea, the concept of inequality is no longer crisp however it becomes fuzzy in the sense of representing partial belonging or de...

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...

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...

in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...

Generalized predictive control with flexible constraints is investigated. To apply fuzzy technique, the flexible parts in the inequality constraints are fuzzified as fuzzy constraints. The optimization problem of the generalized predictive control with flexible inequality constraints is converted into two sub-problems to get the lower and upper bound of the objective values, and then the object...

In this note, we consider a similar type of Gauss inequality for fuzzy integrals. More precisely, we show that the inequality x(S) ∫ ∞

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.

It is well know that when these concepts arose in PhD disertation of Sugeno in 1974 [1], a lot of works has been done as much in the theoretical branch as in the applied. As we know, the classical measure and the corresponding integral are based on the additivity property, but this property is uncommun in the applied context and could be too restrictive for the appliance. For instance, measurem...