=Paper=
{{Paper
|id=None
|storemode=property
|title=Interactive Complex Granules
|pdfUrl=https://ceur-ws.org/Vol-1032/paper-18.pdf
|volume=Vol-1032
|dblpUrl=https://dblp.org/rec/conf/csp/JankowskiSS13
}}
==Interactive Complex Granules==
https://ceur-ws.org/Vol-1032/paper-18.pdf
Interactive Complex Granules
Andrzej Jankowski1 , Andrzej Skowron2 , and Roman Swiniarski3?
1
Institute of Computer Science, Warsaw University of Technology
Nowowiejska 15/19, 00-665 Warsaw, Poland
a.jankowski@ii.pw.edu.pl
2
Institute of Mathematics, The University of Warsaw
Banacha 2, 02-097 Warsaw, Poland
skowron@mimuw.edu.pl
3
Department of Computer Science, San Diego State University
5500 Campanile Drive San Diego, CA 92182, USA
and
Institute of Computer Science Polish Academy of Sciences
Jana Kazimierza 5, 01-248 Warsaw, Poland
rswiniarski@mail.sdsu.edu
As far as the laws of mathematics refer to reality,
they are not certain; and as far as they are certain,
they do not refer to reality.
– Albert Einstein ([2])
Constructing the physical part of the theory and unifying it
with the mathematical part should be considered as one of
the main goals of statistical learning theory
– Vladimir Vapnik
([24], Epilogue: Inference from sparse data, p. 721)
Abstract. Information granules (infogranules, for short) are widely dis-
cussed in the literature. In particular, let us mention here the rough
granular computing approach based on the rough set approach and its
combination with other approaches to soft computing. However, the is-
sues related to interactions of infogranules with the physical world and
to perception of interactions in the physical world by infogranules are
?
This work was supported by the Polish National Science Centre grants 2011/01/B/
ST6/03867, 2011/01/D/ST6/06981, and 2012/05/B/ST6/03215 as well as by the
Polish National Centre for Research and Development (NCBiR) under the grant
SYNAT No. SP/I/1/77065/10 in frame of the strategic scientific research and ex-
perimental development program: “Interdisciplinary System for Interactive Scientific
and Scientific-Technical Information” and the grant No. O ROB/0010/ 03/001 in
frame of the Defence and Security Programmes and Projects: “Modern engineering
tools for decision support for commanders of the State Fire Service of Poland during
Fire & Rescue operations in the buildings”
Interactive Complex Granules 207
not well elaborated yet. On the other hand the understanding of inter-
actions is the critical issue of complex systems. We propose to model
complex systems by interactive computational systems (ICS) created by
societies of agents. Computations in ICS are based on complex granules
(c-granules, for short). In the paper we concentrate on some basic issues
related to interactive computations based on c-granules performed by
agents in the physical world.
Key words: granular computing, rough set, interaction, information
granule, physical object, complex granule, interactive computational sys-
tem
1 Introduction
Granular Computing (GC) is now an active area of research (see, e.g., [16]).
Objects we are dealing with in GC are information granules (or infogranules, for
short). Such granules are obtained as the result of information granulation [26,
28]:
Information granulation can be viewed as a human way of achieving
data compression and it plays a key role in implementation of the strategy
of divide-and-conquer in human problem-solving.
The concept of granulation is rooted in the concept of a linguistic variable intro-
duced by Lotfi Zadeh in 1973 [25]. Information granules are constructed starting
from some elementary ones. More compound granules are composed of finer gran-
ules that are drawn together by indistinguishability, similarity, or functionality
[27].
Computations on granules should be interactive. This requirement is funda-
mental for modeling of complex systems [3]. For example, in [13] this is expressed
as follows
[...] interaction is a critical issue in the understanding of complex
systems of any sorts: as such, it has emerged in several well-established
scientific areas other than computer science, like biology, physics, social
and organizational sciences.
