Interactive computations: toward risk management in interactive intelligent systems
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Abstract
Understanding the nature of interactions is regarded as one of the biggest challenges in projects related to complex adaptive systems. We discuss foundations for interactive computations in interactive intelligent systems (IIS), developed in the Wistech program and used for modeling complex systems. We emphasize the key role of risk management in problem solving by IIS. The considerations are based on experience gained in reallife projects concerning, e.g., medical diagnosis and therapy support, control of an unmanned helicopter, fraud detection algorithmic trading or fire commander decision support.
Keywords
Rough sets Granular computing Interactive computations Interactive intelligent systems Risk management Wisdom TechnologyMathematics Subject Classification
68T05 68T27 68T371 Introduction
Information granules (infogranules, for short) are widely discussed in the literature (see, e.g., Pedrycz et al. 2008). 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 issues related to interactions of infogranules with the physical world and to perception of interactions in the physical world represented by infogranules are not well elaborated yet. On the other hand the understanding of interactions is the critical issue of complex systems (Goldin et al. 2006) in which computations are progressing by interactions among information granules and physical objects.
We extend the existing approach to granular computing by introducing complex granules (cgranules, for short) (Jankowski 2015) making it possible to model interactive computations performed by agents in interactive intelligent systems (IIS) used for modeling of complex systems.
Any agent operates in a local world of cgranules. The agent control is aiming to control computations performed on cgranules from this local world for achieving the target goals.
Computations in IIS are based on cgranules. The risk management in IIS is of the great importance for the success of behaviors of individuals, groups and societies of agents. The risk management tasks are considered as control tasks aiming at achieving the satisfactory performance of (societies of) agents. The novelty of the proposed approach is the use of complex vague concepts as the guards of control actions. These vague concepts are represented, e.g., using domain ontologies. The rough set approach in combination with other soft computing approaches is used for approximation of the vague concepts relative to attributes (features) available to the risk management systems.
This paper is organized as follows. In Sect. 2 an introduction to Interactive Rough Granular Computing (IRGC) is presented. Issues related to reasoning based on adaptive judgment are included in Sect. 3. In Sect. 4 the relatonships of complex granules with the satisfiability relations are outlined. The approach to risk management based on IRGC is discussed in Sect. 6.
This paper covers some issues presented in the plenary talk at the 5th International Conference on Pattern Recognition and Machine Intelligence (PReMi 2013), December 10–14, 3013, Kolkata, India and is a summarization and an extension of Skowron et al. (2012), Jankowski et al. (2013, 2014a, 2014b). Interactive computations on cgranules may be used for modeling computations in Natural Computing Kari and Rozenberg (2008), Rozenberg et al. (2012), Ehrenfeucht et al. (2012). This issue is discussed in the paper in more detail.
2 Interactive rough granular computing (IRGC)
The essence of the proposed approach is the use of IIS implemented using IRGC (Jankowski and Skowron 2009; Skowron and Wasilewski 2011, 2012; Skowron et al. (2012; Jankowski 2015; Skowron et al. 2012). The approach is based on foundations for modeling of IRGC relevant for IIS in which computations are progressing through interactions (Goldin et al. 2006). In IRGC interactive computations are performed on objects called complex granules (cgranules, for short) linking information granules (Pedrycz et al. 2008) (or infogranules, for short) with physical objects called hunks (Heller 1990; Jankowski 2015).
Infogranules are widely discussed in the literature. They can be treated as specifications of compound objects (such as complex hierarchically defined attributes) together with scenarios of their implementations. Such granules are obtained as the result of information granulation (Zadeh 2001):
Infogranules belong to the concepts playing the main role in developing foundations for AI, data mining and text mining (Pedrycz et al. 2008). They grew up as some generalizations from fuzzy sets (Zadeh 1979, 1999, 2001), rough set theory and interval analysis (Pedrycz et al. 2008). The rough set approach is crucial because of necessity to deal with approximations of infogranules by the others, e.g., in inducing classifiers for complex vague concepts. The IRGC is based on the rough set approach in combination with other approaches to soft computing (such as fuzzy sets). However, the issues related to interactions of infogranules with the physical world and their relation to perception of interactions in the physical world are not well elaborated yet (Goldin et al. 2006; Vapnik 1998). On the other hand the understanding of interactions is the critical issue of complex systems (Omicini 2006):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 divideandconquer in human problemsolving.
