The commonly accepted theory of fuzzy numbers (Czogała and Pedrycz, 1985) is that set up by Dubois and Prade (1978), who proposed a restricted class of membership functions, called (L,R)–numbers with shape functions L and R. However, approximations of fuzzy functions and operations are needed if one wants to follow Zadeh’s (Zadeh 1975; 1983) extension principle. It leads to some drawbacks that ...

Fuzzy logic has been successfully applied in various fields, but these applications have usually suffered from the problem of low speed. Typically, calculation of the matching degree requires very high latency, which limits the overall inference speed. In this paper, we prove that the matching degree between two trapezoid-shaped membership functions can be obtained without traversing all the el...

The product safety of food-waste feed is the key factor limiting the development of its industrial chain. In this paper, we construct a method based on data from the testing of food-waste feed with comprehensive evaluation of its product safety by integrating fuzzy mathematics effectively, i.e., the entropy method (EM), and the model of the analytic hierarchy (AHP) process. Furthermore, a hiera...

In almost every work on fuzzy sets, the existence of membership functions taking part in the considered model is assumed and it is not studied in depth whether or not such functions exist. On the other hand, generally the relationship between a certain studied characteristic and its referential set is not problematic since it is usually a matter of direct measurement. However, in a great variet...

In this paper a fuzzy decision-making method is proposed to make local decisions in case of breakdown occuring in a context of product-driven systems. To cope with breakdown uncertainty, three parameters, α, β and γ are created to evaluate the impact of it. Further, a fuzzy rule based on a membership function is designed to decide between centralized and distributed decisions concerning the re-...

It is well-known that the choice of membership functions is a key problem in the design of a fuzzy controller. The aim of this paper is thus to give a further contribution in this direction. In particular, the performance of the Mamdani-type fuzzy controller with piece wise linear membership functions is discussed in details, taking into account features such as overlapping, completeness level,...

Abstract This article presents a development of a fuzzy based nominal characteristic trajectory following (NCTF) controller for continuous motion control. A new structure is proposed in order to achieve excellent performance of tracking to a continuous reference input and also for point-to-point positioning task. The proposed structure maintains the NCTF controller simple configuration which is...

In this paper, we study a pair of fuzzy primal–dual linear programming problems and calculate duality results using an aspiration level approach. We use an exponential membership function, which is in contrast to the earlier works that relied on a linear membership function. As the fuzzy environment causes a duality gap, we investigate how choosing the exponential membership function impacts th...

This paper proposes to analyze two flow line systems in which we include possibilistic data -the priority-discipline is possibilistic instead of probabilisticand measure the performances of the systems with the effectiveness measure “waiting time in queue”. In a previous work we have analyzed and developed a queuing model with uncertain priority-discipline, using Zadeh’s extension principle. Be...

By adding the complement operator (¬), extended regular expressions (ERE ) can encode regular languages non-elementarily more succinctly than regular expressions. The ERE membership problem asks whether a word w of size n belongs to the language of an ERE R of size m. Unfortunately, the best known membership algorithms are either non-elementary in m or otherwise require space Ω(n) and time Ω(n)...