Interactive Rough Granular Computing (IRGC) is an approach for model-
ing interactive computations (see, e.g., [17, 19–23]). Computations in IRGC are
progressing by interactions represented by interactive information granules. In
particular, interactive information systems (IIS) are dynamic granules used for
representing the results of the agent interaction with the environments. IIS can
be also applied in modeling of more advanced forms of interactions such as hi-
erarchical interactions in layered granular networks or generally in hierarchical
modeling. The proposed approach [17, 19–23] is based on rough sets but it can
be combined with other soft computing paradigms such as fuzzy sets or evolu-
tionary computing, and also with machine learning and data mining techniques.
208 A. Jankowski, A. Skowron, R. Swiniarski
The notion of the highly interactive granular system is clarified as the system
in which intrastep interactions [4] with the external as well as with the internal
environments take place. Two kinds of interactive attributes are distinguished:
perception attributes, including sensory ones and action attributes.
In this paper we extend the existing approach by introducing complex gran-
ules (c-granules) making it possible to model interactive computations performed
by agents. Any c-granule consists of three components, namely soft suit, link suit
and hard suit. These components are making it possible to deal with such ab-
stract objects from soft suit as infogranules as well as with physical objects from
hard suit. The link suit of a given c-granule is used as a kind of c-granule inter-
face for expressing interaction between soft suit and and hard suit. Any agent
operates in a local world of c-granules. The agent control is aiming to control
computations performed by c-granules from this local world for achieving the
target goals. Actions (sensors or plans) from link suits of c-granules are used
by the agent control in exploration and/or exploitation of the environment on
the way to achieve their targets. C-granules are also used for representation of
perception by agents of interactions in the physical world. Due to the bounds
of the agent perception abilities usually only a partial information about the in-
teractions from physical world may be available for agents. Hence, in particular
the results of performed actions by agents can not be predicted with certainty.
In Section 2 a general structure of c-granules is described and some illus-
trative examples are included. Moreover, some preliminary concepts related to
agents performing computations on c-granules are discussed. In Section 3 the
agent architecture is outlined. Societies of agents and communication languages
are discussed shortly in Section 4.
This paper is a step in the realization of the Wisdom Technology (WisTech)
programme [6–8].
2 Complex Granules and Physical World
We define the basic concepts related to c-granule relative to a given agent ag.
We assume that the agent ag has access to a local clock making it possible to
use the local time scale. In this paper we consider discrete linear time scale.
We distinguish several kinds of objects in the environment in which the agent
ag operates:
– physical objects (called also as hunks of matter, or hunks, for short) [5] such
as physical parts of agents or robots, specific media for transmitting infor-
mation; we distinguish hunks called as artifacts used for labeling other hunks
or stigmergic markers used for indirect coordination between agents or ac-
tions [9]; note that hunks may change in time and are perceived by the agent
ag as dynamic (systems) processes; any hunk h at the local time t of ag is
represented by the state sth (t); the results of perception of hunk states by
agent ag are represented by value vector of relevant attributes (features);
– complex granules (c-granules, for short) consisting of three parts: soft suit,
link suit, and hard suit (see Figure 1); c-granule at the local time t of ag is
Interactive Complex Granules 209
denoted by G; G receives some inputs and produces some outputs; inputs
and outputs of c-granule G are c-granules of the specified admissible types;
input admissible type is defined by some input preconditions and the output
admissible type is defined by some output postconditions, there are distin-
guished inputs (outputs) admissible types which receive (send) c-granules
from (to) the agent ag control;
• G soft suit consists of
1. G name, describing the behavioral pattern description of the agent
ag corresponding to the name used by agent for identification of the
granule,
2. G type consisting of the types of inputs and outputs of G c-granule,
3. G status (e.g., active, passive),
4. G information granules (infogranules, for short) in mental imagi-
nation of the agent consisting, in particular of G specification, G
implementation and manipulation method(s); any implementation
distinguished in infogranule is a description in the agent ag language
of transformation of input c-granules of relevant types into output
c-granules of relevant types, i.e., any implementation defines an inter-
active computation which takes as input c-granules (of some types)
and produces some c-granules (of some types); inputs for c-granules
can be delivered by the agent ag control (or by other c-granules), we
also assume that the outputs produced by a given c-granule depend
also on interactions of hunks pointed out by link suite as well as
some other hunks from the environment - in this way the semantics
of c-granules is established;
• G link suit consists of
1. a representation of configuration of hunks at time t (e.g., mereologies
of parts in the physical configurations perceived by the agent ag);
2. links from different parts of the configuration to hunks;
3. G links and G representations of elementary actions; using these links
the agent ag may perform sensory measurement or/and actions on
hunks; in particular, links are pointing to the sensors or effectors in
the physical world used by the considered c-granule; using links the
agent ag may, e.g., fix some parameters of sensors or/and actions,
initiate sensory measurements or/and action performance; we also
assume that using these links the agent ag may encode some infor-
mation about the current states of the observed hunks by relevant
information granules;
• G hard suit is created by the environment of interacting hunks encoding
G soft suit, G link suit and implementing G computations;
• soft suit and link suit of G are linked by G links for interactions between
the G hunk configuration representation and G infogranules;
• link suit and hard suit are linked by G links for interactions between the
G hunk configuration representation and hunks in the environment.
