# Fuzzy And Probability Uncertainty Logics Pdf

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- Fuzzy and Probability Uncertainty Logics
- Possibility Theory,Probability Theory,and Fuzzy Set Theory
- Fuzzy logic

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## Fuzzy and Probability Uncertainty Logics

Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Gaines Published Mathematics. Probability theory and fuzzy logic have been presented as quite distinct theoretical foundations for reasoning and decision making in situations of uncertainty. This paper establishes a common basis for both forms of logic of uncertainty in which a basic uncertainty logic is defined in terms of a valuation on a lattice of propositions.

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

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.

The aim of a probabilistic logic also probability logic and probabilistic reasoning is to combine the capacity of probability theory to handle uncertainty with the capacity of deductive logic to exploit structure of formal argument. The result is a richer and more expressive formalism with a broad range of possible application areas. Probabilistic logics attempt to find a natural extension of traditional logic truth tables: the results they define are derived through probabilistic expressions instead. A difficulty with probabilistic logics is that they tend to multiply the computational complexities of their probabilistic and logical components. Other difficulties include the possibility of counter-intuitive results, such as those of Dempster-Shafer theory in evidence-based subjective logic. The need to deal with a broad variety of contexts and issues has led to many different proposals. There are numerous proposals for probabilistic logics.

## Fuzzy logic

In fuzzy mathematics , fuzzy logic is a form of many-valued logic in which the true values of variables may be any real number between 0 and 1 both inclusive. It is employed to handle the concept of partial truth, where the true value may range between completely true and completely false. The term fuzzy logic was introduced with the proposal of fuzzy set theory by Lotfi Zadeh. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or sets are mathematical means of representing vagueness and imprecise information hence the term fuzzy.

In the proposed framework, belief-dependent concepts such as the strategy with the best expected value are formally derivable in higher-order fuzzy logic for any finite matrix game with rational payoffs. In this paper, we propose a semantics for multi-agent reasoning about uncertain beliefs. Using a suitable fuzzy logic for its representation makes it possible to formalize doxastic reasoning under uncertainty in a rather parsimonious way, which is of particular importance, e. As a prominent measure of uncertainty, we apply a fuzzy probability measure to fuzzy doxastic propositions.

Fuzzy evidence theory, or fuzzy Dempster-Shafer Theory captures all three types of uncertainty, i. Therefore, it is known as one of the most promising approaches for practical applications. Quantifying the difference between two fuzzy bodies of evidence becomes important when this framework is used in applications.

*Fuzzy logic has been employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. The term fuzzy logic was introduced with the proposal of fuzzy set theory by Lotfi Zadeh.*