## ABSTRACT

Uncertainty exists in almost all practical applications, and facing high levels of uncertainty can impact performance of systems. Therefore, it is important that these application systems have the ability to handle these uncertainties. There are many sources of uncertainty that FLS faces, such as the presence of noise in the training data, noise affecting the inputs and outputs, and linguistic uncertainties related to linguistic terms in rule-based predecessors. The non-singleton fuzzy logic system (NSFLS) was introduced to model the uncertainty of the input signal as an extension of the singleton fuzzy logic system (SFLS), which is not appropriate when the input data is corrupted due to measurement noise. Fuzzification is the first step in the fuzzy reasoning process. This includes domain transformations where sharp inputs are converted to fuzzy inputs. Fuzzification is the process of converting sharp inputs into fuzzy values. Fuzzy logic control’s (FLC) data manipulation is based on fuzzy set (FS) theory, and fuzzification is necessary and desirable at an early stage. Thus, fuzzy fire can be defined as a mapping from the observed input space to the FS label of a given input discourse universe. Defuzzification is the process of performing output renormalization that converts a set of controller output values to a single point-by-point value and maps the point-by-point values of the controller output to the physical domain. Fuzzy logic system (FLS) is a nonlinear system capable of inferring complex nonlinear relationships between input and output variables. In addition, the system created by the learning algorithm must be able to generalize to a specific area in a multidimensional space for which no training data are provided. In other words, it should be able to interpolate the given input/output data. It is common in many approximations/interpolations within the framework of approximation and interpolation theory. Adaptive filtering has been widely applied and successful in many areas such as image processing, control, and communication.