The interactive processes during transforming inputs of c-granules into out-
puts of c-granules is influenced by
210 A. Jankowski, A. Skowron, R. Swiniarski
1. interaction of hunks pointed out by link suit;
2. interaction of pointed hunks with relevant parts of configuration in link suit.
Agent can establish, remember, recognize, process and modify relations be-
tween c-granules or/and hunks.
A general structure of c-granules is illustrated in Figure 1.
agent behavioral pattern
description used by agent for c-GRANULE G G links between G hunk
c-granule identification (at the local agent ag time) configuration representation
and G infogranules
input/output c-granules (of control type) type defined by
acceptance
input type defined postconditions
by acceptance G name G status G type
G infogranules (e.g., G specification, G G soft_suit
preconditions
implementation and manipulation method(s))
output c-granule
input c-granule G infogranular representation of hunk of admissible
of admissible configurations + G links + output type
input type representations of G elementary actions G link_ suit
environment of interacting hunks G hard_suit
encoding G soft_suit, G link_suit and
implementing G computations G links between hunks
and their configurations)
G interactions with environments
operational semantics: implementation and manipulation method(s) of admisssible
cases of
name, i-ointerpretation (implementation)
types, expected semantics of interactive computations with goals specified by
specification (abstract semantics), i.e., procedures for performing interactive computations by the agent
specification, operational semantics
ag control; this includes checking the expected properties of I/O/C c-granules and other conditions,
e.g., after sensoryspecification
measurements and/or action realisation using links to hunk configuration(s) with the
structure defined by G link_suit;
possible cases of interpretation are often defined relative to different universes of c-granules and hunks)
Fig. 1. General structure of c-granules
In Figure 2 we illustrate how the abstract definition of operation from soft link
interacts with other suits of c-granule. It is necessary to distinguish two cases.
In the first case, the results of operation ⊗ realized by interaction of hunks are
consistent with the specification in the suit link. In the second case, the result
specified in the soft suit can be treated only as an estimation of the real one
which may be different due to the unpredictable interactions in the hard suit.
Figure 3 illustrates c-granules corresponding to sensory measurement. Note that
in this case, the parameters fixed by the agent control may concern sensor selec-
tion, selection of the object under measurement by sensor and selection of sensor
parameters. They are interpreted as actions selected from the link suit. In the
perception of configuration of hunks of c-granule are distinguished infogranules
representing sensor, object under measurement and the configuration itself. The
links selected by the agent control represent relations between states of hunks
and infogranules corresponding to them in the link suit.
Interactive Complex Granules 211
infogranues
G1 in soft_suit
corresponding
to specification and
G2 G1 G 2
implementation
soft_suit of operation
programs, actions or
plans implementing
‘G1’ representation
… ‘G1 G2’ of configuration of hunks for
‘G2’
consisting of representations of
link_suit arguments of , programs for
computing , etc.
