The present article proposes a fuzzy set-based classifier with a better learning and generalization capability. The proposed classifier exploits the feature-wise degree of belonging of a pattern to all classes, generalization in the fuzzification process and the combined class-wise contribution of features effectively. The classifier uses a -type membership function and product aggregation reas...

In this paper, we propose a new machine learning approach based on AFS (Axiomatic Fuzzy Sets) fuzzy logic, in attempt to provide a better model with interpretability. First, we will concisely present the AFS theory. Second, we will propose new membership functions for fuzzy sets and their logic operations. Third, we will design a new machine learning algorithm based on the new membership functi...

In this work, we extend the genetic lateral tuning of membership functions [1] based on the linguistic 2-tuples representation [2], in order to also perform a tuning of the support amplitude of the membership functions. To do so, we present a new symbolic representation which extends the linguistic 2-tuples representation model with a parameter β to represent the amplitude variation of the supp...

The present study considers a fuzzy color system in which three membership functions are constructed on the RGB color triangle. This system can process a fuzzy input (as the membership values of subjects) to an RGB system and output the center of gravity of three weights associated with respective grades. Three membership functions are applied to the RGB color triangle relationship. By treating...

This paper introduces an advanced codebook model for foreground-background segmentation. The improvement is two-fold. First, to cope with changing global lumination, we develop the conventional codebook with confidence functions. Similarities of both brightness and normalized color-vector are integrated confidence-weightedly to form overall similarity. A designed codeword-update progress also c...

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...