Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorf...

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

Considering the space of all non–negative measurable functions F(X,A) linked to a fixed measurable space (X,A), the Lebesgue integral can be seen as an additive, continuous from below functional L on F(X,A), related to a measure m : A → [0,∞] given by m(A) = L(1A). We introduce several other integrals which can be seen as special functionals on F(X,A). For example, the Choquet integral [7] is a...

This is the first paper in a series of two papers describing a novel generalization of classical hidden Markov models using fuzzy measures and fuzzy integrals. In this paper, we present the theoretical framework for the generalization and, in the second paper, we describe an application of the generalized hidden Markov models to handwritten word recognition. The main characteristic of the gener...

It is a familiar fact that inequalities have become very popular method using fractional integrals, and this has been the driving force behind many studies in recent years. Many forms of inequality studied, resulting introduction new trend theory. The aim paper to use fuzzy order relation introduce various types inequalities. On interval space, defined level by level. With help relation, firstl...

This is the first paper in a series of two papers describing a novel generalization of classical hidden Markov models using fuzzy measures and fuzzy integrals. In this paper, we present the theoretical framework for the generalization and, in the second paper, we describe an application of the generalized hidden Markov models to handwritten word recognition. The main characteristic of the gener...

We introduce the notion of scalar fuzzy McShane and Henstock integrals for number valued functions we discuss their relationship give a version Gordon theorem [24].

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

The concept of an interval-valued capacity is motivated by the goal to generalize a capacity, and it can be used for representing an uncertain capacity. In this paper, we define the discrete intervalvalued capacities, a measure of the entropy of a discrete interval-valued capacity, and, Choquet integral with respect to a discrete interval-valued capacity. In particular, we discuss the Choquet i...