links for storing
infogranules G1
and G2 in hunks
h1
… h links for reading a
h2
representation of
hard_suit G1 G2 from h
Fig. 2. Explanation of roles of different suits of a c-granule for operation ⊗
Figure 4 illustrates how an interactive information (decision) system is cre-
ated and updated during running of c-granule implementation according to sce-
nario(s) defined in the soft suit and related G links. Such information (decision)
systems are used for recording information about the computation steps during
c-granule implementation run. Note that the structure of this information sys-
tem is different from the classical definition [14, 15, 18]. In particular, this system
is open because of links to physical objects as well as interactions are changing
(often in unpredictable way) in time. In our approach, the agent can be also
interpreted as c-granule. However, this is a c-granule of higher order with em-
bedded control. One can also consider another situation when the c-granules are
autonomous but this is out of scope of this article. Instead of this one can con-
sider interactions in societies of agents. We assume that for any agent ag there is
distinguished a family of elementary c-granules and constructions on c-granules
leading to more compound c-granules. The agent ag is using the constructed
granules for modeling attention and interaction with the environment. Note that
for any new construction on elementary granules (such as network of c-granules)
should be defined the corresponding c-granule. This c-granule should have ap-
propriate soft suit, link suit and hard suit so that the constructed c-granule will
satisfy the conditions of the new c-granule construction specification. Note that
one of the constraints on such construction may follow from the interactions
which the agent ag will have at the disposal in the uncertain environment.
212 A. Jankowski, A. Skowron, R. Swiniarski
specification given by input
c-granule
soft_suit output:
input:
perform the sensory information system
measurement by sensor s in specification representing the
the hunk configuration h implementation scenario sensory measurement
process by sensor s
(i) establish links with the
sensor and the hunk link_suit:
under measurement, with the representation of the
(ii) in interaction with dynamic hunk configuration h
link_suit select the and links from sensor
relevant action ac and representation to the physical
parameters p for the sensor s labeled by selected
action relevant for ac(p) (action ac with relevant
initiation the sensory parameters p) initiating the
measurement, sensory measurement and the
(iii) record in the s hunk on which the
corresponding measurement is performed
information system the
results of sensory
measurements on the hard_suit: dynamic hunk
basis of the properties of configuration h in the
the states of sensor environment with the
during the measurement physical sensor s
process.
Fig. 3. Interactions caused by sensors
3 Agent Architecture Framework
Agents may be treated as generalized c-granules with embedded control struc-
ture.
Any agent ag is defined over several classes of c-granules. Among them are:
– senbot (sensory bot) - class of c-granules representing possible states of the
agent sensory measurements with at most one distinguished c-granule at the
local time moment t of agent ag;
– imbot (imagination bot)- class of all possible c-granules which can be con-
structed by the agent ag from sensory measurements with at most one dis-
tinguished c-granule at the local time moment t of agent ag;
– embot (emotional bot)- subclass of imbot class representing emotional con-
cepts of the agent ag;
– nebot (needs bot)- subclass of imbot class representing concepts of the agent
ag needs;
– enabot (environment action bot) - subclass of imbot class specifying the
agent ag elementary actions in the environment;
– imobot (imagination operation bot) - subclass of imbot class specifying the
agent ag elementary operations (different from elementary actions) on c-
granules from imbot;
Interactive Complex Granules 213
link_suit consisting of hunk configuration representation at time t together
with links to hunks (labeled by elementary actions or /and plans);
input c-granules for the considered c-granule are defined, e.g., by
some parts of the configuration representation or values of
control paremeters
decisions
S(t) values of decision
values of
values of attributes at time
conditional
control t’’>t’
(hierarchical)
parameters corresponding to
attributes
at time t output c-granules
at time t‘ >t
for for the
representing
conditional considered c-
curent results of
attributes granule
measurements
row of decision system corresponding to implementation of c-granule
links (labeled by actions or /and plans) at time t represent relations between
infogranules and hunks defined by representation of hunk configuration of the
global state S(t) defined by the agent control system
Fig. 4. Example: Row of interactive information (decision) system corresponding to
registration of computation of c-granule according to implementation scenario
– abot (attention bot) - subclass of imbot class representing c-granules cur-
rently under attention by the agent ag;
– activebot - subclass of imbot class representing c-granules currently active;
– passivebot - subclass of imbot class representing c-granules currently passive;
– metbot (method bot) - subclass of imbot representing methods of manipu-
lation on c-granules (construction, destruction, modification, join, classifiers
construction);
– metabot (method adaptation bot) subclass of imbot representing c-granules
used for adaptation or/and modification of the given methods of manipula-
tion on c-granules.
