Interactive Rough-Granular Computingin Wisdom Technology

Andrzej Jankowski1, Andrzej Skowron2, and Roman Swiniarski3

1 Institute of Computer Science, Warsaw University of TechnologyNowowiejska 15/19, 00-665 Warsaw, Poland

a.jankowski@ii.pw.edu.pl2 Institute of Mathematics, Warsaw University

Banacha 2, 02-097 Warsaw, Polandskowron@mimuw.edu.pl

3 Department of Computer Science, San Diego State University5500 Campanile Drive San Diego, CA 92182, USA

andInstitute of Computer Science Polish Academy of Sciences

Jana Kazimierza 5, 01-248 Warsaw, Polandrswiniarski@mail.sdsu.edu

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. Understanding of interactions is the critical issue of complexsystems. Interactions in physical world are represented by informationgranules. We propose to model complex systems by interactive intelli-gent systems (IIS) created by societies of agents. Computations in IISare based on complex granules (c-granules, for short). Adaptive judge-ment allows us to reason about c-granules and interactive computationsperformed on them. In adaptive judgement, different kinds of reason-ing are involved such as deduction, induction, abduction or reasoning byanalogy as well as intuitive judgement. In modeling of mental parts of c-granules, called information granules (infogranules, for short), we use theapproach based on the rough set methods in combination with other softcomputing approaches. Issues related to interactions among objects inthe physical and mental worlds as well as adaptive judgement belong tothe fundamental issues in Wisdom Technology (WisTech). In the paperwe concentrate on some basic issues related to interactive computationsover c-granules. WisTech was developed over years of work on differentreal-life projects. It can also be treated as a basis in searching for solu-tions of problems in such areas as Active Media Technology and WisdomWeb of Things.

Key words: granular computing, rough sets, interactions, informationgranule, physical object, complex granule, interactive intelligent system,active media technology

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[25, 27]: Information granulation can be viewed as a human way of achievingdata compression and it plays a key role in implementation of the strategy ofdivide-and-conquer in human problem-solving.

The concept of granulation is rooted in the concept of a linguistic variableintroduced by Lotfi Zadeh in 1973. Information granules are constructed start-ing from some elementary ones. More compound granules are composed of finergranules that are drawn together by indistinguishability, similarity, or function-ality [26].

Understanding of interactions of objects on which are performed computa-tions is fundamental for modeling of complex systems [3]. This requirement isfundamental for modeling of complex systems [3]. For example, in [13] this isexpressed in the following way: [...] interaction is a critical issue in the un-derstanding of complex systems of any sorts: as such, it has emerged in severalwell-established scientific areas other than computer science, like biology, physics,social and organizational sciences.

Interactive Rough Granular Computing (IRGC) is an approach for modelinginteractive computations (see, e.g., [19, 21–23]) based on rough sets in combi-nation with other soft computing approaches such as fuzzy sets or evolutionarycomputing, and also with machine learning and data mining techniques. Thenotion of the highly interactive granular system is clarified as the system inwhich intrastep interactions [4] with the external as well as with the internalenvironments take place.

We extend the existing approach by introducing complex granules (c-granules)making it possible to model interactive computations performed by agents oper-ating in the physical world. Any c-granule consists of three components, namelysoft suit, link suit and hard suit. These components are making it possible todeal with such abstract objects from soft suit as infogranules as well as withphysical objects from hard suit. The link suit of a given c-granule is used as akind of c-granule interface for expressing interaction between soft suit and andhard suit. Any agent operates in a local world of c-granules. The agent controlis aiming to control computations performed by c-granules from this local worldfor 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 theenvironment on the way to achieve their targets. C-granules are also used byagents for representation of perception of interactions in the physical world. Dueto the bounds of the agent perception abilities usually only a partial informationabout the interactions from physical world may be available for agents. Hence,in particular the results of performed actions by agents can not be predictedwith certainty.

