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# Complex Adaptive Systems and Interactive Granular Computing

Andrzej Skowron

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Andrzej Skowron. Complex Adaptive Systems and Interactive Granular Computing. 15th IFIP International Conference on Computer Information Systems and Industrial Management (CISIM), Sep 2016, Vilnius, Lithuania. pp.17-22, 10.1007/978-3-319-45378-1_2 . hal-01637517

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Distributed under a Creative Commons Attribution 4.0 International License
Complex Adaptive Systems
and
Interactive Granular Computing

Andrzej Skowron

Institute of Mathematics, Warsaw University
Banacha 2, 02-097 Warsaw, Poland
skowron@mimuw.edu.pl
and
Systems Research Institute
Polish Academy of Sciences
Newelska 6, 01-447 Warsaw, Poland

**Extended abstract**

We discuss an approach to modeling of computations performed by Complex Adaptive Systems (CAS) based on Interactive Granular Computing (IGrC).

Complex adaptive systems (CAS) are made up of multiple interacting elements and have the capacity to change and learn from experience. The key problems of complex systems are difficulties with their formal modeling and simulation<fnref n="1" />. Some approaches to modeling CAS are based on agent-based models and/or complex network-based models (see, e.g., [17, 36]).

Decision support in solving problems related to CAS [36, 33, 6] 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). In Granular Computing (GrC), all such constructed and/or induced objects are called granules.

To model, crucial for CAS, interactive computations [2] performed by agents, we extend the existing GrC approach to Interactive Granular Computing (IGrC) by introducing *complex granules* (*c-granules* or *granules*, for short).

*Interactive granular computations (computations in IGrC, for short)* were proposed as computational models for complex systems. Reasoning about the properties of computations in IGrC are based on *adaptive judgment*.

Computations in this model are performed on *c-granules* thanks to which it is possible to register, analyze, and synthesize the properties of interactions between physical objects perceived by agents.

We assume that the states of certain physical objects, occurring within a specific domain of activity of a given *c-granule*, are directly measurable. However, the states of other objects are perceived (approximated) indirectly using

<footnote n="1">¹ https://en.wikipedia.org/wiki/Complex_adaptive_system</footnote>
measurable states, obtained by interactions of physical objects from a particu-
lar domain of c-granule's activity. Each measurable state of a c-granule (at a
given moment of the agent's time) corresponds to a concept. This concept is
understood as a set of situations (configurations of physical objects), perceived
within this very c-granule, and, thanks to interactions, leads to a specific state.
In the proposed approach, the concept of a measurable state means that such
states are represented by, e.g., the values of a corresponding attribute or by the
satisfiability degrees of corresponding to states concepts/formulas. Following the
aggregation of c-granules, more complex c-granules, corresponding to structural
objects, their properties, or relations over measurable states (e.g., preference
relations), can be represented by c-granules. C-granules are used by agents for
perceiving current situations or states and undertaking, on this basis, of relevant
actions.

The fundamental intuition behind the concept of a c-granule is the following: the control of an agent *ag* uses her/his c-granules for perceiving and/or accessing fragments of the surrounding physical world. Each c-granule consists of three architectural layers:

1. *Soft suit*, i.e., configurations of hunks which represent the properties of the *ag*’s environment of activity (including the properties of the present, past, and expected phenomena, as well as expected properties of interaction plans and/or the results of some interactions, potentially activated by a c-granule).

2. *Link suit*, i.e., communication channels (links) which transmit the results of interactions among accessible fragments of the agent’s environment of activities and the results of interactions among different representations of properties in the soft suit; according to the weight (significance) of the current *ag*’s needs, links may have assigned priorities, which reflect the results of judgment, performed by *ag*.

3. *Hard suit*, i.e., configurations of hunks accessible by links from the link suit.

The hard suits, link suits, and soft suits of more compound c-granules are
defined using the relevant networks over already defined c-granules. The networks
are satisfying some constraints which can be interpreted as definitions of types
of networks. The link suits of such more compound granules are responsible for
transmission of interactions between the hard suits and soft suits represented
by the corresponding networks. The results and/or properties of transmitted
interactions are recorded in the soft suits.

Any c-granule is making it possible to record in its soft suit the perceived
by it interactions in its hard suit which are transmitted by the link suit to the
soft suit. This is typical for sensory measurement. On the other hand, a c-granule
may cause some interactions in its hard suit by transmitting through its link suit
some interactions from the soft suit. However, the c-granule may perceive the
results (or properties) of such caused in the hard suit interactions only by using
the soft suit. This is done on the basis of the transmitted results (or properties)
of these caused interactions in the hard suit by transmitting them back through
the link suit to the soft suit. These results (or properties) may be different from
the predicted ones which can be a priori stored in soft suit. This is typical for
performing of actions initiated by c-granules.