The language of c-granule names consists of
– set of names of existing c-granules;
– set of names of new generated c-granules.
Types of objects relative to c-granules in imbot:
– set of types of existing c-granules;
– set of types of new generated c-granules.
There are some distinguished c-granules of the agent ag:
– Meaning relation (Mean) - a distinguished c-granule representing a relation
between c-granules and their names.
214 A. Jankowski, A. Skowron, R. Swiniarski
– Type relation (TypeMean) - a distinguished c-granule representing a relation
between c-granules and their types.
– Reference relation (Ref) - a distinguished c-granule representing a relation
between c-granules and ’related’ names.
– Jbot (Judgment bot) - a distinguished c-granule representing actual collec-
tion of strategies of approximate reasoning used by the agent ag for judgment
and risk assessment in the current environment and agent situation.
– Cobot (control bot) - a distinguished c-granule representing actual collection
of strategies of approximate reasoning used by the agent ag for control,
adaptation, and modification of all the agent ag c-granules.
– Metacobot (meta-control bot) - a distinguished c-granule representing actual
collection of strategies of approximate reasoning used by the agent ag for
cobot control, adaptation, and modification.
The generalized c-granules corresponding to agents are defined using also the
above classes of c-granules for defining corresponding suits of such generalized
c-granules. The details of such construction will be presented in our next papers.
Here, we would like to note only that there is a quite general approach for defining
new c-granules from the simpler already defined.
Figure 5 illustrates an idea of transition relation related to a given agent ag.
The relation is defined between configurations of ag at time t and the measure-
ment time next to t. A configuration of ag at time t consists of all configurations
of c-granules existing at time t. A configuration of c-granule G at time t consists
of G itself as well as all c-granules selected on the basis of links in the link suit of
G at time t. These are, in particular all c-granules pointed by links correspond-
ing to the c-granules stored in the computer memory during the computation
process realised by c-granule as well as c-granules corresponding to perception
at time t of the configuration of hunks at time t.
agent configuration at
the time unit next to t
(not necessarily
agent configuration at satisfying the
time t predicted results):
(with a predicted the result of
granule’s structure at interactions caused
the time unit next to t) by undertaken actions
and unpredicted
interactions with the
environment
(parallel) realization by the
agent of selected actions,
sensory measurements,
new information granule
construction/destruction,
etc.
Fig. 5. Transiton relation of the agent ag
Interactive Complex Granules 215
4 Societies of Agents and Communication Languages
We assume that the agents can perceive behavioral patterns of other agents of
their groups and based on this they can try to exchange some messages [10].
It is worthwhile to mention that at the beginning agents do not have common
understanding of the meaning of such messages. In the consequence, this leads
to misunderstanding, not comfortable situation for agents (in terms of hierarchy
of their needs represented by nebot). However, after series of trials they have a
chance to set up common meaning of some behavioral patterns. In other words,
they start to create common c-granules which use agreed links to other hunks
or infogranules and also descriptions of some details about actions related to
meaning or methods of implementation of the infogranule contents. For exam-
ple, at the beginning the messages could be linked to warning situations or to
identifications of some sources for satisfiability of some agent needs. This kind
of simple messages could be passed by very simple behavioral pattern. Next,
based on these very simple behavioral patterns the agents can develop more
compound messages related to c-granules corresponding to common plans of co-
operation of group of agents or/and competition with other groups of agents.
This very general framework could be implemented in many ways using differ-
ent AI paradigms. Especially, many models from Natural Computing could be
quite helpful (e.g., modification of cellular automata or evolutionary program-
ming). However, our proposal is to implement this general scheme by agents
having soft suit and link suit built up on the hierarchies of interactive infor-
mation (decision) systems linked to configurations of hunks. Starting from the
simplest case when we have just one attribute and one message to be passed up
to quite complex system this approach based on rough sets is quite convenient
for implementation by computers well prepared for manipulation on tables of
data.