We propose to model complex systems by IIS created by societies of agents. Computations in the discussed IIS are based on cgranules (Jankowski 2015) (see Fig. 1). Any cgranule consists of three components, namely soft_suit, link_suit and hard_suit. These components are making it possible to deal with such abstract objects from soft_suit as infogranules as well as with physical objects from hard_suit. The link_suit of a given cgranule is used as a kind of cgranule interface for handling interaction between soft_suit and and hard_suit.[...] interaction is a critical issue in the understanding of complex systems of any sorts: as such, it has emerged in several wellestablished scientific areas other than computer science, like biology, physics, social and organizational sciences.
Any agent operates in a local world of cgranules. The agent control is aiming to control computations performed on cgranules from this local world for achieving the target goals. Actions (sensors or plans) from link_suits of cgranules are used by the agent control in exploration and/or exploitation of the environment on the way to achieve the agent targets. Cgranules 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 interactions from physical world may be available for agents. Hence, in particular the results of performed actions by agents can not be predicted with certainty. For more details on IRGC based on cgranules the reader is referred to Jankowski (2015).
One of the key issues of the approach to cgranules presented in Jankowski (2015) is some kind of integration of investigation of physical and mental phenomena. The integration follows from suggestions presented by many scientists. For illustration let us consider following two quotations strongly related to the research on IRGC based on cgranules:
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 (Einstein 1921)
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.
A special role in IRGC play information (decision) systems from the rough set approach (Pawlak 1982, 1991; Pawlak and Skowron 2007; Stepaniuk 2008). They are used to record processes of interacting configurations of hunks. In order to represent interactive computations (used, e.g., in searching for new features) information systems of a new type, namely interactive information systems, are needed (Skowron and Wasilewski 2011, 2012; Jankowski 2015).– Vladimir Vapnik (Vapnik 1998, p. 721)
3 Adaptive Judgment
Adaptive judgment in IIS is a mixture of reasoning based on deduction, abduction, induction, case based or analogy based reasoning, experience, perceived changes in the environment. Metaheuristics from natural computing are used to support judgment (see Fig. 3). Let us also note the following remark (Thiele 2010):
We would like to stress that still much more work should be done to develop approximate reasoning methods about complex vague concepts for making progress in development of IIS, in particular for the risk management in IIS. This idea was very well expressed by Leslie Valiant:^{1}Practical judgment is not algebraic calculation. Prior to any deductive or inductive reckoning, the judge is involved in selecting objects and relationships for attention and assessing their interactions. Identifying things of importance from a potentially endless pool of candidates, assessing their relative significance, and evaluating their relationships is well beyond the jurisdiction of reason.
It is worthwhile to mention two more views. The first one by Lotfi A. Zadeh, the founder of fuzzy sets and the computing with words paradigm (see Zadeh (1999) and also http://www.cs.berkeley.edu/~zadeh/presentations.html):A fundamental question for artificial intelligence is to characterize the computational building blocks that are necessary for cognition. A specific challenge is to build on the success of machine learning so as to cover broader issues in intelligence. [...] This requires, in particular a reconciliation between two contradictory characteristics – the apparent logical nature of reasoning and the statistical nature of learning.
and the view by Judea Pearl included as the motto of this paper.Manipulation of perceptions plays a key role in human recognition, decision and execution processes. As a methodology, computing with words provides a foundation for a computational theory of perceptions  a theory which may have an important bearing on how humans make  and machines might make  perceptionbased rational decisions in an environment of imprecision, uncertainty and partial truth. [...] computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language.
