Computational Intelligence: Methods and Techniques by Professor Leszek Rutkowski (auth.)

By Professor Leszek Rutkowski (auth.)

This e-book makes a speciality of quite a few suggestions of computational intelligence, either unmarried ones and people which shape hybrid equipment. these strategies are this present day mostly utilized problems with synthetic intelligence, e.g. to strategy speech and normal language, construct professional platforms and robots. the 1st a part of the booklet provides tools of data illustration utilizing assorted suggestions, specifically the tough units, type-1 fuzzy units and type-2 fuzzy units. subsequent a variety of neural community architectures are provided and their studying algorithms are derived. additionally, the relations of evolutionary algorithms is mentioned, particularly the classical genetic set of rules, evolutionary ideas and genetic programming, together with connections among those thoughts and neural networks and fuzzy platforms. within the final a part of the ebook, a number of tools of information partitioning and algorithms of computerized information clustering are given and new neuro-fuzzy architectures are studied and in comparison. This well-organized sleek method of tools and methods of clever calculations comprises examples and workouts in each one bankruptcy and a preface via Jacek Zurada, president of IEEE Computational Intelligence Society (2004-05).

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This ebook makes a speciality of numerous concepts of computational intelligence, either unmarried ones and people which shape hybrid tools. these thoughts are at the present time regularly utilized problems with man made intelligence, e. g. to procedure speech and traditional language, construct specialist platforms and robots. the 1st a part of the booklet offers equipment of data illustration utilizing various strategies, specifically the tough units, type-1 fuzzy units and type-2 fuzzy units.

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8. 71) NegC (XO ) = U \ CX = {x2 , x3 , x8 , x9 , x10 } . 9 for the set of features P1 and P2 . 3 Set approximation 41 which is illustrated by Fig. 12. 74) = U \ U = ∅. 12. 13). 13. 75) PX = PX 42 3. Methods of knowledge representation using rough sets and P -rough set otherwise P X = P X. 11 The set X is called a) roughly P -definable set, if ⎧ ⎨ PX = ∅ ⎩ P X = U, b) internally P -non definable set, if ⎧ ⎨ PX = ∅ ⎩ P X = U, c) externally P˜ -non definable set, if ⎧ ⎨ PX = ∅ ⎩ P X = U, d) totally P -non definable set, if ⎧ ⎨ PX = ∅ ⎩ P X = U.

34 3. 5. Example of equivalence class [(5; 4)]P Their family is the set of all square fields visible in Figs. 5. 45) = Ent (x2 ) : x = (x1 ; x2 ) ; x1 ; x2 = 0; . . ; 9} = [x]P = {x = (x1 ; x2 ) ∈ U : Ent (x1 ) = x1 ∧ Ent (x2 ) = x2 } : x = (x1 ; x2 ) ; x1 ; x2 = 0; . . ; 9} . 3 Set approximation In the space U , certain sets X may exist. We can infer that particular objects x ∈ U belong to sets X based on the knowledge of values of their features. The set of available features P ⊆ Q is usually limited and the determination of membership of the object to a specific set may not be unequivocal.

This definition says that the object x ∈ X is an element of the upper approximation, if the whole equivalence class, to which it belongs, has a non-empty intersection with the set X. In other words, if at least one element of a given equivalence class belongs to the set X, then each element of this equivalence class belongs to the upper approximation of the set X. 5, elements of classes [x3 ]C , [x4 ]C , and [x8 ]C belong to the set XF , hence CXF = {x3 } ∪ {x4 , x5 } ∪ {x8 } = {x3 , x4 , x5 , x8 } .

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