It has to be underlined that the behavioral patterns are complex vague con-
cepts. Hence, some advanced methods for approximation of these concepts should
be used. Usually these methods are based on hierarchical learning (see, e.g., [11,
1]). Note that often in satisfiability checking for vague concept, actions or/and
plans are used. In the rough set approach it is important to remember that
the attribute values are given only for some examples from reality. Moreover, if
we use a large number of attributes or/ and hierarchical learning this will not
guarantee the exact description of reality in terms of perceived vague concepts.
Languages of agents consist of partial descriptions of situations (or their
indiscernibility or similarity classes) perceived by agents as well as description of
approximate reasoning schemes about the situations and their changes by actions
and /or plans. The situations may be represented in hierarchical modeling by
structured objects (e.g., relational structures over attribute value vectors or/and
indiscernibility (similarity classes) of such structures). In reasoning about the
situation changes one should take into account that the predicted actions or/and
planes may depend not only on the changes of past situations but also on the
performed actions and plane in the past. This is strongly related to the idea of
perception pointed out in [12]:
216 A. Jankowski, A. Skowron, R. Swiniarski
The main idea of this book is that perceiving is a way of acting. It
is something we do. Think of a blind person tap-tapping his or her way
around a cluttered space, perceiving that space by touch, not all at once,
but through time, by skillful probing and movement. This is or ought to
be, our paradigm of what perceiving is.
Figure 6 illustrates this idea.
features higher
of level
history of sensory
histories action
measurements and
selected lower level …
actions over a period of
time
…
time a1 … ac1 …
x1 1
x2 2
… …
Fig. 6. Action in perception.
Note that the expression of the language may be used without its ’support’ in
corresponding link suit and hard suit of c-granules under the assumption that
there are fixed coding methods between expressions and hunks by the agent.
However, the languages should contain more general expressions for communi-
cation usually requiring the usage of expressions representing classes of hunks
rather than single hunks. This follows from the fact that the agents have bounded
abilities for discernibility of perceived objects. In our approach the situations and
reasoning schemes about situations are represented by c-granules.
Note that different behavioral patterns may be indiscernible relative to the set
of attributes used by the agent. Hence, it follows that the agents perceive objects
belonging to the same indiscernibility or/and similarity class in the same way.
This is an important feature making it possible to use generalization by agents.
For example, the situations classified by a given set of characteristic functions
of induced classifiers (used as attributes) may be indiscernible. On the other
hand, a new situation unseen so far may be classified to indiscernibility classes
which allows agents to make generalizations. The new names created by agents
are names of new structured objets or their indiscernibility (similarity) classes.
Agents should be equipped with adaptation strategies for discovery of new
structured objects and their features (attributes). This is the consequence of the
fact that the agents are dealing with vague concepts. Hence, the approximations
of these concepts represented by the induced classifiers evolve with changes in
uncertain data and imperfect knowledge.
Interactive Complex Granules 217
5 Conclusions and Future Research
The outlined research on the nature of interactive computations is crucial for
understanding complex systems. Our approach is based on complex granules
(c-granules) performing computations through interaction with physical objects
(hunks). Computations of c-granules are controlled by the agent control. More
compound c-granules create agents and societies of agents. Other issues outlined
in this paper such as interactive computations performed by societies for agents,
especially communication language evolution and risk management in interactive
computations will be discussed in more detail in our next papers.
References
1. J. Bazan. Hierarchical classifiers for complex spatio-temporal concepts. Transac-
tions on Rough Sets IX: Journal Subline LNCS 5390 (2008) 474–750.
2. A. Einstein. Geometrie und Erfahrung (Geometry and Experience). Julius Sprin-
ger, Berlin, 1921.
3. D. Goldin, S. Smolka, P. Wegner (Eds.). Interactive Computation: The New
Paradigm. Springer, 2006.
4. Y. Gurevich. Interactive algorithms 2005. In: Goldin et al. [3], pp. 165–181.
5. M. Heller. The Ontology of Physical Objects. Four Dimensional Hunks of Matter.
Cambridge Studies in Philosophy, Cambridge University Press, Cambridge, UK,
1990.
6. A. Jankowski, A. Skowron. A wistech paradigm for intelligent systems. Transac-
tions on Rough Sets VI: Journal Subline LNCS 4374 (2007) 94–132.
