The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper appro...

Many approaches have been proposed for mining fuzzy association rules. The membership functions, which critically influence the final mining results, are difficult to define. In general, multiple criteria are considered when defining membership functions. In this paper, a multi-objective genetic-fuzzy mining algorithm is proposed for extracting membership functions and association rules from qu...

Abstract: A simple Bayesian approach to nonparametric regression is described using fuzzy sets and membership functions. Membership functions are interpreted as likelihood functions for the unknown regression function, so that with the help of a reference prior they can be transformed to prior density functions. The unknown regression function is decomposed into wavelets and a hierarchical Baye...

we study the problem of reconstructing binary images from four projections data in a fuzzy environment. given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. we provide an iterative algorithm based on fuzzy integer programming and linear membership functions.

the linear multiobjective transportation problem is a special type of vector minimum problem in which constraints are all equality type and the objectives are conicting in nature. this paper presents an application of fuzzy goal programming to the linear multiobjective transportation problem. in this paper, we use a special type of nonlinear (hyperbolic and exponential) membership functions to ...

In neuro-fuzzy approaches different membership functions are used for modeling the system's rule set. Two wellknown membership function types are triangle functions and trapezoid functions. In our contribution we demonstrate that trapezoid functions with larger core regions are the more appropriate functions for calculating the membership degrees within neuro-fuzzy systems. If regions of the da...

In this paper, we propose a novel fuzzy expert system for detection of Coronary Artery Disease, using cuckoo search algorithm. This system includes three phases: firstly, at the stage of fuzzy system design, a decision tree is used to extract if-then rules which provide the crisp rules required for Coronary Artery Disease detection. Secondly, the fuzzy system is formed by setting the intervals ...