Algebraic Semantics of Proto-Transitive Rough Sets

Preface Rough sets over generalized transitive relations like proto-transitive ones have been initiated by the present author in the year 2012 [1]. Subsequently [2], approximation of proto-transitive relations by other relations was investigated and the relation with rough approximations was developed towards constructing semantics that can handle fragments of structure. It was also proved that difference of approximations induced by some approximate relations need not induce rough structures. In this research we develop different semantics of proto transitive rough sets (PRAX) after characterizing the structure of rough objects and also develop a theory of dependence for general rough sets and use it to internalize the Nelson-algebra based approximate semantics developed earlier [2]. The theory of rough dependence initiated later [3] by the present author is extended in the process. This monograph is reasonably self-contained and includes proofs and extensions of representation of objects that were not part of earlier papers. A. Mani is an active researcher in algebra, logic, rough sets, vagueness, philosophy and foundations of Mathematics. She has published extensively on the subjects in a number of international peer-reviewed journals for more than a decade. Her current affiliations include the University of Calcutta in Kolkata and Division-R of STVROM. She is active in various academic groups like ISRS, IRSS, ASL and FOM. She is also a teacher, free software activist, feminist, consultant in statistical and soft computing and service provider.