Data Mining, Rough Sets and Granular Computing by Lotfi A. Zadeh (auth.), Professor Tsau Young Lin, Professor

By Lotfi A. Zadeh (auth.), Professor Tsau Young Lin, Professor Yiyu Y. Yao, Professor Lotfi A. Zadeh (eds.)

During the previous few years, information mining has grown swiftly in visibility and value inside of info processing and choice research. this is often par­ ticularly actual within the realm of e-commerce, the place facts mining is relocating from a "nice-to-have" to a "must-have" prestige. In a special notwithstanding comparable context, a brand new computing technique referred to as granular computing is rising as a strong software for the belief, research and layout of information/intelligent platforms. In essence, information mining offers with summarization of knowledge that's resident in huge info units, whereas granular computing performs a key function within the summarization approach by way of draw­ ing jointly issues (objects) that are similar via similarity, proximity or performance. during this viewpoint, granular computing has a place of centrality in facts mining. one other technique which has excessive relevance to info mining and performs a principal position during this quantity is that of tough set thought. primarily, tough set thought should be seen as a department of granular computing. even though, its purposes to info mining have predated that of granular computing.

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Which facilitates the learning of such models from example data, is presented. The induction of additive Cartesian granule feature models falls into the category of supervised learning algorithms. Within this framework. the task of the learner is to model the dependence of an output variable or feature Y on one or more input (/J, ... e. approximate a function y = g(j). For classification domain features (h, problems. the target variable Y is discrete. taking values from the finite set {Class], ...

Unlike evidential logic rules, no weights are associated with the features Fi. Figure 3: Conjunctive rule structure. 3 Approximate reasoning using Cartesian granule feature models This section describes the approximate reasoning process that is used in order to perform inference and decision-making within the framework of Cartesian granule feature models. In short, for classification problems, the system accepts as input an object or event description in terms of a data vector Data (raw data), performs approximate reasoning given this data, the result of which is a discrete value CLASS, the classification of the input object.

C},andi:;t:j (ii)UA = X ;=1 In other words, P provides a minimal, or the most efficient covering of X. A trivial example of a partition of X is provided by {A, -,AI -,A denotes the complement of A} for any subset A of X. Definition: When each Ai is a fuzzy set, afuzzy partition [6] for X is defined and the following properties, corresponding to (i) and (ii) above, must hold: V i,jE{l, ... ,c},andVkE{l, ... ,n} c (ii) L,uAi (xk ) =1 VkE{l, ... ,n} i=l This type of partition is sometimes known as afuzzy mutually exclusive partition [1].

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