Mining Numerical Data - A Rough Set Approach.- Definability and Other Properties of Approximations for Generalized Indiscernibility Relations.- Variable Consistency Bagging Ensembles.- Classical and Dominance-Based Rough Sets in the Search for Genes under Balancing Selection.- Satisfiability Judgement under Incomplete Information.- Irreducible Descriptive Sets of Attributes for Information Systems.- Computational Theory Perception (CTP), Rough-Fuzzy Uncertainty Analysis and Mining in Bioinformatics and Web Intelligence: A Unified Framework.- Decision Rule-Based Data Models Using TRS and NetTRS - Methods and Algorithms.- A Distributed Decision Rules Calculation Using Apriori Algorithm.- Decision Table Reduction in KDD: Fuzzy Rough Based Approach.

Volume XI of the Transactions on Rough Sets (TRS) provides evidence of f- ther growth in the rough set landscape, both in terms of its foundations and applications. This volume provides further evidence of the number of research streams that were either directly or indirectly initiated by the seminal work on rough 1 sets by Zdzis law Pawlak (1926-2006) . Evidence of the growth of various rough 2 set-based research streams can be found in the rough set database . Thisvolumecontainsarticlesintroducingadvancesinthefoundationsand- plicationsofroughsets.These advancesinclude: calculusofattribute-value pairs useful in mining numerical data, de?nability and coalescence of approximations, variable consistency generalization approach to bagging controlled by measures of consistency, classical and dominance-based rough sets in the search for genes, judgementaboutsatis?abilityunderincompleteinformation,irreducibledescr- tive sets of attributes for information systems useful in the design of concurrent data models, computational theory of perceptions (CTP) and its characteristics and the relation with fuzzy-granulation, methods and algorithms of the Net- TRS system, a recursive version of the apriori algorithm designed for parallel processing, and decision table reduction method based on fuzzy rough sets. Theeditorsandauthorsofthisvolumeextendtheirgratitudetothereviewers of articles in this volume, Alfred Hofmann, Ursula Barth, Christine Reiss and the LNCS sta? at Springer for their support in making this volume of the TRS possible.