By Janusz T. Starczewski

ISBN-10: 3642295193

ISBN-13: 9783642295195

ISBN-10: 3642295207

ISBN-13: 9783642295201

This booklet generalizes fuzzy common sense platforms for various different types of uncertainty, including

- semantic ambiguity as a result of restricted notion or lack of knowledge approximately detailed club functions

- loss of attributes or granularity coming up from discretization of genuine data

- vague description of club functions

- vagueness perceived as fuzzification of conditional attributes.

Consequently, the club uncertainty might be modeled by way of combining tools of traditional and type-2 fuzzy common sense, tough set conception and probability theory.

In specific, this publication offers a few formulae for enforcing the operation prolonged on fuzzy-valued fuzzy units and offers a few simple buildings of generalized doubtful fuzzy common sense platforms, in addition to introduces numerous of the right way to generate fuzzy club uncertainty. it's fascinating as a reference publication for under-graduates in larger schooling, grasp and health care provider graduates within the classes of desktop technology, computational intelligence, or fuzzy keep an eye on and type, and is mainly devoted to researchers and practitioners in undefined.

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**Extra resources for Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty**

**Example text**

Therefore, some approximation of this result can be applied to adaptive network fuzzy inference systems with small computational costs. Is seems somehow unexpectedly, that this result in [0, mF ] have the same form as the approximate result of Karnik and Mendel derived without the context of the drastic product t-norm [Karnik and Mendel 2000; Mendel 2001]. 8 1 Fig. 5 Extended Algebraic Product T-Norm Based on the Product for Trapezoidal Fuzzy Truth Intervals In the case of the product-based extension of the product t-norm, an interesting result has been derived in [Starczewski 2009b] under assumption that arguments are trapezoidal fuzzy truth intervals or triangular fuzzy truth numbers as well.

1 Rough-Fuzzy Sets The most straightforward combination of rough sets and fuzzy sets can be deﬁned as rough approximations of a fuzzy set, called a rough-fuzzy set [Dubois and Prade 1990b]. Rough-fuzzy sets are deﬁned in the presence of equivalence relations identically as original rough sets, whereas the object of approximation is a fuzzy set. 21. Let R be an equivalence relation on a universe X, and A be a fuzzy set in X. Let Xi , i = 1, 2 . , be subinterval partitions of X induced by the equivalence relation R.

Introduction to Metamathematics. : Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms. : Triangular Norms. : Fuzzy sets and fuzzy logic: Theory and applications. : Foundations of fuzzy systems. : Representation of associative functions. : Rough Approximations Under level Fuzzy Sets. W. ) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 78–83. : O logice tr´ ojwarto´sciowej (on three-valued logic). : Untersuchungen u ¨ber den aussagenkalk¨ ul. : A survey on fuzzy implication functions.

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