4 Complex Granules and Satisfiability
In the approach based on cgranules, the judgment for checking values of descriptors (or more compound formulas) pointed by links from simple cgranules is based on interactions of some physical parts considered over time and/or space (called hunks) and pointed by links of cgranules. The judgment for the more compound cgranules is defined by a relevant family of procedures also realized by means of interactions of physical parts.
Let us explain in more detail the above claims.
In the discussed example of elementary cgranules, \(Tok(i)\) is a set of hunks and \(Type(i)\) is a set of descriptors (elementary infogranules), respectively, pointed by link represented by \(\models _{i}\). The procedure for computing the value of \(h \models _{i} \alpha \), where \(h\) is a hunk and \(\alpha \) is an infogranule (e.g., descriptor or formula constructed over descriptors) is based on interaction of \(\alpha \) with the physical world represented by hunk \(h\).
The agent control can aggregate some simple cgranules into more compound cgranules, e.g., by selecting some constraints on subsets of \(I\) making it possible to select relevant sets of simple cgranules and consider them as a new more compound cgranule. In constraints also values in descriptors pointed by links in elementary cgranules can be taken into account and sets of such more compound cgranules can be aggregated into new cgranules. Values of new descriptors pointed by links of these more compound granules are computed by new procedures. The computation process again is realized by interaction of the physical parts represented by hunks pointed by links of elementary cgranules included in the considered more compound cgranule as well as by using the procedure for computing of values of more compound descriptors from values of descriptors included in elementary cgranules of the considered more compound cgranule. Note that this procedure is also realized in the physical world thanks to relevant interactions.
In hierarchical modeling aiming at inducing of relevant cgranules (e.g., for approximation of complex vague concepts), one can consider so far constructed cgranules as tokens. For example, they can be used to define structured objects representing corresponding hunks and link them using new satisfiability relations (from a given family) to relevant higher order descriptors together with the appropriate procedures (realized by interactions of hunks) for computing values of these descriptors. This approach generalizes hierarchical modeling developed for infogranules (see, e.g., Nguyen et al. 2004; Bazan 2008) to hierarchical modeling of cgranules which is important for many reallife projects.
5 Agent and Interactive Computations on Complex Granules
It is worthwhile mentioning that contrary to the existing computation models realized by Turing machine the results of interactions can be only predicted by the agent control but the prediction can be in general different from the results of real interactions between agent and the environment due to uncertainty, e.g., unpredictable interactions in the environment. In particular, this is the consequence of uncertain information about the environment which the agent has due to bounds on available resources, e.g., available (or discovered so far) for agent sensors necessary for perception agent strategies.
The point of view that the interactive computations on complex granules are progressing due to interactions with the physical world have are important for Natural Computing too. The agentobserver trying to understand such computations is dependent on the physical world. This argument is supported by the following point of view (see Deutsch et al. 2000, p. 268):
The agent hypotheses about the models of computations can be verified only through interactions within the physical world. These models should be adaptively changed when deviations of the predicted from the perceived real trajectories of computations are becoming significant (see Fig. 11).It seems that we have no choice but to recognize the dependence of our mathematical knowledge (...) on physics, and that being so, it is time to abandon the classical view of computation as a purely logical notion independent of that of computation as a physical process.
The issues discussed in this section are raising a question about the control of interactive granular computations. In the next section we emphasize importance of the risk management by the agent control.
6 Risk Management in IIS
Since the very beginning, all human activities were done at risk of failure. Recent years have shown the low quality of risk management in areas such as finance, economics, and many others. In this context, improvement in the risk management has a particular importance for the further development of complex systems. The importance of risk management illustrates the following example from financial sector. Many of financial risk management experts consider Basel II rules^{2} as a causal factor in the credit bubble prior to the 20072008 collapse. Namely, in Basel II one of the principal factors of financial risk management was
outsourced to companies that were not subject to supervision, credit rating agencies.
