Transactions on Rough Sets I by Colonel Wm. T. McLyman

By Colonel Wm. T. McLyman

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They assume truth values which lie between 0 and 1, in other words, they are probable, not true. Besides, instead of true inference rules we have now decision rules, which are neither true nor false. They are characterized by three coefficients, strength, certainty and coverage factors. Strength of a decision rule can be understood as a counterpart of truth value of the inference rule, and it represents frequency of the decision rule in a database. Thus employing decision rules to discovering patterns in data boils down to computation probability of conclusion in terms of probability of the premise and strength of the decision rule, or – the probability of the premise from the probability of the conclusion and strength of the decision rule.

In [30] 139–156 54 16. : Informaton granulation and approximation in a decision-theoretical model of rough sets. In [30] 491–520 17. : Approximation spaces and information granulation (submitted). In: Fourth International Conference on Rough Sets and Current Trends in Computing (RSCTC’04), Uppsala, Sweden, June 1-5, 2004. Lecture Notes in Computer Science. Springer-Verlag, Heidelberg, Germany (2004) 18. : Rough Sets: Theoretical Aspects of Reasoning about Data. Volume 9 of System Theory, Knowledge Engineering and Problem Solving.

Let be formulas in For (A) where A is the set of attributes in S = (U, A). We say that and are equivalent in S, or simply, equivalent if S is understood, in symbols if and only if and This means that if and only if We need also approximate equivalence of formulas which is defined as follows: Besides, we define also approximate equivalence of formulas with the accuracy which is defined as follows: Now, we define the notion of a decision algorithm, which is a logical counterpart of a decision table.

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