The challenges we face in today’s world are increasingly complex, and effectively managing uncertainty when modeling control problems can yield significant benefits. However, the complexity of these models often leads to higher computational costs. Therefore, main contribution this article is use theory shadowed type-2 fuzzy sets address search space exploration harmony algorithm by employing t...

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-knownmetric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied. © 2007 Elsevier B.V. ...

In this paper, following the ideas of (continuous) t-norm and interval numbers, a concept of (continuous) interval-valued t-norm is proposed. Based on the interval-valued fuzzy set and the continuous interval-valued t-norm, we propose a notion of interval-valued fuzzy metric space, which is a generalization of fuzzy metric space in the sense of George and Veeramani [Fuzzy Sets and Systems 64 (1...

This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X,R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approxima...

This paper presents a literature review of applications using type-2 fuzzy systems in the area of image processing. Over the last years, there has been a significant increase in research on higher-order forms of fuzzy logic; in particular, the use of interval type-2 fuzzy sets and general type-2 fuzzy sets. The idea of making use of higher orders, or types, of fuzzy logic is to capture and repr...

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have...

Interval type-2 fuzzy logic system; Interval type-2 fuzzy PID controller; Inverted pendulum system; Hardware-in-the-loop (HIL) simulation Abstract In this study, we propose an embedded real-time interval type-2 fuzzy proportional – integral – derivative (IT2F-PID) controller which is a parallel combination of the interval type-2 fuzzy proportional – integral (IT2F-PI) controller and the interva...

Interval type-2 fuzzy set (IT2FS) offers interesting avenue to handle high order information and uncertainty in decision support system (DSS) when dealing with both extrinsic and intrinsic aspects of uncertainty. Recently, multiple attribute decision making (MADM) problems with interval type-2 fuzzy information have received increasing attentions both from researchers and practitioners. As a re...