fuzzy control systems have had various applications in a wide range of science and engineering in recent years. since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). conceptually, there are two types of stability for control systems: lyapunov stability (a special case ...

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...

Risk assessment is a popular and important tool in decision making process. Risk assessment is generally performed using models and model is a function of some parameters which are usually affected by uncertainty. Here, we consider that model parameters are affected by epistemic uncertainty. To represent epistemic uncertainty in general triangular fuzzy number or trapezoidal fuzzy numbers are u...

In this paper, a micromilling type-2 fuzzy tool condition monitoring system based on multiple AE acoustic emission signal features is proposed. The type-2 fuzzy logic system is used as not only a powerful tool to model acoustic emission signal, but also a great estimator for the ambiguities and uncertainties associated with the signal itself. Using the results of root-mean-square error estimati...

Due to importance of correlation measure in data analysis, some researchers have shown great interest in the concept of correlation measure for extensions of fuzzy sets, in particular, for a new extension known as hesitant fuzzy set (HFS). Recently, an extension of HFS called the weighted hesitant fuzzy set (WHFS) has been developed by Zhang and Wu [1] to allow the membership of a given element...

Fuzzy measures can flexibly describe the relative importance of decision criterion as well as their interactions in multicriteria decision making. Based on the diamond pairwise comparison, a new identification method of 2-order additive fuzzy measure is proposed. The relative weight and the interaction degree can be obtained simultaneously for every pair of criteria in the diamond pairwise comp...

—It is known that processing of data under general type-1 fuzzy uncertainty can be reduced to the simplest case – of interval uncertainty: namely, Zadeh's extension principle is equivalent to level-by-level interval computations applied to α-cuts of the corresponding fuzzy numbers. However, type-1 fuzzy numbers may not be the most adequate way of describing uncertainty, because they require tha...

Uncertainty is an inherent part of image segmentation in real world applications. The use of new methods for handling incomplete information is of fundamental importance. Type-1 fuzzy sets used in conventional image segmentation cannot fully handle the uncertainties. Type-2 fuzzy sets and cloud model can handle such uncertainties in a better way because they provide us with more design degrees ...

For a mapping, fuzzy sets obtained by Zadeh's extension principle are images of other fuzzy sets on the domain of the mapping under the mapping. Some relationships between images of level sets of one or two fuzzy sets under a mapping and another fuzzy set obtained from the one or two fuzzy sets by Zadeh's extension principle are known. In the present paper, the known results are extended to mor...

A step by step methodology for learning fuzzy rules is presented. This methodology tries to be general enough to give a framework within which diierent learning methods in an environment of uncertainty and imprecision could be developed. The nal product will always be an uncertainty distribution on the diierent rules representing the behaviour of the system. The particular uncertainty distribut...