The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

This paper addresses the issue of piecewise integral sliding mode control for T-S fuzzy systems. Integral sliding mode control (ISMC) is chosen to stabilize the T-S fuzzy system because of its superior capability in treating uncertainties. Individual integral sliding surfaces are designed in different operating regions of the T-S fuzzy system. Conditions on existence of the sliding mode in the ...

A fuzzy integral sliding mode control method based on the finite time stable theory and integral sliding mode control theory is proposed to solve a class of complex network problems. The complex networks are expressed by T-S fuzzy models with bounded approximation errors by using the approximation capability of T-S fuzzy models. The paper proposes fuzzy dynamic integral sliding mode control sch...

Introducing more types of integrals will provide more choices todeal with various types of objectives and components in real problems. Firstly,in this paper, a (T) fuzzy integral, in which the integrand, the measure andthe integration result are all multi-valued, is presented with the introductionof T-norm and T-conorm. Then, some classical results of the integral areobtained based on the prope...

The paper deals with a recently proposed approach to combining classifiers by means of fuzzy aggregation. The approach relies on the quasi-Sugeno integral and on the t-conorm integral as a generalization of the Choquet and Sugeno integral, which have been used for combining classifiers so far. New theoretical development is presented, in particular a proposition concerning the λ measures used i...

T he concept of fuzzy integral was initiated by Dubois and Prade [11] and then investigated by Kaleva [21], Goetschel and Voxman [20], Nanda [23] and others. In [33], the Henstock integral of fuzzy-valued functions is defined, while the fuzzy Riemann integral and its numerical integration was investigated byWu in [34]. In [7], the authors introduced some quadrature rules for the integral of fuz...

This paper studies Lebesgue integral of a fuzzy closed set-valued stochastic process with respect to the time t. Firstly, a progressively measurable fuzzy closed set-valued stochastic process is discussed and an almost everywhere problem in the former Aumann type Lebesgue integral of the level-set process is pointed out. Secondly, a new definition of the Lebesgue integral by decomposable closur...

Keywords: Fuzzy measure Sugeno integral Choquet integral Stolarsky's inequality a b s t r a c t Recently Flores-Franulič, Román-Flores and Chalco-Cano proved the Stolarsky type inequality for Sugeno integral with respect to the Lebesgue measure k. The present paper is devoted to generalize this result by relaxing some of its requirements. Moreover, Stolar-sky inequality for Choquet integral is ...

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...