In many contexts, type-2 fuzzy sets (T2 FS) are obtained from a type-1 set to which we wish add uncertainty. However, in the current representation, there is no restriction on shape of footprint uncertainty and embedded (ESs) that can be considered acceptable. This leads, usually, loss semantic relationship between T2 FS concept it models. As consequence, interpretability some ESs explainabilit...

a novel technique is investigated for pid controller adaptation in order to control thetemperature of a liquid-phase reactor tank by using a heat exchanger system. as for nonlinearity,time delay problems and model uncertainties introduced by the heat exchanger, an interval type-2fuzzy system (it2fs) is implemented to enhance and improve the total control performance.moreover, the fuzzy inferenc...

Defuzzification of type-2 fuzzy sets is a computationally intense problem. This paper proposes a new approach for defuzzification of interval type-2 fuzzy sets. The collapsing method converts an interval type-2 fuzzy set into a representative embedded set (RES) which, being a type-1 set, can then be defuzzified straightforwardly. The novel Representative Embedded Set Theorem (REST), with which ...

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

Fuzzy Logic Systems are widely recognized to be successful at modelling uncertainty in a large variety of applications. While recently interval type-2 fuzzy logic has been credited for the ability to better deal with large amounts of uncertainty, general type2 fuzzy logic has been a steadily growing research area. All fuzzy logic systems require the accurate specification of the membership func...

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

Based on the analysis of the rough set model on a tolerance relation and the fuzzy rough set, two types of fuzzy rough sets models on tolerance relations are constructed and researched. Then we propose the optimistic and pessimistic multi-granulation fuzzy rough sets models in a fuzzy tolerance approximation space with the point view of granular computing. In these models, the fuzzy lower and u...