Of course, now we do have a new “improved” version of Basel II, called Basel III. However, according to an OECD^{3} the mediumterm impact of Basel III implementation on GDP growth is negative and estimated in the range of \(0.05\%\) to \(0.15\%\) per year (see also Slovik and Cournède 2011).
On the basis of experience in many areas, we have now many valuable studies on different approaches to risk management. Currently, the dominant terminology is determined by the standards of ISO 31K [1]. However, the logic of inferences in risk management is dominated by the statistical paradigms, especially by Bayesian data analysis initiated about 300 years ago by Bayes, and regression data analysis initiated by about 200 years ago by Legendre and Gauss. On this basis, resulted many detailed methodologies specific for different fields. A classic example is the risk management methodology in the banking sector, based on the recommendations of Basel II standards for risk management mathematical models (Shevchenko 2011). The current dominant statistical approach is not satisfactory because it does not give effective tools for inferences about the vague concepts and relations between them (see the included before sentences by L. Valiant).

a sciencefriendly language for articulating risk management knowledge, and

a mathematical machinery for processing that knowledge, combining it with data and drawing new risk management conclusions about a phenomenon.
Adding both mentioned above components is an extremely difficult task and binds to the core of AI research very accurately specified by the Turing test. With regard to our applications, properly adapted version of the test boils down to the fact that on the basis of a “conversation” with a hidden risk management expert and a hidden machine one will not be able to distinguish who is the man and who is the machine.
We propose to extend the statistical paradigm by adding the two discussed components for designing of the high quality risk management systems supported by IIS.
For the risk management in IIS one of the most important task is to develop strategies for inducing approximations of vague complex concepts making it possible to check their satisfiability (to a degree). A typical example of such vague concept is the statement of the form: “now we do have very risky situation”. The starting point for development of strategies for inducing approximations of such vague complex is based on observation that the activation of actions performed by agents is based on satisfiability of such concepts.
 1.
concepts from risk sources,
 2.
current situation description represented by a hierarchy of concepts defined by the input sensors and context data,
 3.
concepts from risk consequences.
One can consider the mentioned above tasks of approximation of vague complex concepts initiating actions as the complex game discovery task (see Fig. 13) from data and domain knowledge. The agents use the discovered games for achieving their targets in the environment. The discovery process often is based on hierarchical learning supported by domain knowledge Jankowski (2015), Bazan (2008). It is also worthwhile mentioning that such games are evolving in time (drifting in time) together with data and knowledge about the approximated concepts and the relevant strategies for adaptation of games used by agents are required. These adaptive strategies are used to control the behavior of agents toward achieving by them targets. Note that also these strategies should be learned from available uncertain data and domain knowledge.
7 Conclusions
The approach for modeling interactive computations based on cgranules was presented and its importance for the risk managements was outlined.
The presented approach seems also to be of some importance for developing computing models in different areas such as natural computing (e.g., computing models for metaheuristics or computations models for complex processes in molecular biology), computing in distributed environments under uncertainty realized by multiagent systems (e.g., in social computing), modeling of computations for feature extraction (constructive induction) for approximation of complex vague concepts, hierarchical learning, discovery of planning strategies or strategies for coalition formation by IIS as well as for approximate reasoning about interactive computations based on such computing models.
In our research, we plan to further develop the foundations of interactive computations based on cgranules toward tools for modeling and analysis of computations in Natural Computing (Rozenberg et al. 2012), Wisdom Web of Things (Zhong et al. 2013) or CyberPhysical Systems (LamnabhiLagarrigue et al. 2014).
Footnotes
Notes
Acknowledgments
This work was supported by the Polish National Science Centre (NCN) grants DEC2011/01/D/ST6/ 06981, DEC2012/05/B /ST6/03215, DEC2013/09/B/ST6/01568 as well as by the Polish National Centre for Research and Development (NCBiR) under the grant O ROB/0010/ 03/001.
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