In works dealing with capacities (fuzzy measures) and the Choquet integral on finite spaces, it is usually considered that all subsets of the universe are measureable. Hence, all functions are integrable in the sense of Choquet. We consider the situation where some subsets are not measurable (not feasible), so that there are nonintegrable functions. Since this is a severe limitation in applicat...

Recently, the study of fuzzy integral inequalities has gained much attention. The most popular method is using the Sugeno integral 1 . The study of inequalities for Sugeno integral was initiated by Román-Flores et al. 2, 3 and then followed by the others 4–11 . Now, we introduce some basic notation and properties. For details, we refer the reader to 1, 12 . Suppose that Σ is a σ-algebra of subs...

Abstract: Recently, the two most general and well-known fuzzy integrals (Sugeno's integral and Choquet's integral) were characterized. It was also shown how both integrals fitted the same formal model, and they only differed in the operators used. In this paper we try to analyze whether it is possible to improve those characterization theorems, and we also study the possibility of defining othe...

This paper proposes a generation method of facial expressions using fuzzy measure and fuzzy integral for robotic heads. Human’s emotion state can be represented by a fuzzy measure which can effectively deal with ambiguity. Because facial expressions are usually ambiguous such that it is difficult to discern emotions and assign a sharp boundary to each emotion. In this method, users can adjust t...

Based on the concept of an interval-valued function which is motivated by the goal to represent an uncertain function, we define the Choquet integral with respect to a fuzzy measure of intervalvalued functions. We also discuss convergence in the C mean and convergence in a fuzzy measure of sequences of measurable interval-valued functions. In particular, we investigate the convergence theorem f...

In this paper we studied two different classifiers fusion algorithms exploiting the combination weights expressed over the entire data space and the combination with data dependent weights. The following aggregation schemes are employed in the study: the majority vote, the averaging, the combination via Choquet integral with the − λ fuzzy measure, the combination via space partitioning and clas...

Decision fusion is one of hot research topics in classification area, which aims to achieve the best possible performance for the task at hand. In this paper, we investigate the usefulness of this concept to improve change detection accuracy in remote sensing. Thereby, outputs of two fuzzy change detectors based respectively on simultaneous and comparative analysis of multitemporal data are fus...

In the cumulative prospect theory (CPT) the preference (utility functional) is represented by the difference of two Choquet integrals. We investigate representations of the corresponding functional by two fuzzy integrals, specially the difference representations of the asymmetric Choquet integral with respect to a signed fuzzy measure with bounded chain variation. We discuss non-monotone, real ...

The purpose of this work is to design a fuzzy integral controller to force the switching of a bioprocess between two different metabolic states. A continuous baking yeast culture is divided in two sub-models: a respiro-fermentative with ethanol production and a respirative with ethanol consumption. The switching between both different metabolic states is achieved by means of tracking a referenc...

In the present paper using homotopy analysis method (HAM), we approximate a special case of fuzzy integral equations. The fuzzy integral and integro-differential equations have a wide range of applications in science and engineering. In this paper HAM can be to find the exact solution or an approximate solution of the problem. Within this paper the HAM is used to obtain A series solution of int...