We propose an extension of the Sugeno integral for negative numbers, in the spirit of the symmetric extension of Choquet integral, also called Šipoš integral. Our framework is purely ordinal, since the Sugeno integral has its interest when the underlying structure is ordinal. We begin by defining negative numbers on a linearly ordered set, and we endow this new structure with a suitable algebra...

This paper clari es the connection between multiple criteria decisionmaking and decision under uncertainty in a qualitative setting relying on a nite value scale. While their mathematical formulations are very similar, the underlying assumptions di er and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent ...

We propose the concepts of superadditive and of subadditive transformations of aggregation functions acting on non-negative reals, in particular of integrals with respect to monotone measures. We discuss special properties of the proposed transforms and links between some distinguished integrals. Superadditive transformation of the Choquet integral, as well as of the Shilkret integral, is shown...

An overview of the use of the discrete Sugeno integral as either an aggregation tool or a utility function is presented in the qualitative framework of two decision paradigms: multi-criteria decision-making and decision-making under uncertainty. The parallelism between the representation theorems in both settings is stressed, even if a basic requirement like idempotency should be explicitely st...

This paper discusses multi-objective controller synthesis for the fuzzy T-S (Takagi-Sugeno) model. Various performance specifications are included. Both the state-feedback controller and the dynamic feedback controller are presented. They are in the format of a PDC (parallel distributed compensation) controller which is essentially a nonlinear controller. The controller synthesis is formulated ...

In this paper, the path tracking (PT) control for automatic steering of vehicles is studied. The Takagi–Sugeno (T–S) fuzzy model of vehicle obtained from a nonlinear model is considered and a fuzzy controller is designed. The stability analysis is discussed using Lyapunov’s approach combined with the linear matrix inequalities (LMI) approach. Finally, simulation results are given to demonstrate...

This study applies technique parallel distributed compensation (PDC) for position control of a Magnetic levitation system. PDC method is based on nonlinear Takagi-Sugeno (T-S) fuzzy model. It is shown that this technique can be successfully used to stabilize any chosen operating point of the system. All derived results are validated by experimental and computer simulation of a nonlinear mathema...

This paper deals with the tracking control for nonlinear systems described by uncertainty Takagi-Sugeno (T-S) fuzzy models. An H∞ robust observer based control is proposed for guaranteeing tracking performances of closed loop nonlinear systems. The design conditions obtained using Lyapunov approach are given in terms of solvability as a set of Linear Matrix Inequities (LMIs). To illustrate the ...

In this paper, optimal control for stochastic linear singular Takagi-Sugeno (T-S) fuzzy system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using ACP approach. The solution of this novel method is compared with the ...

Sugeno integral was invented a few decades ago as a natural fuzzy-number analogue of the classical integral. Sugeno integral has many interesting applications. It is reasonable to expect that it can be used in all application areas where classical integrals are used, and in many such areas it is indeed useful. Surprisingly, however, it has never been used in fuzzy control, although in tradition...