In this paper we define the fuzzy integral of a positive, measurable function, with respect to a fuzzy measure. We show that the monotone convergence theorem and Fatou’s lemma are still true in this new setting. We study some of the properties of this integral, and show that it coincides with another fuzzy integral defmed in the literature. Our main result is a convergence theorem, that is in a...

In this paper the position control of a linear induction motor using adaptive fuzzy backstepping design with integral action is proposed. First, the indirect field oriented control for LIM is derived. Then, an integral backstepping design for indirect field oriented control of LIM is proposed to compensate the uncertainties which occur in the control. Finally, the fuzzy integral-backstepping co...

Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although several similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, no one has considered the use of the Sugeno integral to define them. Since the Sugeno integral provides an expected-value-like operation, it can be a useful tool i...

The present paper discusses an application of fuzzy measure and corresponding fuzzy integral for the evaluation of students failure reasons. From the result it is clearly seen that Choquet Integral has a good choice in Decision making.

This paper provides a discussion on difference representations of the asymmetric Choquet integral with respect to a signed fuzzy measure with bounded chain variation. There are given difference representations of the Choquet integral with respect to a signed fuzzy measure based on its representation as difference of two fuzzy measures.

In this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable. Cordially dedicated to Professor Paolo de Lucia on the occasion of his 80-th birthday with esteem and admiration

We consider the aggregation operators which are ⊕-additive for commonotone functions. The main result is that any operator is expressed by a kind of general fuzzy integral which uses a family of fuzzy measures connected by a ⊕-additive Cauchy’s equations. In particular, the family of fuzzy measures can be obtained by a ⊕-fitting pseudomultiplication. In this case, the aggregation operator is ex...