# Difference between fuzzy set theory and crisp set theory pdf

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- Difference Between Fuzzy Set and Crisp Set
- Possibility Theory,Probability Theory,and Fuzzy Set Theory
- Possibility Theory,Probability Theory,and Fuzzy Set Theory

## Difference Between Fuzzy Set and Crisp Set

The comparison could be made on very different levels, that is, mathematically, semantically, linguistically, and so on. Fuzzy set theory is not or is no longer a uniquely defined mathematical structure, such as Boolean algebra or dual logic. It is rather a very general family of theories consider, for instance, all the possible operations defined in chapter 3 or the different types of membership functions. In this respect, fuzzy set theory could rather be compared with the different existing theories of multivalued logic.

Unable to display preview. Download preview PDF. Skip to main content. This service is more advanced with JavaScript available. Advertisement Hide. Authors Authors and affiliations H. Since L. Zadeh proposed the concept of a fuzzy set in , the relationships between probability theory and fuzzy set theory have been further discussed.

Both theories seem to be similar in the sense that both are concerned with some type of uncertainty and both use the [0, 1] interval for their measures as the range of their respective functions At least as long as one considers normalized fuzzy sets only!

Other uncertainty measures, which were already mentioned in chapter 4, also focus on uncertainty and could therefore be included in such a discussion. The comparison between probability theory and fuzzy set theory is difficult primarily for two reasons: 1. This process is experimental and the keywords may be updated as the learning algorithm improves. This is a preview of subscription content, log in to check access. Zimmermann 1 1. Aachen Germany. Personalised recommendations.

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## Possibility Theory,Probability Theory,and Fuzzy Set Theory

Fuzzy set and crisp set are the part of the distinct set theories, where the fuzzy set implements infinite-valued logic while crisp set employs bi-valued logic. Previously, expert system principles were formulated premised on Boolean logic where crisp sets are used. This gave commencement to the development of the fuzzy set theory to imitate human thinking. For an element in a universe, that comprise fuzzy sets can have a progressive transition among several degrees of membership. While in crisp sets the transition for an element in the universe between membership and non-membership in a given set is sudden and well defined. Defined by precise and certain characteristics. Property Elements are allowed to be partially included in the set.

## Possibility Theory,Probability Theory,and Fuzzy Set Theory

In mathematics , fuzzy sets a. Fuzzy sets were introduced independently by Lotfi A. In classical set theory , the membership of elements in a set is assessed in binary terms according to a bivalent condition — an element either belongs or does not belong to the set. Fuzzy sets generalize classical sets, since the indicator functions aka characteristic functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1. The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics.

*The comparison could be made on very different levels, that is, mathematically, semantically, linguistically, and so on. Fuzzy set theory is not or is no longer a uniquely defined mathematical structure, such as Boolean algebra or dual logic.*