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- W1671458032 abstract "Abstract—New concepts of rough natural number systems,recently introduced by the present author, are used to improvemost rough set-theoretical measures in general Rough Set theory(RST) and measures of mutual consistency of multiple models ofknowledge. In this research paper, the explicit dependence on theaxiomatic theory of granules of [1] is reduced and more resultson the measures and representation of the numbers are proved. I. INTRODUCTIONRough and Fuzzy set theories have been the dominantapproaches to vagueness and approximate reasoning from amathematical perspective. In rough set theory (RST), vagueand imprecise information are dealt with through binary rela-tions (for some form of indiscernibility) on a set or covers ofa set or through more abstract operators. In classical RST [2],starting from an approximation space consisting of a pair ofa set and an equivalence over it, approximations of subsets ofthe set are constructed out of equivalence partitions (these arecrisp or definite) that are also regarded as granules in manysenses. Most of the developments in RST have been within theZFC or ZF set-theoretic framework of mathematics. In suchframe works, rough sets can be seen as pairs of sets of the form(A, B), with A ⊆ B or more generally as in the approachesof the present author as collections of some sense definiteelements of the form {a" @default.
- W1671458032 created "2016-06-24" @default.
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- W1671458032 date "2011-02-13" @default.
- W1671458032 modified "2023-09-27" @default.
- W1671458032 title "DIALECTICS OF COUNTING AND MEASURES OF ROUGH THEORIES" @default.
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