By using the concepts of fuzzy number fuzzy measures and fuzzy valued functions a theory of fuzzy integrals is investigated. In this paper we have established the fuzzy version of Generalised monotone Convergence theorem and generalised Fatous lemma. 1. Introduction In the preceding paper [2], it is introduced that a concept of fuzzy number fuzzy measures, defined the fuzzy integral of a functi...

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...

Since the 2-DOF rehabilitation robot actuated by pneumatic muscle actuators (PMAs) has highly nonlinear and time-varying behavior due to gas compression and nonlinear elasticity of bladder containers, it is difficult to achieve excellent control performance using classical control methods. Here, this study proposes a novel Takagi-Sugeno(T-S) fuzzy approach to improve tracking performance. The T...

Our paper deals with the necessary properties in Fuzzy Measures. Therefore, it belongs to Fuzzy Mathematical Analysis. The Possibility Theory was created by Zadeh in a paper of 1978. As general purpose, to obtain a way to model flexible restrictions constructed from vague pieces of information. If we study the counterparts of expectations (from Probability Theory) in Possibility Theory, we obta...

We introduce bi-capacities as a natural generalization of capacities (or fuzzy measures) through the identity of Choquet integral of binary alternatives with fuzzy measures. We examine the underlying structure and derive the Möbius transform of bi-capacities. Next, the Choquet and Sugeno integrals w.r.t bicapacities are introduced. It is shown that symmetric and asymmetric integrals are recover...

The Takagi-Sugeno (T-S) fuzzy multiple-variable integral control system with fuzzy state observer is designed for the coordinated control of multi-input-multi-output (MIMO) nonlinear boilerturbine system whose operating points vary within a wide range. Linear models are first derived from the original nonlinear model on several operating points. Next the fuzzy multi-variable integral controller...

In order to measure fuzzy event, credibility measure is proposed as a non-additive set function. In this paper, this concept is extended to fuzzy sets. First, a mean measure is defined by Lebesgue integral and some properties are investigated such as the monotonicity theorem, self-duality theorem and subadditivity theorem. Furthermore, by using Sugeno integral, an equilibrium measure is propose...

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, 35195-363, Iran Full list of author information is available at the end of the article Abstract In this paper, we give an upper bound for the Sugeno fuzzy integral of log-convex functions using the classical Hadamard integral inequality. We pr...

We present some integrals for vector measurable multifunctions with respect to a fuzzy measure obtained by scalarization. Calculus rules, relationships between these integrals and the vector integrals defined until now and some convergence results are presented. Key–words: fuzzy measure, fuzzy integral, measurable multifunction.

Fuzzy measures generalize additive and probabilities. Their advantage with respect to ones is that they permit model interactions between objects. Mesiar introduced in 1999 k-order Pan-additive fuzzy k-maxitive ones. They are related the Möbius transform generalizations. In this paper we introduce some other transforms call ( M a x , + ) ? represent convenient way when use genetic algorithms me...