Constructing rough mereological granules of classifying rules and classifying algorithms

• Authors: Lech Polkowski;Andrzej Skowron
• Venue: Technologies for constructing intelligent systems
• Year: 2002

Rough Set Theory cf. [3] was conceived as an approach toward analysis of uncertainty as well as incompleteness. Its basic assumptions going back to logical and philosophical analysis by - among others - Leibniz, Frege and Russell - is that objects perceived by a given set of attributes should be regarded as indiscernible whenever the attributes have same values on them (Leibnizian identity). Sets of objects which may be represented as unions of classes of the indiscernibility relation are then complete (exact, certain) while all other sets may be described by means of approximations with complete sets. The framework of rough sets allows for construction of classifying as well as decision rules and algorithms cf. [9] as well as for many applications to real life problems (op. cit.).Rough Mereology cf. [6], [7], [8], [11] is a paradigm based on the predicate of being a part to a degree and as such falls in the province of mereological theories of reasoning based on the notion of a part which go back to the tradition of the Polish School in particular to the work of S. Lesniewski cf. [2]. 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. We present applications of Rough Mereology to the important theoretical idea put forth by Lotfi Zadeh [12], [13] i.e. Granularity of Knowledge. Granules of Knowledge are constructed in the framework of Rough Mereology via its class operator which allows for aggregation of objects close enough (or, similar in a satisfactory degree) with respect to the rough inclusion operator (which measures the degree of being a part for pairs of objects). This allows for constructing Logics for reasoning in Multi-Agent environment. We present a basic outline of this approach. We propose a formal language for encoding reasoning schemes (the Synthesis Grammar) and here we carry the idea of Synthesis Grammar to a higher level of abstraction by constructing Granules of classifying rules as well as classifying algorithms. We finally discuss briefly the analogy between rough mereological and neural computations leading to the idea of hybrid rough-neural computation schemes.