**Theory of Fuzzy Logic**

**Chapter 1**

**Provisional chapter**

**Introductory Chapter: Which Membership Function is**

**Introductory Chapter: Which Membership Function is** 

Fuzzy logic systems are widely used for control, system identification, pattern recognition problems, and many more applications from industry to academia. The membership functions (MFs) play vital role in the overall performance of fuzzy representation. The MFs are the building blocks of fuzzy set theory, that is, fuzziness in a fuzzy set is determined by its MF. Accordingly, the shapes of MFs are important for a particular problem since they effect on a fuzzy inference system. They may have different shapes such as triangular, trapezoidal, Gaussian, and so forth. The only condition a MF must really satisfy is that it must vary

The MFs can be of any shape and form as long as it maps the given data with desirable degree of memberships. As far as choice of MFs is concerned, it is us to decide. This is where fuzzy system offers individual degrees of freedom. With experience, one will come to know which

As there are infinite number of ways to characterize fuzziness, there are infinite number of ways to graphically depict the MFs that describe this fuzziness. The choice of which of the methods to use depends entirely on the problem size and problem type. Instead of choosing the shape of MF, setting the interval and number of MFs are also very important. For instance, to model a temperature control system by fuzzy logic, it is really important to know how

**2. How to choose an appropriate membership function?**

shape of MF is good for the application under consideration.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

DOI: 10.5772/intechopen.79552

**Appropriate in Fuzzy System?**

**Appropriate in Fuzzy System?**

Additional information is available at the end of the chapter

Ali SadollahAdditional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79552

**1. Role of membership functions**

Ali Sadollah

between 0 and 1.

#### **Introductory Chapter: Which Membership Function is Appropriate in Fuzzy System? Introductory Chapter: Which Membership Function is Appropriate in Fuzzy System?**

DOI: 10.5772/intechopen.79552

Ali Sadollah

Additional information is available at the end of the chapter Ali SadollahAdditional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.79552
