Computational Intelligence: Methods and Techniques by Leszek Rutkowski

By Leszek Rutkowski

This booklet makes a speciality of a number of thoughts of computational intelligence, either unmarried ones and people which shape hybrid tools. these options are at the present time as a rule utilized problems with synthetic intelligence, e.g. to method speech and typical language, construct specialist structures and robots. the 1st a part of the ebook provides tools of information illustration utilizing diversified recommendations, particularly the tough units, type-1 fuzzy units and type-2 fuzzy units. subsequent a number of neural community architectures are provided and their studying algorithms are derived. furthermore, the relations of evolutionary algorithms is mentioned, specifically the classical genetic set of rules, evolutionary suggestions and genetic programming, together with connections among those thoughts and neural networks and fuzzy platforms. within the final a part of the booklet, a number of tools of information partitioning and algorithms of computerized facts clustering are given and new neuro-fuzzy architectures are studied and in comparison. This well-organized glossy method of equipment and methods of clever calculations comprises examples and workouts in each one bankruptcy and a preface through Jacek Zurada, president of IEEE Computational Intelligence Society (2004-05).

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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 situation is described by the terms of lower and upper approximation of set X ⊆ U .

What differentiates one object from another and makes other objects similar, these are the values of their features. Let us denote by Vq the set of values that the feature q can take. The value of feature q of the object x will be denoted as vxq . , vqxn . In this chapter the rough sets theory will be presented in the form of a series of definitions illustrated by examples. 1 will allow the reader an easier handling of them. 1. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

G. from 100 to 300 thousand people, then some cities will be indiscernible with respect to the feature (attribute) “number of inhabitants”. Moreover, in the description of any given object, we only consider a limited number of features, adequate to a given purpose. Quite often, we want to reduce that number to the necessary minimum. These are the problems dealt with by the theory of rough sets. In order to facilitate further discussion, we shall introduce several notions and symbols. First, we shall define the universe of discourse U .

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