Rough sets, rough mereology and uncertainty

Abstract

35 years ago Zdzisław Pawlak published the article in which He proposed a novel idea for reasoning about uncertainty. He proposed to present knowledge as classification ability and in consequence the playground for His theory was proposed as approximation space, i.e., a set along with an equivalence relation on it, equivalence classes representing categories to which objects in the set were to be assigned. This point of view was stressed in the monograph ‘Rough Sets. Theoretical Aspects of Reasoning about Data’ (1992) 25 years ago. The application tint was given to rough sets by transferring center of gravity of the theory from approximation spaces to decision/information systems, i.e., data tables in the attribute—value format. In the same year the first collective monograph appeared accompanying the first workshop on rough sets: ‘Intelligent Decision Support. Handbook of Applications and Advances of Rough Set Theory’ edited by Roman Słowiński. The effect of those 10 years was emergence of notions like a decision rule, a reduct, a core, of algorithms for finding certain, minimal and optimal rules, for finding reducts, analyses of relations between rough sets and other paradigms describing uncertainty and emergence of hybrid approaches like rough-fuzzy sets etc. Still 10 years elapsed and a monograph on foundations of rough sets was possible (2002): ‘Rough Sets. Mathematical Foundations’ by this author, and, some other outlines of rough set theory appeared. Rough set research grew, extending its scope by entering realms of morphology, intelligent agents theory, linguistics, behavioral robotics, mereology, granular computing, acquiring many applications in diverse fields. In this chapter we try to sum up our personal experience and results and in a sense to unify them into a coherent conceptual scheme following the main themes of rough set theory: to understand uncertainty and to cope with it in data. In this work, we use the term ‘thing’ to denote a being in general, denoted with x, y, z, . and the term ‘object’ to denote beings in the universes of information/decision systems, denoted u, v,w, . ; truth values are denoted with letters r, s, .