a central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. in this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. the main stages of the modeling process are represented as fuzz...

The aim of this paper is to present experimental validation results of an energy management system for hybrid electrical vehicles based on type-2 fuzzy logic. The energy management system (EMS) is designed by extracting knowledge from several experts using surveys. The consideration of interval type-2 fuzzy sets enables modeling the uncertainty in the answers of the experts. The validation of t...

The paper describes a Neuro-fuzzy approach with additional moving average window data filter and fuzzy clustering algorithm that can be used to forecast electrical load using the Takagi-Sugeno (TS) type multi-input single-output (MISO) neurofuzzy network efficiently. The training algorithm is efficient in the sense that it can bring the performance index of the network, such as the sum squared ...

We present a simple framework which enables us to consider the well-known sup-t-norm and inf-residuum products of relations as two particular cases of a single, more general type of product. We present basic properties of the framework and consequences for the theory of fuzzy relations. Informally, the paper implies that in many cases of fuzzy relational modeling, such as in solving fuzzy relat...

This text provides an introduction to the use of fuzzy sets and fuzzy logic for the approximation of functions and modeling of static and dynamic systems. The concept of a fuzzy system is first explained. Afterwards, the motivation and practical relevance of fuzzy modeling are highlighted. Two types of rule-based fuzzy models are described: the linguistic (Mamdani) model and the Takagi–Sugeno m...

In this paper, we will consider the application of notions and techniques from fuzzy logic, fault trees, and Markov modeling to robot fault tolerance. Fuzzy logic lends itself to quantitative reliability calculations in robotics. The crisp failure rates which are usually used are not actually known, while fuzzy logic, due to its ability to work with the actual approximate (fuzzy) failure rates ...

This paper proposes a novel method for on-line modeling and robust adaptive control via Takagi–Sugeno (T-S) fuzzy models for nonaffine nonlinear systems, with external disturbances. The T-S fuzzy model is established to approximate the nonaffine nonlinear dynamic system in a linearized way. The so-called second type adaptive law is adopted, where not only the consequent part (the weighting fact...

Fuzzy sets and logic have been largely used for the treatment of the uncertainty, vagueness and ambiguity found in the modeling of real problems. However, there may exist also the case when there is uncertainty related to the membership functions to be used in the modeling of fuzzy sets and fuzzy numbers, as there are many ways to define the shape of this kind of number. Thus, one can use, for ...