7. A. Jankowski, A. Skowron. Wisdom technology: A rough-granular approach. In:
M. Marciniak, A. Mykowiecka (Eds.), Bolc Festschrift, Springer, Heidelberg, Lec-
tures Notes in Computer Science, vol. 5070. 2009, pp. 3–41.
8. A. Jankowski, A. Skowron. Practical Issues of Complex Systems Engineering:
Wisdom Technology Approach. Springer, Heidelberg, 2014. (in preparation).
9. L. Marsh. Stigmergic epistemology, stigmergic cognition. Journal Cognitive Sys-
tems 9 (2008) 136–149.
10. M. Minsky. Emotion Machine: Commonsense Thinking, Artificial Intelligence, and
the Future of the Mind. Simon & Schuster, New York, 2006.
11. S. H. Nguyen, J. Bazan, A. Skowron, H. S. Nguyen. Layered learning for concept
synthesis. Transactions on Rough Sets I: Journal Subline LNCS 3100 (2004) 187–
208.
12. A. Noë. Action in Perception. MIT Press, 2004.
13. A. Omicini, A. Ricci, M. Viroli. The multidisciplinary patterns of interaction from
sciences to computer science. In: Goldin et al. [3], pp. 395–414.
14. Z. Pawlak. Information systems - theoretical foundations. Information Systems 6
(1981) 205–218.
15. Z. Pawlak. Rough Sets: Theoretical Aspects of Reasoning about Data, System
Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic
Publishers, Dordrecht, The Netherlands, 1991.
16. W. Pedrycz, S. Skowron, V. Kreinovich (Eds.). Handbook of Granular Computing.
John Wiley & Sons, Hoboken, NJ, 2008.
17. A. Skowron, J. Stepaniuk, R. Swiniarski. Modeling rough granular computing
based on approximation spaces. Information Sciences 184 (2012) 20–43.
218 A. Jankowski, A. Skowron, R. Swiniarski
18. A. Skowron, Z. Suraj (Eds.). Rough Sets and Intelligent Systems. Professor Zdzis-
law Pawlak in Memoriam. Series Intelligent Systems Reference Library, Springer,
2013.
19. A. Skowron, M. Szczuka. Toward interactive computations: A rough-granular ap-
proach. In: J. Koronacki, Z. Raś, S. Wierzchoń, J. Kacprzyk (Eds.), Advances in
Machine Learning II: Dedicated to the Memory of Professor Ryszard S. Michalski,
Springer, Heidelberg, Studies in Computational Intelligence, vol. 263. 2009, pp.
23–42.
20. A. Skowron, P. Wasilewski. Information systems in modeling interactive compu-
tations on granules. In: M. Szczuka, M. Kryszkiewicz, S. Ramanna, R. Jensen,
Q. Hu (Eds.), Proceedings of RSCTC 2010, Springer, Heidelberg, Lectures Notes
in Computer Science, vol. 6086. 2010, pp. 730–739.
21. A. Skowron, P. Wasilewski. Information systems in modeling interactive compu-
tations on granules. Theoretical Computer Science 412(42) (2011) 5939–5959.
22. A. Skowron, P. Wasilewski. Toward interactive rough-granular computing. Control
& Cybernetics 40(2) (2011) 1–23.
23. A. Skowron, P. Wasilewski. Interactive information systems: Toward perception
based computing. Theoretical Computer Science 454 (2012) 240–260.
24. V. Vapnik. Statistical Learning Theory. John Wiley & Sons, New York, NY, 1998.
25. L. A. Zadeh. Outline of a new approach to the analysis of complex systems and
decision processes. IEEE Trans. on Systems, Man and Cybernetics SMC-3 (1973)
28–44.
26. L. A. Zadeh. Fuzzy sets and information granularity. In: Advances in Fuzzy Set
Theory and Applications, North-Holland, Amsterdam. 1979, pp. 3–18.
27. L. A. Zadeh. Toward a theory of fuzzy information granulation and its centrality
in human reasoning and fuzzy logic. Fuzzy Sets and Systems 90 (1997) 111–127.
28. L. A. Zadeh. A new direction in AI: Toward a computational theory of perceptions.
AI Magazine 22(1) (2001) 73–84.