Rough Sets and Interactive Granular Computing

Abstract

Decision support in solving problems related to complex systems requires relevant computation models for the agents as well as methods for incorporating reasoning over computations performed by agents. Agents are performing computations on complex objects (e.g., (behavioral) patterns, classifiers, clusters, structural objects, sets of rules, aggregation operations, (approximate) reasoning schemes etc.). In Granular Computing (GC), all such constructed and/or induced objects are called granules. To model, crucial for the complex systems, interactive computations performed by agents, we extend the existing GC approach to Interactive Granular Computing (IGC) by introducing complex granules (c-granules or granules, for short). Many advanced tasks, concerning complex systems may be classified as control tasks performed by agents aiming at achieving the high quality computational trajectories relative to the considered quality measures over the trajectories. Here, new challenges are to develop strategies to control, predict, and bound the behavior of the system. We propose to investigate these challenges using the IGC framework. The reasoning, which aims at controlling the computational schemes from time-to-time, in order to achieve the required targets, is called an adaptive judgement. This reasoning deals with granules and computations over them. Adaptive judgement is more than a mixture of reasoning based on deduction, induction and abduction. Due to the uncertainty the agents generally cannot predict exactly the results of actions (or plans). Moreover, the approximations of the complex vague concepts initiating actions (or plans) are drifting with time. Hence, adaptive strategies for evolving approximations of concepts are needed. In particular, the adaptive judgement is very much needed in the efficiency management of granular computations, carried out by agents, for risk assessment, risk treatment, and cost/benefit analysis. In the lecture, we emphasize the role of the rough set based methods in IGC. The discussed approach is a step towards realization of the Wisdom Technology (WisTech) program, and is developed over years of experiences, based on the work on different real-life projects.

Rough sets: past, present, and future

“…Recently, it was also emphasized (see e.g., Jankowski 2017 ; Jankowski et al. 2014b , 2015 ; Skowron and Jankowski 2016a , b , c ; Skowron et al. 2012a , 2016 ) that for many applications, information systems should be considered as open objects (complex granules) rather than closed objects (complex granules), where they are open to interact with the environment, consisting physical objects as well as other information systems grounded on physical objects too.…”

“…In general, by fixing the control parameters, e.g., space-time location, position of sensors or/and actuators etc., the agent prepares the ground for obtaining an information system describing the properties of real physical objects. These real physical objects along with the set-up of the control tools (i.e., space-time-angle of sensors or cameras) generates a complex granule (c-granule, for short) (Jankowski 2017 ; Skowron and Jankowski 2016b ). These c-granules, parts of c-granules, relationships among them, features of parts of the c-granules, and links of c-granules all together help to transmit the results of interactions with objects to the so called information tables (see Fig.…”

“…This process is also based on adaptive judgment (Jankowski 2017 ; Jankowski et al. 2014b , 2015 ; Skowron and Jankowski 2016a , b , c ; Skowron et al. 2012a , 2016 ) with roots not only in logic, but also in psychology and phenomenology (Martin 2006 ) (see Fig.…”

“…The extension of GrC to interactive granular computing (IGrC) requires generalization of the basic concepts such as complex granules (including both physical and abstract parts), information (decision) systems as well as methods of inducing hierarchical structures of information (decision) systems (Jankowski 2017 ; Jankowski et al. 2014b , 2015 ; Skowron and Jankowski 2016a , b , c ; Skowron et al. 2012a , 2016 ) and interactions among information systems.…”

Algebraic Semantics of Generalized RIFs

“…Specific versions of a GGS and granular operator spaces have been studied in [3] by the present author for handling a very large spectrum of rough set contexts. GGS has the ability to handle adaptive situations as in [38,39] through special morphisms -this is again harder to express without partial operations.…”