Download PDF by Richard Jensen;Qiang Shen: Computational Intelligence and Feature Selection: Rough and

By Richard Jensen;Qiang Shen

ISBN-10: 0470229756

ISBN-13: 9780470229750

ISBN-10: 0470377917

ISBN-13: 9780470377918

The tough and fuzzy set techniques awarded the following open up many new frontiers for persevered study and improvement

Computational Intelligence and have choice presents readers with the historical past and basic principles at the back of function choice (FS), with an emphasis on recommendations according to tough and fuzzy units. For readers who're much less conversant in the topic, the ebook starts off with an creation to fuzzy set idea and fuzzy-rough set thought. construction in this starting place, the ebook presents:

  • A serious evaluation of FS tools, with specific emphasis on their present obstacles

  • application documents enforcing significant algorithms, including the required directions and datasets, on hand on a similar site

  • assurance of the historical past and primary rules at the back of FS

  • a scientific presentation of the prime tools reviewed in a constant algorithmic framework

  • Real-world purposes with labored examples that illustrate the facility and efficacy of the FS techniques lined

  • An research of the linked components of FS, together with rule induction and clustering equipment utilizing hybridizations of fuzzy and tough set theories

Computational Intelligence and have choice is a perfect source for complicated undergraduates, postgraduates, researchers, engineers. although, its common presentation of the underlying techniques makes the booklet significant to experts and nonspecialists alike.

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Extra info for Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches (IEEE Press Series on Computational Intelligence)

Example text

The second axiom states that elements in y’s neighborhood are in the equivalence class of y. The final axiom states that any two elements in F are related via S. Obviously this definition degenerates to the normal definition of equivalence classes when S is nonfuzzy. The family of normal fuzzy sets produced by a fuzzy partitioning of the universe of discourse can play the role of fuzzy equivalence classes [86]. Consider 34 SET THEORY the crisp partitioning of a universe of discourse, U, by the attributes in Q: U/Q = {{1, 3, 6}, {2, 4, 5}}.

3 Complement The relative complement (or set theoretic difference) of A in B is the set of all elements that are members of B but not of A. This is denoted B − A (or B \ A). More formally, B − A = {x|(x ∈ B) and not (x ∈ A)}. In some situations, all sets may be considered to be subsets of a given universal set U. In this case, U − A is the absolute complement (or simply complement) of A, and is denoted A or Ac . More formally, Ac = {x|(x ∈ U) and not (x ∈ A)}. 2 A ∪ Ac = U A ∩ Ac = ∅ (Ac )c = A A−A=∅ A − B = A ∩ Bc FUZZY SET THEORY A distinct approach to coping with reasoning under uncertain circumstances is to use the theory of fuzzy sets [408].

The adoption of fuzzy sets helps to ease the requirement for encoding uncertain domain knowledge. For example, labels like small, medium, and large have an intuitive appeal to represent values of some physical attributes. However, if they are defined with a semantic interpretation in terms of crisp intervals, such as small = {x|x > 0, x 1} medium = {x|x > 0, x ≈ 1} the representation may lead to rather nonintuitive results. This is because, in practice, it is not realistic to draw an exact boundary between these intervals.

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Computational Intelligence and Feature Selection: Rough and Fuzzy Approaches (IEEE Press Series on Computational Intelligence) by Richard Jensen;Qiang Shen

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