The reasoning making it possible to derive relevant information c-granulesfor solutions of the target tasks is based on interactions between many c-granules

and is called adaptive judgement. Adaptive rational judgement and adaptive in-tuitive judgement are two main kinds of adaptive judgement [8]. In some sensethis is some kind of dialogue and/or discussion between c-granules representingdifferent perspectives for the problem solving. For example, any agent classifyinga new object typically uses some arguments for and against. One should makesome kind of dialogue between such “arguments”. It is a good idea to distinguishdialogue and discussion [2]: A key difference between a dialogue and an ordinarydiscussion is that, within the latter, people usually hold relatively fixed positionsand argue in favor of their views as they try to convince others to change. Whena given agent has enough time and recourses then this agent can continue suchkind of “internal agent dialogue” until acceptable solutions will be achieved. Itis a good example of “slow thinking” [9]. However, in practice usually agent doesnot have “enough time and recourses”. Thus agent has to make the decision fast.In many practical cases “lack of decision is the worst decision”. In order to “sur-vive” in such situations agent has to make a decision based on agent hierarchy ofvalues representing current agent priorities of needs, habits, intuitions, emotionsand others. This way of thinking corresponds in many aspects to “fast think-ing” (Kehneman and Tversky [9]) or it corresponds to concept of “discussions”([2]). In some sense this approach to problem solving has roots in the Socratesapproach to logic. According to “Dialogues” of Plato, Socrates prefers conceptof “dia-logos” instead of logos. In other words, the problem solving process is aresult of some kind of interaction processes like “dialogue” or/and “discussion”between agent internal c-granules and/or with other agents. Two agent processesare important for realisation of interactions:

1. Adaptive intuitive judgement - corresponds to making decisions mainly basedon agent current hierarchy of values which represents current agent prioritiesof needs, habits, intuitions, emotions and others. They are computed fastusing simple heuristics. One can observe strong relationships of adaptiveintuitive judgement with “fast thinking” [9] or “internal discussions” [2] aswell as to some extent with reactive agents. The rules of adaptive intuitivejudgement are subject of continuous adaptive change toward improvementof the quality of non perfect judgement (it is result of interactions withenvironment).

2. Adaptive rational judgement - corresponds to making decisions mainly basedon rational (i.e., acceptable and verifiable by agent) inference rules. Onecan observe strong relationships of adaptive rational judgment with “slowthinking” [9], “internal dialogue” [2] as well as to some extent with deliber-ative agents. The rules of adaptive rational judgement are subject of ratherrare changes (relative to the dynamic speed of changes of the analyzed phe-nomena). The changes typically are results of important new discoveries,paradigm shifts (e.g., science revolution according to Thomas Kuhn) and/orlanguage meaning shifts.

Definitely, in the language used by agents for dealing with adaptive judgmentsome deductive systems known from logic may be applied to closed worlds forreasoning about knowledge relative to them. This may happen, e.g., if the agent

languages are based on classical mathematical logic. However, if we move to in-teractions in open worlds then new specific rules or patterns relative to a givenagent or group of agents in such worlds should be discovered. Such rules or pat-terns are influenced by uncertainty because they are induced by agents underuncertain knowledge about the environment. Hence, considering only the abso-lute truth becomes unsatisfactory. Deduction and induction as well as abductionor analogy based reasoning may be involved in adaptive judgement. Among thetasks for adaptive judgement are the following ones supporting reasoning toward:searching for relevant approximation spaces, discovery of new features, selectionof relevant features, rule induction, discovery of inclusion measures, strategies forconflict resolution, adaptation of measures based on the minimum descriptionlength principle, reasoning about changes, perception (action and sensory) at-tributes selection, adaptation of quality measures over computations relative toagents, adaptation of object structures, discovery of relevant context, strategiesfor knowledge representation and interaction with knowledge bases, ontology ac-quisition and approximation, learning in dialogue of inclusion measures betweeninformation granules from different languages (e.g., the formal language of thesystem and the user natural language), strategies for adaptation of existing mod-els, strategies for development and evolution of communication language amongagents in distributed environments, strategies for risk management in distributedcomputational systems.

The question arises about the logical tools relevant for the above mentionedtasks of adaptive judgement on computations performed on c-granules. First letus observe that the satisfiability relations in the IRGC framework can be treatedas tools for constructing new c-granules. If fact, for a given satisfiability relation,the semantics of formulas over c-granules relative to this relation is defined. Inthis way the candidates for new relevant c-granules can be obtained. We wouldlike to emphasize a very important feature. The relevant satisfiability relationfor the considered problems is not given but it should be induced (discovered)on the basis of a partial information encoded in information (decision) systemsobtained as results of aggregation (e.g., join with constraints [17]) of other infor-mation (decision) systems. For real-life problems, it is often necessary to discovera hierarchy of satisfiability relations before we obtain the relevant target level.Information granules constructed at different levels of this hierarchy finally leadto relevant ones for approximation of complex vague concepts expressed in natu-ral language. The rough set approach in combination with other soft computingapproaches is used in inducing approximations of complex vague concepts andreasoning schemes over them [20].

