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 prior few years, information mining has grown swiftly in visibility and value inside info processing and selection research. this can be par­ ticularly real within the realm of e-commerce, the place information mining is relocating from a "nice-to-have" to a "must-have" prestige. In a distinct although comparable context, a brand new computing method referred to as granular computing is rising as a strong software for the perception, research and layout of information/intelligent platforms. In essence, facts mining bargains with summarization of data that's resident in huge facts units, whereas granular computing performs a key position within the summarization technique by means of draw­ ing jointly issues (objects) that are comparable via similarity, proximity or performance. during this point of view, granular computing has a place of centrality in info mining. one other technique which has excessive relevance to info mining and performs a significant function during this quantity is that of tough set idea. primarily, tough set concept will be seen as a department of granular computing. notwithstanding, its functions to information mining have predated that of granular computing.

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Each feature Fi is associated with a weight term WiCLASS that reflects the importance of this feature to the class CLASS. Figure 2 Evidentiallogic rule structure. On the other hand, a product model will consist of a collection of conjunctive rules; one for each class in the problem domain. A conjunctive ruIe structure is depicted in Figure 3. As is the case in evidentiallogic rules, CLASS can be viewed as a fuzzy set consisting of a single crisp value and the body of each rule consists of a collection of Cartesian granule features Fi, whose values FiCLASS correspond to fuzzy sets defined over the Cartesian granule universes ni, for the output or 52 dependent variable value CLASS.

Extensional function dependencies are universal decision rules. We will give a brief formulation. Let us recall some notions from [7]. Let A = {AI, A 2 , ••• , An} and B = {Bb B2' ... ' Bm} be two sets of attributes of a relational database. c = (al,a2, ... ,an ), d = (b l ,b2, ... ,bm ) be two tuples of attributes values of A and B respectively. Let G ai , G bj be elementary granules corresponding to ai and bj,i = 1,2 ... n,j = 1,2 ... m respectively. Let Pc = niG ail Qd = njGbj be the respective intersections.

Number of Reads for Different Methods on Data Set 1 ( C1 ( C7 ( C13 54) ( C2 51) ( C8 37) ( C14 37) ( C3 56) ( C9 41) ( C15 53) ( C4 52) ( C10 41) ( C16 Table 14. 28 Table 15. Computing Times for Different Methods on Data Set 2 Granule Apriori Apriori Apriori Subset Hybrid Real Reads 12963 18750 18750 18750 Logical Reads 1128489 0 0 0 Reads Table 16. Number of Reads for Different Methods on Data Set 2 ( Cl ( C7 ( C13 ( C19 ( C25 ( C31 ( C37 ( C43 18) 61) 56) 37) 21) 8) 42) 58) ( C2 ( C8 ( C14 ( C20 ( C26 ( C32 ( C38 ( C44 24) 5) 11) 34) 23) 58) 15) 35) ( C3 ( C9 ( C15 ( C21 ( C27 ( C33 ( C39 ( C45 18) 59) 50) 11) 9) 35) 59) 51) Table 17.

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