Fuzzy membership function-dependent switched control for nonlinear systems with memory sampled-data informationMEMBERSHIP functions (Fuzzy logic)DISCRETE-time systemsLINEAR matrix inequalitiesFUZZY systemsCHARACTERISTIC functionsSoft Computing - In this paper, a fuzzy memory-based coupling sampled-data control (...
A fuzzy set is completely characterized by its membership function (MF). Since most fuzzy sets in use have a universe of discourse X consisting of the real line R, it would be impractical to list all the pair defining a membership function. A more convenient and concise way to define an ...
,ϕ(xN)} be a set of mapped samples in the feature space, where ϕ(·) is a mapping function. Kernel fuzzy within, between, and total class scatter matrices can be defined asSWϕ=∑i=1C∑j=1Nuijm(ϕ(xj)−μi)(ϕ(xj)−μi)T,SBϕ=∑i=1C∑j=1Nuijm(μi−μ...
A membership function can have various forms, such as triangle, trapezoid, Gaussian and bell-shaped. Some of the membership function forms are shown in Fig. 7.1. A triangular membership function is the simplest and is a collection of three points forming a triangle as shown below: Sign in ...
It is also possible to configure the shape of membership function to cope with the given problem in the best possible way. It can be performed using “context configuration” parameter. By default, this parameter’s value is 1; higher numbers make the context shorter, and lower numbers cause...
The membership function μA(x) maps each element x to a membership value, which represents the level of membership of x in A. Different membership functions can be associated with different inputs and outputs. In essence, they are weighting factors for the outcomes of fuzzy rules. Gaussian ...
mij is the membership function cluster center of the j-th node corresponding to the i-th variable; σij is the width of the membership functions the j-th node corresponding to the i-th variable; ψi is the algebraic product of the membership degree of the i-th node in the reasoning la...
Fuzzification is used to transform crisp input sets to fuzzy sets. Note that a crisp set is converted to a linguistic variable (LV) for each indicator. The LV is decomposed into linguistic terms (LTs). We use a membership function (MF) to quantify an LT. ...
However, given the fact that most of the real-world data are not normally distributed, the cluster centroid usually is not identical with the centre of the Gaussian membership function, and thus, Gaussian membership functions may not be able to accurately represent the distribution of the ...
they could express errors in the judgments, consequently their decision-making process must be simple and efficient, to maximize their ability to make decisions. In particular, the weight could be assigned by means of the membership function of the fuzzy theory. Considering the following equation: ...