Issues related to interactions among objects in the physical and mental worldsas well as to adaptive judgement about interactive computations on c-granulesbelong to the fundamental issues in Wisdom Technology (WisTech) [6, 7] basedon the following meta-equation:

WISDOM = INTERACTIONS+ADAPTIVE JUDGEMENT+KNOWLEDGE.

Wistech can be treated as a basis in searching for solutions of problems relatedto the goals of Active Media Technology (AMT) as well as of Wisdom Web ofThings (W2T) [28, 10].

In Section 2 a general structure of c-granules is described and some illus-trative examples are included. Moreover, some preliminary concepts related toagents performing computations on c-granules are discussed. Comments on riskmanagement in IIS are presented in Section 3.

This paper covers some issues of the keynote talk at AMT 2013.

2 Complex Granules and Physical World

In this section we discuss the basic concepts related to c-granule relative to agiven agent ag. Let us assume that the agent ag has access to a local clockmaking it possible to use the local time scale. In this paper we consider discretelinear time scale.

We distinguish several kinds of objects in the environment in which the agentag operates:

– physical objects (called also as hunks of matter, or hunks, for short) [5] suchas physical parts of agents or robots, specific media for transmitting informa-tion; we distinguish hunks called as artifacts used for labeling other hunks orstigmergic markers used for indirect coordination between agents or actions[11]; note that hunks may change in time and are perceived by the agentag as dynamic (systems) processes; any hunk h at the local time t of ag isrepresented by the state sth(t); the results of perception of hunk states byagent 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 isdenoted by G; G receives some inputs and produces some outputs; inputsand outputs of c-granule G are c-granules of the specified admissible types;input admissible type is defined by some input preconditions and the outputadmissible type is defined by some output postconditions, there are distin-guished inputs (outputs) admissible types which receive (send) c-granulesfrom (to) the agent ag control;

• G soft suit consists of

1. G name, describing the behavioral pattern description of the agentag corresponding to the name used by agent for identification of thegranule,

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, Gimplementation and manipulation method(s); any implementationdistinguished in infogranule is a description in the agent ag languageof 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-granulescan be delivered by the agent ag control (or by other c-granules), wealso assume that the outputs produced by a given c-granule dependalso on interactions of hunks pointed out by link suite as well assome other hunks from the environment - in this way the semanticsof c-granules is established;

• G link suit consists of1. 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 onhunks; in particular, links are pointing to the sensors or actuators inthe physical world used by the considered c-granule; using links theagent ag may, e.g., fix some parameters of sensors or/and actions,initiate sensory measurements or/and action performance; we alsoassume that using these links the agent ag may encode some infor-mation about the current states of the observed hunks by relevantinformation granules;

• G hard suit is created by the configuration of interacting hunks encodingG soft suit, G link suit and implementing G computations;

• soft suit and link suit of G are linked by G links for interactions betweenthe G hunk configuration representation and G infogranules;

• link suit and hard suit are linked by G links for interactions between theG hunk configuration representation and hunks in the environment.

The interactive processes during transforming inputs of c-granules into out-puts of c-granules are influenced by (i) interaction of hunks pointed out bylink suit and (ii) interaction of pointed hunks with relevant parts of configura-tion in link suit.

Agent can establish, remember, recognize, process and modify relations be-tween c-granules or/and hunks. Agents and societies of agents may be also rep-resented as (generalized) c-granules [7]. A general structure of c-granules is il-lustrated in Figure 1. Figure 2 illustrates c-granules corresponding to sensorymeasurement. Note that in this case, the parameters fixed by the agent con-trol may concern sensor selection, selection of the object under measurement bysensor and selection of sensor parameters. They are interpreted as actions se-lected from the link suit. In the perception of hunk configuration of c-granule aredistinguished infogranules representing sensor(s), object(s) under measurementand the configuration itself. The links selected by the agent control representrelations between states of hunks and infogranules corresponding to them in thelink suit. Figure 3 illustrates how an interactive information (decision) systemis created and updated during running of c-granule implementation accordingto scenario(s) defined in the soft suit and related G links. Such information (de-cision) systems are used for recording information about the computation steps

name, i-o types, expected semantics specification, operational semantics

specification

G soft_suit

G hard_suit

agent behavioral pattern description used by agent for

c-granule identification

input type defined by acceptance preconditions

G links between G hunk configuration representation

and G infogranules

environment of interacting hunks encoding G soft_suit, G link_suit and

implementing G computations

operational semantics: implementation and manipulation method(s) of admisssible cases of interpretation (implementation) of interactive computations with goals specified by

specification (abstract semantics), i.e., procedures for performing interactive computations by the agent ag control; this includes checking the expected properties of I/O/C c-granules and other conditions,

e.g., after sensory 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)

c-GRANULE G (at the local agent ag time)

