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# What is Defuzzification

The fuzzy logic’s approach for a problem’s solution involves the fuzzification of the problem’s data by representing them with properly defined fuzzy sets, the evaluation of the fuzzy data in order to express the problem’s solution in the form of a unique fuzzy set and the defuzzification of this fuzzy set in order to translate the problem’s mathematical solution to the natural language for use with the original real-life problem. The most popular defuzzification method is the Centre of Gravity (COG) Technique in which the corresponding system’s fuzzy outputs are represented by the coordinates of the COG of the level’s section contained between the graph of the membership function expressing those outputs and the OX axis.
Published in Chapter:
Use of Grey Numbers for Evaluating a System's Performance Under Fuzzy Conditions
Michael Voskoglou (Graduate Technological Educational Institute of Western Greece, Greece)
DOI: 10.4018/978-1-7998-3479-3.ch023
Abstract
In the present research, a method using Grey Numbers as tools is developed for assessing a system's mean performance, which is useful when utilizing qualitative grades and not numerical scores for this purpose. Although this new method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers as tools developed in an earlier work, it reduces the required computational burden, since it requires the calculation of two components only (instead of three in the case of the Triangular Fuzzy Numbers) for obtaining the mean value of the Grey Numbers involved. Examples are also presented on student and athlete assessment illustrating the new method and showing that the system's quality performance, calculated by the traditional GPA index, may lead to different assessment conclusions.
More Results
Translating the membership degree of fuzzy sets into a particular choice or real value.
A process that converts fuzzy terms to conventional expressions quantified by real-valued functions.
Defuzzification is the last step in fuzzy inference mechanism. The process of converting fuzzy values from the combined output of fuzzy rules in crisp values (numerical values). The input to the defuzzification process is an aggregate set and the output from this process is a single number.
Is the process of producing a quantifiable result in fuzzy logic, given fuzzy sets and corresponding membership degrees.
The process of representing a system’s fuzzy data by a crisp number.
Assignment of fuzzy values to a numerical output value.
Process of producing a quantifiable result (crisp) in fuzzy logic. Typically, a fuzzy system will have a number of rules that transform a number of variables into a “fuzzy” result, that is, the result is described in terms of membership in fuzzy sets.
The process of representing a system’s fuzzy outputs by a crisp number.