Titlebook: Mathematics of Fuzzy Sets and Fuzzy Logic; Barnabas Bede Book 2013 Springer-Verlag Berlin Heidelberg 2013 Artificial Neural Network.Fuzzy

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https://doi.org/10.1007/978-3-642-35221-8Artificial Neural Network; Fuzzy Control; Fuzzy Differential Equation; Fuzzy Inference System; Fuzzy Log

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Mathematics of Fuzzy Sets and Fuzzy Logic978-3-642-35221-8Series ISSN 1434-9922 Series E-ISSN 1860-0808

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Fuzzy Sets,The concept of a . is fundamental in Mathematics and intuitively can be described as a collection of objects possibly linked through some properties. A classical set has clear boundaries, i.e. . ∈ . or . ∉ . exclude any other possibility.

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Fuzzy Relations,(Classical relation). A subset . ⊆ .×. where . and . are classical sets, is a classical relation.

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Fuzzy Arithmetic,Often, we have to perform operations with uncertain parameters. In this case we will have to define the fuzzy counterparts of the classical operations between real numbers..We begin our discussion on fuzzy arithmetic with Zadeh’s extension principle. It serves for extending a real-valued function into a corresponding fuzzy function.

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Possibility Theory,Let . be a set, adopted as the universe of discourse in what follows. We ask the question whether a value for a variable is possible. The answer will be a fuzzy set when the problem we are considering has uncertainties that are not of statistical type.

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Fuzzy Transform,Fuzzy Transform was proposed in Perfilieva in [121] and Perfilieva [120] and it is an approximation method based on fuzzy sets. Also, it can be seen as a fuzzy set-based analogue of the Fourier Transform. In the present chapter we follow in great lines the presentation and discussion in Bede-Rudas [23].

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