G infogranules (e.g., G specification, G implementation and manipulation method(s))

G name

input c-granule of admissible

input type

input/output c-granules (of control type)

output c-granule of admissible output type

G interactions with environments

G link_ suit

G infogranular representation of hunk configurations + G links +

representations of G elementary actions

type defined by acceptance

postconditions

G links between hunks

and their configurations)

G type G status

Fig. 1. General structure of c-granules

during the c-granule implementation run. Note that the structure of such infor-mation systems is different from the classical definition [14, 15, 20]. In particular,such systems are open due to the fact that links to physical objects as well asinteractions are changing (often in unpredictable way) in time. We assume thatfor any agent ag there is distinguished a family of elementary c-granules andconstructions on c-granules leading to more compound c-granules. The agent agis using the constructed granules for modeling attention and interaction with theenvironment. Note that for any new construction on elementary granules (suchas network of c-granules) should be defined the corresponding c-granule. Thisc-granule should have appropriate soft suit, link suit and hard suit so that theconstructed c-granule will satisfy the conditions of the new c-granule construc-tion specification. Note that one of the constraints on such construction mayfollow from the interactions which the agent ag will have at the disposal in theuncertain environment.In the construction o new c-granules information systemsplay the fundamental role (see, e.g., [1, 21, 17]).

It is worthwhile mentioning that the interactive computations based on c-granules are different from Turing computations. In IRGC computations areprogressing due to controlled by actions interactions among different physicalobjects and their interactions with inforgranules. One can imagine operationsnon-computable in the Turing sense which are computable in IRGC. In Figure 4we illustrate how the abstract definition of operation from soft link interacts

(physical) context of interactive

measurement processes selected by

control

measurement result infogranule

measurement action plan infogranule

G hard_suit G link_suit

perception of hunk configuration

Inclusing sensor(s) and measurement target(s)

representation of sensor(s)

representation of hunks under

measurements

G elementary actions related to configuration of sensor(s)

and measurement targets

hunks under measurements

sensor(s)

other hunks

links between hunks and perception of hunk configuration

links between hunks and

actions

G soft_suit

Fig. 2. Interactions caused by sensors.

with other suits of c-granule. It is necessary to distinguish two cases. In the firstcase, the results of operation ⊗ realized by interaction of hunks are consistentwith the specification in the suit link. In the second case, the result specified inthe soft suit can be treated only as an estimation of the real one returned as theresult of interactions which may be different from the estimated result due tothe unpredictable interactions in the hard suit.

A transition relation related to a given agent ag is defined between configu-rations of ag at time t and the time moment next to t. A configuration of ag attime t consists of all configurations of c-granules existing at time t. A configura-tion of c-granule G at time t consists of G itself as well as all c-granules selectedon the basis of links in the link suit of G at time t. These are, in particular allc-granules pointed by links corresponding to the c-granules stored in the com-puter memory during the computation process realised by c-granule as well asc-granules corresponding to perception at time t of the configuration of hunksat time t.

Note that the transition relation is making it possible to predict the nextpossible configurations. However, the real successive configuration may be dif-ferent from all of the predicted ones due to unpredictable interactions in theenvironment.

Languages of agents consists of special c-granules called expressions. Fromone hand side any expression may be used without its ’support’ in correspond-

S(t) values of control

parameters at time t

for conditional attributes

values of decision attributes at time

t’’>t’corresponding to output c-

granules for the considered c-

granule

values of conditional

(hierarchical) attributes

at time t‘ >t representing

curent results of measurements

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

link_suit consisting of representation of configurations of hunks at time t together with links to hunks (labeled by elementary actions or /and plans); some parts of the

configuration represent input c-granules for the considered c-granule

decisions

row of decision system corresponding to implementation of c-granule

Fig. 3. Example: Row of interactive information (decision) system corresponding toregistration of computation of c-granule according to implementation scenario.

