In this paper, set-membership identification is used to derive a simple algorithm which is a sign version of the normalized least mean square algorithm. Convergence analysis is carried out.With some simulation examples. the performance of the algorithm, in the cases of slow and fast variations of a parameter is compared with the modified Dasgupta-Huang optimal bounding ellipsoid algorithm. These examples show the performance of the proposed-algorithm.

In this paper we show how the classical and modern adaptive filter algorithms can be introduced in a unified way. The Max normalized least mean squares (MAX-NLMS), N-Max NLMS, the family of SPU-NLMS, SPU transform domain adaptive filter (SPU-TDAF), and SPU subband adaptive filter (SPU-SAF) are particular algorithms are established in a unified way. Following this, the concept of set-membership (SM) adaptive filtering is extended to this framework, and a unified approach to derivation of SM and SM-SPU adaptive filters is presented. The SM-NLMS, SM-TDAF, SM-SAF, SM-SPU-NLMS, and SM-SPUSAF are presented based on this approach. Also, this concept is extended to the SPU affine projection (SPU-AP) and SPUTDAF algorithms and two new algorithms which are called SM-SPU-AP and SM-SPU-TDAF algorithms, are established. These novel algorithms are computationally efficient. The good performance of the presented algorithms is demonstrated in system identification application.

The aim of this paper is robust identification of smart foam, as an electroacoustic transducer, considering un modelled dynamics due to nonlinearities in behaviour at low frequencies and measurement noise at high frequencies as existent uncertainties. set membership estimation combined with model error modelling technique is used where the approach is based on worst case scenario with unknown but bounded uncertainties. The outcome is a robust identified model which consists of a nominal model with its uncertainty bounds that fits exactly the H∞ robust control scheme which has been utilized in active noise control in recent years. While the nominal model has the desired physical characteristics as cut-off frequency and the anticipated slope and flatness before and after this frequency, respectively, it is maintained in the acceptably tight uncertainty upper and lower limits, thus validating the identification procedure. Looseness and tightness of uncertainty strip has also been discussed regarding nonlinearities and measurement noise in low and high frequency regions. Meanwhile the identified nominal model can also be utilized in non-robust noise control methods due to its lower order, reflecting the advantage of the applied identification approach.

One advantage of process incapability index over the classical process capability index is that it provides uncontaminated separation between process accuracy and process precision. However, the value of the index is difficult to determine accurately when process parameters cannot be determined precisely. In such a case, fuzzy set theory can be applied to obtain more flexible and sensitive information. In this paper, a fuzzy process incapability index is proposed when the specification limits are assumed to be type-2 fuzzy. When the process mean and variance are unknown and when the observations are measured imprecisely, three fuzzy estimators are considered. A simulation study is conducted based on the Thin-Film-Transistor Liquid-Crystal Display (TFT-LCD) fuzzy process. By applying the total integral value method to the membership function of a fuzzy index, it becomes easier to make a comparison of the quality of different processes.

In this paper we present some properties of set-norm exhaustive set multi functions and also of atoms and pseudo-atoms of set multi functions taking values in the family of non-empty subsets of a commutative semi group with unity.

In this paper we define the Soft set Product as a product of many soft sets and afterwards we extend it to the HyperSoft set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft set. We also present several applications of the Soft set Product to Fuzzy (and fuzzy-extensions)  Soft set Product and to IndetermSoft set and IndetermHyperSoft set.