Hybrid Rough Sets and Applications in Uncertain by Lirong Jian

By Lirong Jian

As a strong method of info reasoning, tough set conception has confirmed to be beneficial in wisdom acquisition, choice research and forecasting, and data discovery. having the ability to increase some great benefits of different delicate know-how theories, hybrid tough set thought is readily rising as a mode of selection for determination making less than doubtful stipulations. preserving the advanced arithmetic to a minimal, Hybrid tough units and functions in doubtful Decision-Making offers a scientific advent to the tools and alertness of the hybridization for tough set conception with different similar tender know-how theories, together with likelihood, gray structures, fuzzy units, and synthetic neural networks. It additionally: Addresses the diversity of uncertainties which may come up within the sensible program of data illustration platforms Unveils a unique hybrid version of chance and tough units Introduces gray variable precision tough set versions Analyzes the benefits and drawbacks of varied useful purposes The authors study the scope of program of the tough set idea and speak about how the combo of variable precision tough units and dominance relatives can produce probabilistic choice principles out of choice characteristic determination tables of choice activities. whole with a variety of circumstances that illustrate the explicit software of hybrid equipment, the textual content adopts the most recent achievements within the concept, approach, and alertness of tough units.

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Discernibility function f2(A) is the attribute set distin­ guished between elementary set 2 and the elementary sets 1, 3, 4, 5. 8. 8. Similarly, f1( A) = ( a1 + a3 )a3(a1 + a3 )( a1 + a3 ) = a3 f2( A) = ( a1 + a3 )( a1 + a3 )a1( a1 + a3 ) = a1 f3( A) = ( a1 + a3 )( a1 + a3 )a3(a1 + a3 ) = a3 f4 ( A) = ( a1 + a3 )a1a3( a1 + a3 ) = a1a3 f5 ( A) = ( a1 + a3 )( a1 + a3 )( a1 + a3 )a3 = a3 According to f1(A), we can draw a conclusion without considering a1; according to f2(A), we can draw a con­ clusion without considering a3; according to f3(A), we can draw a conclusion without considering a1; accord­ ing to f4(A), the attribute values a1 and a3 have to be considered, because the attribute value has a reduct {a1, a3}; according to f5(A), we can draw a conclusion without considering a1.

2 Heuristic Algorithm of Attribute Reduct The heuristic attribute reduct method generally starts from the core attribute of the system, and the attributes are divided into the attribute set until the latter is a reduct according to the sequence of descending importance. There are some kinds of attribute importance that are often used, such as the attribute importance based on dependability, the attribute importance based on information entropy, and the attribute importance based on the property frequency in a discernable matrix, and so on.

The equivalence class of indiscernibility relation is called as the element set or the atom in S, while the empty set is also the element of approximation space S. Equivalence class corresponds to the expressions of knowledge granularities, which is the basis of the main concepts in rough set, such as approximation, dependence, reduct, and so on. 2 Set and Approximations of Set The definition of set in the rough set theory is relevant with the available information (knowledge) and the understanding of the relevant universe elements.

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