ing link suit and hard suit of the c-granule defining the expression, i.e., onlysoft suit may fully characterize expression. This can be done under the assump-tion that there are fixed reliable coding methods (representing, e.g., reading andstoring methods) between soft suit and hard suit of the expression by the agent.On the other hand, under the same assumption as before, one may consideronly hard link as an object characterizing the considered expression. Expres-sions for communication are usually representing classes of hunks rather thansingle hunks. This follows from the fact that the agents have bounded abilitiesfor discernibility of perceived objects. Different behavioral patterns may be in-discernible relative to the set of attributes used by the agent. Hence, it followsthat the agents perceive objects belonging to the same indiscernibility or/andsimilarity class in the same way. This is an important feature making it possibleto use generalization by agents. For example, the situations classified by a givenset of characteristic functions of induced classifiers (used as attributes) may beindiscernible. On the other hand, a new situation unseen so far may be classifiedto indiscernibility classes which allows agents to make generalizations. The newnames created by agents are names of new structured objets or their indiscerni-bility (similarity) classes. Languages of agents consist of partial descriptions ofsituations (or their indiscernibility or similarity classes) perceived by agents aswell as description of approximate reasoning schemes about the situations andtheir changes by actions and/or plans. The situations may be represented in hier-archical modeling by structured objects (e.g., relational structures over attributevalue vectors or/and indiscernibility (similarity classes) of such structures). Inreasoning about the situation changes [18] one should take into account that thepredicted actions or/and planes may depend not only on the changes recognizedin the past situations but also on the performed actions and plans in the past.

G1

G2 G1 G2

soft_suit

‘G1’

‘G2’ ‘G1 G2’

link_suit

h1

h2 h

hard_suit

links for storing infogranules G1 and G2 in hunks

links for reading a representation of

G1 G2 from h

representation of configuration of hunks for consisting of representations of

arguments of , programs for computing , etc.

…

…

programs, actions or plans implementing

infogranues in soft_suit

corresponding to specification and

implementation of operation

Fig. 4. Computability of operation ⊗ in IRGC.

This is strongly related to the idea of perception pointed out in [12]: The mainidea of this book is that perceiving is a way of acting. It is something we do. Thinkof a blind person tap-tapping his or her way around a cluttered space, perceivingthat space by touch, not all at once, but through time, by skillful probing andmovement. This is or ought to be, our paradigm of what perceiving is. Agentsshould be equipped with adaptation strategies for discovery of new structuredobjects and their features (attributes). This is the consequence of the fact thatthe agents are dealing with vague concepts. Hence, the approximations of theseconcepts represented by the induced classifiers evolve with changes in uncertaindata and imperfect knowledge.

3 Risk Managemant in IIS

For the risk management in IIS one of the most important task is to developstrategies for inducing approximations of vague complex concepts which are nextused for activation of actions performed by agents on the basis of satisfiability(to a degree) of these concepts in a given situation. A typical example is thestatement of the form: “now we do have very risky situation”. The develop-ment of strategies for inducing approximations of such vague complex conceptsare based the activation of actions performed by agents. These vague complexconcepts are represented by the agent hierarchy of needs.

In risk management one should consider a variety of complex vague conceptsand relations between them as well as reasoning schemes related, e.g., to the

bow-tie diagram (see Figure 5). One can consider the mentioned above task

Input sensor and context data

Output sensor actions and scenario

plan recommendations

Cause1

Cause 2

Cause 3 Consequence4

Consequence 2

Consequence 3

Consequence 1

Event

Escalation controls

Mitigation and recovery controls

Prevention controls

Escalation factor

Risk consequnces ontology Risk sources ontology

Abduction + Induction + Deduction

RISK INFERENCE ENGINE based on practical wisdom implemented by

interactions + adaptive judgment + knowledge sources

Fig. 5. Bow-tie diagram.

of approximation of vague complex concepts initiating actions as the task ofdiscovery of complex games (see Figure 6) from data and domain knowledgewhich the agents are playing in the environment attempting to achieve theirtargets. The discovery process can be based on hierarchical learning supportedby domain knowledge [7, 1]. It is also worthwhile mentioning that such games areevolving in time when the data and knowledge about the approximated conceptsare changing (drifting in time) and the relevant adaptive strategies for suchgames are required. These adaptive strategies are used to control the behaviorof agents toward achieving by them targets. Note that also these strategies shouldbe learned from data and domain knowledge.

actions initiated on the basis of judgment about satisfiability (to a degree) of their guards

