Download Computational Intelligence: Methods and Techniques by Leszek Rutkowski PDF

By Leszek Rutkowski

This e-book specializes in a variety of recommendations of computational intelligence, either unmarried ones and people which shape hybrid tools. these concepts are this day generally utilized problems with synthetic intelligence, e.g. to strategy speech and common language, construct specialist structures and robots. the 1st a part of the ebook offers tools of data illustration utilizing various innovations, specifically the tough units, type-1 fuzzy units and type-2 fuzzy units. subsequent quite a few neural community architectures are awarded and their studying algorithms are derived. additionally, the family members of evolutionary algorithms is mentioned, specifically the classical genetic set of rules, evolutionary innovations and genetic programming, together with connections among those concepts and neural networks and fuzzy platforms. within the final a part of the e-book, a variety of equipment of knowledge partitioning and algorithms of computerized facts clustering are given and new neuro-fuzzy architectures are studied and in comparison. This well-organized smooth method of tools and methods of clever calculations contains examples and routines in each one bankruptcy and a preface by means of Jacek Zurada, president of IEEE Computational Intelligence Society (2004-05).

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39) Their family is the set P1∗ = {[0; 1); [1; 2); [2; 3); [3; 4); [4; 5); [5; 6); [6; 7); [7; 8); [8; 9); [9; 10)}. 3 shows the exemplary equivalence class [1]P1 . 3. 4. 33]P2 For P2 -indiscernibility relation, infinitely many ten-element equivalence classes are formed. These are sets of numbers from the space U with the same decimal part [x]P2 = {x ∈ U : x − Ent (x) = x − Ent (x)} . 42) = [x]P2 = {x ∈ U : x − Ent (x) = x} : x ∈ [0; 1) . 33]P2 . e. there are infinitely many one-element equivalence classes of Q-indiscernibility relation and each element of space U forms its own class.

23. 24. 25. 26. 27. 28. 29. 2 Basic terms One of methods to present the information on objects characterized by the same set of features is the information system. 1 The information system is referred to an ordered 4-tuple SI = U, Q, V, f [1], Vq where U is the set of objects, Q is the set of features (attributes), V = q∈Q is the set of all possible values of features, while f : U ×Q → V is called the information function. We can say that vqx = f (x, q), of course f (x, q) ∈ Vq . The notation vqx = fx (q), which treats the information function as a family of functions, will be considered as equivalent.

Methods of knowledge representation using rough sets Therefore, the attribute c1 in the given decision table is insignificant, and due to that, its removal will not impact the quality of approximation of family of sets D∗ . 2. 5) are of low significance. 29 Any given subset of the set of conditional attributes C ⊂ C is called a rough D-reduct of the set of attributes C, and the approximation error of this reduct is defined as follows: ε(C,D) (C ) = γC (D∗ ) − γC (D∗ ) . 5). 2. 6 Application of LERS software LERS (Learning from Examples based on Rough Sets) software [67] has been created by RS Systems company.

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