Based on a set of criteria and a measuring lattice, we introduce relational measures as generalizations of fuzzy measures. The latter have recently made their way from the interval [0, 1] ⊆ IR to the ordinal or even to the qualitative level. We proceed further and introduce relational measures and relational integration. First ideas of this kind, but for the real-valued linear orderings stem fr...

To describe expert uncertainty, it is often useful to go beyond additive probability measures and use non-additive (fuzzy) measures. One of the most widely and successfully used class of such measures is the class of Sugeno λ-measures. Their success is somewhat paradoxical, since from the purely mathematical viewpoint, these measures are – in some reasonable sense – equivalent to probability me...

This paper looks at a new method of modelling non-l inear dynamic processes, using grid-type Sugeno fuzzy models and a priori knowledge. The proposed hybrid fuzzy convolution dynamic model consists of a non-linear fuzzy steady-state static, and a gain-independent impulse response model-based dynamic part. The modelling of non-linear pH processes is chosen as a realistic case study for the demon...

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision ...

In the last few decades the Choquet integral and the Sugeno integral have had several applications in many fields of mathematics, soft computing, pattern recognition and decision analysis [4, 5, 7, 17, 21]. It shows up in the recently published papers that some new types of integrals on symmetric scales are useful tools for applications in decision making problems [6, 8, 12, 21]. The Sugeno int...

Many applications e.g. in approximate reasoning, data summarisation, information retrieval etc. can profit from the use of fuzzy quantifiers like “almost all” or “many”, which provide flexible means of information aggregation, and are capable of extracting meaningful linguistic summaries from large amounts of raw data. However, as will be shown by a number of counterexamples, existing approache...

In this paper, we introduce a robust state feedback controller design using Linear Matrix Inequalities (LMIs) and guaranteed cost approach for Takagi-Sugeno fuzzy systems. The purpose on this work is to establish a systematic method to design controllers for a class of uncertain linear and non linear systems. Our approach utilizes a certain type of fuzzy systems that are based on Takagi-Sugeno ...

This paper considers gradual set-oriented functions and their application to fuzzy sets. An example, taken in the context of flexible querying of databases, is provided by the condition “the average salary of \RXQJ employees is DURXQG ”. The evaluation of this condition leads to apply the gradual set-oriented property “the average salary is DURXQG ” to the fuzzy set made of \RXQJ employees. The...

This paper proposes a Takagi-Sugeno neuro-fuzzy inference system for direct torque and stator reactive power control applied to a doubly fed induction motor. The control variables (d-axis and q-axis rotor voltages) are determined through a control system composed by a neuro-fuzzy inference system and a first order Takagi-Sugeno fuzzy logic controller. Experimental results are presented to valid...