. . .

action guards: complex vague concepts

Fig. 6. Games based on complex vague concepts

4 Conclusions and Future Research

The outlined research on the nature of interactive computations is crucial forunderstanding 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. Morecompound c-granules create agents and societies of agents. Other issues outlinedin this paper such as interactive computations performed by societies for agents,especially communication language evolution and risk management in interac-tive computations the reader is referred to [7]. Further development of the IRGCbased on c-granules for risk management in real-life projects is one of our futureresearch direction. IRGC seems to be a good starting point for better under-standing computations in nature as well as for constructing the physical part ofthe statistical learning theory and unifying it with the mathematical part of thistheory (see motto of his article). Interactive computations based on c-granulescreate a good background for modeling computations in AMT and W2T. Yetanother research direction is related to relationships of interactive computabilitybased on c-granules and Turing computability.

Acknowledgements

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 Pol-

ish 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 experimental de-

velopment 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”.

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. D. Bohm, F. D. Peat. Science, Order, and Creativity. Bantam, New York, NY,1987. (pp. 240-247).

3. D. Goldin, S. Smolka, P. Wegner (Eds.). Interactive Computation: The NewParadigm. 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, 1990.6. A. Jankowski, A. Skowron. A WisTech paradigm for intelligent systems. In:

Transactions on Rough Sets VI: Journal Subline. pp. 94–132.7. A. Jankowski, A. Skowron. Practical Issues of Complex Systems Engineering:

Wisdom Technology Approach. Springer, Heidelberg, 2013.

8. D. Kahneman. Maps of bounded rationality: Psychology for behavioral economics.The American Economic Review 93 (2002) 1449–1475.

9. D. Kahneman. Thinking, Fast and Slow. Farrar, Straus and Giroux, New York,2011.

10. J. Liu. Active media technologies (AMT) from the standpoint of the WisdomWeb. In: Y. Li, M. Looi, N. Zhong (Eds.), Advances in Intelligent IT - ActiveMedia Technology 2006, Proceedings of the 4th International Conference on ActiveMedia Technology, AMT 2006, June 7-9, 2006, Brisbane, Australia. IOS Press,2006, Frontiers in Artificial Intelligence and Applications, vol. 138.

11. L. Marsh. Stigmergic epistemology, stigmergic cognition. Journal Cognitive Sys-tems 9 (2008) 136–149.

12. A. Noe. 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 AcademicPublishers, 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. Hierarchical modelling in searching for complex pat-terns: Constrained sums of information systems. Journal of Experimental andTheoretical Artificial Intelligence 17 (2005) 83–102.

18. A. Skowron, J. Stepaniuk, A. Jankowski, J. G. Bazan, R. Swiniarski. Rough setbased reasoning about changes. Fundamenta Informaticae 119(3-4) (2012) 421–437.

19. A. Skowron, J. Stepaniuk, R. Swiniarski. Modeling rough granular computingbased on approximation spaces. Information Sciences 184 (2012) 20–43.

20. A. Skowron, Z. Suraj (Eds.). Rough Sets and Intelligent Systems. Professor Zdzis-law Pawlak in Memoriam. Series Intelligent Systems Reference Library, Springer,2013.

21. A. Skowron, M. Szczuka. Toward interactive computations: A rough-granular ap-proach. In: J. Koronacki, Z. Ras, S. Wierzchon, J. Kacprzyk (Eds.), Advances inMachine Learning II: Dedicated to the Memory of Professor Ryszard S. Michalski,Springer, Heidelberg, Studies in Computational Intelligence, vol. 263. 2009, pp.23–42.

22. A. Skowron, P. Wasilewski. Information systems in modeling interactive compu-tations on granules. Theoretical Computer Science 412(42) (2011) 5939–5959.

23. A. Skowron, P. Wasilewski. Interactive information systems: Toward perceptionbased 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. Fuzzy sets and information granularity. In: Advances in Fuzzy Set

Theory and Applications, North-Holland, Amsterdam. 1979, pp. 3–18.26. 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) 111–127.27. L. A. Zadeh. A new direction in AI: Toward a computational theory of perceptions.

AI Magazine 22(1) (2001) 73–84.28. N. Zhong, J. H. Ma, R. Huang, J. Liu, Y. Yao, Y. X. Zhang, J. Chen. Research

challenges and perspectives on Wisdom Web of Things (W2T). The Journal ofSupercomputing 64 (2013) 862–882.