Towards a Unified Modeling and Knowledge-Representation by Vassilis G. Kaburlasos

By Vassilis G. Kaburlasos

By ‘model’ we suggest a mathematical description of an international point. With the proliferation of pcs numerous modeling paradigms emerged less than computational intelligence and tender computing. An advancing expertise is at the moment fragmented due, to boot, to the necessity to deal with types of facts in numerous software domain names. This examine monograph proposes a unified, cross-fertilizing strategy for knowledge-representation and modeling in response to lattice theory. The emphasis is on clustering, type, and regression functions. it's proven how rigorous research and layout should be pursued in delicate computing utilizing traditional (hard computing) tools. in addition, non-Turing computation might be pursued. the fabric this is multi-disciplinary according to our on-going examine released in significant clinical journals and meetings. Experimental effects by means of quite a few algorithms are tested widely. appropriate paintings through different authors can be provided either commonly and comparatively.

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Then ∃a in L such that θ(a) = a. 3 Positive Valuation Functions Consider the following function in a lattice. Definition 3-22 A valuation v in a lattice (L,≤) is a real function v: L→R which satisfies v(x)+v(y) = v(x∧y)+v(x∨y), x,y∈L. A valuation is called monotone iff x≤y implies v(x)≤v(y), and positive iff x

2 Other Modeling Paradigms 9 1990; Motoda et al. 1991; Fujihara et al. 1997). Data clustering algorithms (Jain et al. 1999) are popular for knowledge discovery. Moreover, knowledge-modeling procedures (Chandrasekaran et al. 1992) as well as knowledge management models have been proposed (Hou et al. 2005). Knowledge discovery from databases, also known as data mining (Cios et al. 1998), bridges several technical areas including databases, humancomputer interaction, statistical analysis, and machine learning (ML).

1989; Kearns and Vazirani 1994; Long and Tan 1998); other applications have also considered hyperboxes for learning (Salzberg 1991; Wettschereck and Dietterich 1995; Dietterich et al. 1997). 4 A Probability Space 37 Note also that learning general lattice intervals beyond lattice RN is carried out implicitly in Valiant (1984) as well as in Kandel et al. (1995) where conjunctive normal forms (CNF) are computed in a Boolean lattice. None of the above algorithms employs lattice theory. This work engages explicitly lattice theory for learning hyperboxes in the unit hypercube U.

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