The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341–356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2–3) (1990) 191–209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough...

By fuzzy random programming, we mean the optimization theory dealing with fuzzy random decision problems. This paper presents a new concept of chance of fuzzy random events and then constructs a general framework of fuzzy random chance-constrained programming (CCP). We also design a spectrum of fuzzy random simulations for computing uncertain functions arising in the area of fuzzy random progra...

In recent years, many researchers have focused on applying the fuzzy set theory to generate fuzzy rules from training instances to deal with the Iris data classification problem. In this paper, we propose a new method to automatically generate weighted fuzzy rules from training instances by using genetic algorithms to handle the Iris data classification problem, where the attributes appearing i...

Fuzzy logic is a powerful method because of its ability to allow the knowledge in the model to be extracted and interpreted by knowledge system. Fuzzy modeling is an approach which implements the fuzzy logic in the process of modeling the system. But in the construction of the complex system, there is a limitation of fuzzy model due to the large number of related input and output, dealing with ...

In this paper, the fuzzy system has been used for fault detection and diagnosis of a yeast fermentation bioreactor based on measurements corrupted by noise. In one case, parameters of membership functions are selected in a conventional manner. In another case, using certainty factors between normal and faulty conditions the optimal values of these parameters have been obtained through the g...

In this paper, the idea of the neuro-fuzzy learning algorithm has been extended, by which the tuning parameters in the fuzzy rules can be learned without changing the fuzzy rule table form used in usual fuzzy applications. A new neuro-fuzzy learning algorithm in the case of the fuzzy singleton-type reasoning method has been proposed. Due to the flexibility of the fuzzy singleton-type reasoning ...

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...

The need for trading off interpretability and accuracy is intrinsic to the use of fuzzy systems. The obtaining of accurate but also human-comprehensible fuzzy systems played a key role in Zadeh and Mamdani’s seminal ideas and system identification methodologies. Nevertheless, before the advent of soft computing, accuracy progressively became the main concern of fuzzy model builders, making the ...

An adaptive fuzzy PID controller with gain scheduling is proposed in this paper. The structure of the proposed gain scheduled fuzzy PID (GS FPID) controller consists of both fuzzy PI-like controller and fuzzy PD-like controller. Both of fuzzy PIlike and PD-like controllers are weighted through adaptive gain scheduling, which are also determined by fuzzy logic inference. A modified genetic algor...

One of the important issues in the design of fuzzy classifier is the formation of fuzzy if-then rules and the membership functions. This paper presents a Genetic Algorithm (GA) approach to obtain the optimal rule set and the membership function. To develop the fuzzy system the membership functions and rule set are encoded into the chromosome and evolved simultaneously using Genetic Algorithm. A...