We introduce and study implicator and coimplicator integrals, and investigate their possible application in defining the possibility and necessity of fuzzy sets. First, the definition and properties of implicators and coimplicators on bounded posets are discussed. Then, in analogy with the theory of seminormed and semiconormed fuzzy integrals, implicator and coimplicator integrals are defined. ...

In this research a generalization of Takagi-Sugeno fuzzy controllers is presented. In this generalization all or some of the inputs of the fuzzy controllers are fuzzy numbers. Also, it is proved that this generalization is well defined, which means that if the inputs of a generalized Takagi-Sugeno fuzzy controller are singleton fuzzy sets, then the generalized Takagi-Sugeno fuzzy controller wil...

This paper deals with qualitative evaluation processes when the worth of items is computed by means of Sugeno integral. One limitation of this approach is the coarse ranking of items it produces. In order to refine this ranking, generalizations of leximin and leximax to Sugeno integrals are studied. Numerical encodings of such generalized lexicographic methods are described by means of mappings...

Sugeno integral was invented a few decades ago as a natural fuzzy 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 in deed useful Surprisingly however it has never been used in fuzzy control although in traditional control cl...

When controlling Takagi-Sugeno fuzzy systems, verification of some sector conditions is usually assumed. However, setpoint changes may alter the sector bounds. Alternatively, setpoint changes may be considered as an offset addition in many cases, and hence affine Takagi-Sugeno models may be better suited to this problem. This work discusses a nonconstant change of variable in order to carry out...

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...

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...