Rough Mereological Calculi of Granules: A Rough Set Approach To Computation

Rough Mereology is a paradigm allowing for a synthesis of main ideas of two potent paradigms for reasoning under uncertainty: Fuzzy Set Theory and Rough Set Theory. Approximate reasoning is based in this paradigm on the predicate of being a part to a degree . We present applications of Rough Mereology to the important theoretical idea put forth by Lotfi Zadeh (1996, 1997), i.e., Granularity of Knowledge: We define granules of knowledge by means of the operator of mereological class and we extend the idea of a granule over complex objects like decision rules as well as decision algorithms. We apply these notions and methods in the distributed environment discussing complex problems of knowledge and granule fusion. We express the mechanism of complex granule formation by means of a formal grammar called Synthesis Grammar defined over granules of knowledge, granules of classifying rules, or over granules of classifying algorithms. We finally propose hybrid rough‐neural schemes bridging rough and neural computations.