Lattice Ordered Evaluation Method of Equipment Response Event to Voltage Sag

Considering the multi-valued mapping relationship of equipment response event to voltage sag, a lattice ordered evaluation method is proposed in this study. Each possible resulting state of equipment response event is described by an interval number. The interval numbers is with the characteristics of lattice order presented by the upper and lower probabilities. The possibility degree matrix is introduced to compare resulting states without satisfying the axioms of connectedness. Personal computer is simulated and compared testing results. The results have shown the validity and feasibility.

Using Dempster-Shafer Theory in Data Mining

The origins of Dempster-Shafer theory (DST) go back to the work by Dempster (1967) who developed a system of upper and lower probabilities. Following this, his student Shafer (1976), in their book “A Mathematical Theory of Evidence” developed Dempster’s work, including a more thorough explanation of belief functions, a more general term for DST. In summary, it is a methodology for evidential reasoning, manipulating uncertainty and capable of representing partial knowledge (Haenni & Lehmann, 2002; Kulasekere, Premaratne, Dewasurendra, Shyu, & Bauer, 2004; Scotney & McClean, 2003). The perception of DST as a generalisation of Bayesian theory (Shafer & Pearl, 1990), identifies its subjective view, simply, the probability of an event indicates the degree to which someone believes it. This is in contrast to the alternative frequentist view, understood through the “Principle of I sufficient reasoning”, whereby in a situation of ignorance a Bayesian approach is forced to evenly allocate subjective (additive) probabilities over the frame of discernment. See Cobb and Shenoy (2003) for a contemporary comparison between Bayesian and belief function reasoning. The development of DST includes analogies to rough set theory (Wu, Leung, & Zhang, 2002) and its operation within neural and fuzzy environments (Binaghi, Gallo, & Madella, 2000; Yang, Chen, & Wu, 2003). Techniques based around belief decision trees (Elouedi, Mellouli, & Smets, 2001), multi-criteria decision making (Beynon, 2002) and non-paramnteric regression (Petit-Renaud & Denoeux, 2004), utilise DST to allow analysis in the presence of uncertainty and imprecision. This is demonstrated, in this article, with the ‘Classification and Ranking belief Simplex’ (CaRBS) technique for object classification, see Beynon (2005a).

Using Dempster-Shafer Theory in Data Mining

The origins of Dempster-Shafer theory (DST) go back to the work by Dempster (1967) who developed a system of upper and lower probabilities. Following this, his student Shafer (1976), in his book “A Mathematical Theory of Evidence” added to Dempster’s work, including a more thorough explanation of belief functions. In summary, it is a methodology for evidential reasoning, manipulating uncertainty and capable of representing partial knowledge (Haenni & Lehmann, 2002; Kulasekere, Premaratne, Dewasurendra, Shyu, & Bauer, 2004; Scotney & McClean, 2003).

An algebraic treatment of imprecise probabilities

This is a survey paper about an algebraic approach to imprecise probabilities. In the first part of it, we outline the work by Walley on imprecise probabilities and the more algebraic approach of Fedel et al.. Then, in the second part we will present some work in progress about a general treatment of upper and lower probabilities over many-valued events and of upper and lower previsions of gambles, by means of Universal Algebra.