C-granules are generated by an agent *ag* depending on the specific configu-
rations of spatio-temporal portions of physical matter (called hunks [5]) related
to the *ag*. It should be underlined that any typical active c-granule is a dynami-
cally changing entity. It means that all components of c-granules (i.e., soft suite,
link suite and hard suite) are usually subject to continuous changes.

Many advanced tasks, concerning complex systems may be classified as con-
trol tasks performed by agents aiming at achieving the high quality computa-
tional trajectories of c-granules relative to the considered quality measures over
the trajectories. Here, new challenges are to develop strategies to control, pre-
dict, and bound the behavior of the system. We propose to investigate these
challenges using the IGrC 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 judgment*. Adaptive judgment plays a crucial role in the assessment of what is currently important, and what is less important. Therefore, it constitutes the basis for the evaluation and improvement of interaction plans that are being implemented. In a sense, judgment [14, 4, 3, 13, 35] may be treated as an elaboration of the concept of rational reasoning (especially about the properties of computations in IGrC) due to the necessity of taking into account not only mechanisms of logical reasoning, but also mechanisms that influence decisions, which are being made. These mechanisms pertain, e.g., to perception, emotions, instinct, habits, intuition, fast thinking [13], and experience. Thus, adaptive judgment is not only limited to deduction, induction, and abduction. A deeper understanding of the concept of adaptive judgment should be supported by psychology and phenomenology [16]. This reasoning deals with granules and computations over them. 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 inducing changes in approximations of concepts are needed. In particular, the adaptive judgement is very much needed in the efficiency management of interactive granular computations, carried out by agents, for risk assessment, risk treatment, and cost/benefit analysis.

Thanks to c-granules, it is possible to register both the results of sensory
measures and their hierarchical aggregations, which are performed to discover
new c-granules. The hierarchical c-granules discovered in this manner may ensure
a deeper understanding of a perceived situation (see [1]). The statement above
about the aggregation of c-granules (representing hierarchical aggregations of
the results of sensory measures) refers to the main, according to Valiant<fnref n="2" />, AI
challenge, which is the characterization of “computational building blocks” [34]
for perception.

The key role in the proposed approach is played by the techniques of adaptive
and interactive discovery of c-granules (through interactions with the environ-

<footnote n="2">² http://www.seas.harvard.edu/directory/valiant</footnote>
ment) and their further use. It turns out that in order to perform computations
on c-granules, *ecarithms*, as understood by Valiant [33], should be used instead
of classical algorithms. Apart from the analogy to Valiant’s *ecarithms*, the IGrC-
based proposed algorithms display a number of other features, which correspond
to the motivations of scientific research in other domains (*e.g.*, learning systems,
CAS, soft-computing, multi-agent systems, natural computations). The Wistech
IGrC model is also related to the very foundations of AI, in particular, to the
understanding of the essence of machine learning.

In particular, in Complex Systems Engineering (CSE)[7], the design and im-
plementation of a complex project may be seen as the process of discovering,
learning, processing (including communicating), and developing concepts (rep-
resented as c-granules), which are necessary to deal with a given project. The key
to success in managing any complex project is a skillful approximation of com-
plex vague concepts, represented by c-granules, and a skillful use of c-granules by
those, who are in charge of a given project. Such approximations are responsible,
*e.g.*, for initiation of actions performed by agents [7].

It is worth mentioning that the proposed model of interactive computations
on c-granules differs from the Turing model.

The main ideas presented in the book have their roots in the research on
rough sets, initiated by Zdzisaw Pawlak [20, 22, 31, 21]. At this point, we are
particularly referring to Pawlak's approach to such concepts as: concept approx-
imations, information systems, decision tables (as they are understood in a rough
set theory) and Boolean reasoning about vague concepts.

The presented approach to the Wistech IGrC model is an extension of the
joint research with Dr. Andrzej Jankowski [10, 19, 8, 30, 28, 9, 12, 11, 26, 27] The
approach is a step towards realization of the Wisdom Technology (WisTech)
program [8, 10, 9, 29, 7] in combination with IGrC, and is developed over years
of experiences, based on the work on different real-life projects. The discussed
model is called the Wistech IGrC model.

The results of the research presented in this paper may also be analyzed from
the point of view of their potential contribution to advancements in dynamically
developing scientific disciplines, such as CSE [18, 25], granular computational
models [23], interactive computational models [2], models of natural computing
[24], models of learning systems [33], or models of computations performed by
multi-agent systems [32, 15].

Other issues such as communication language evolution and risk management
in interactive computations will be discussed in more detail in our next papers
(see also [7]).

Acknowledgements

The author would like to express his deepest gratitude to Dr. Andrzej Jankowski
for the close cooperation of the development the IGrC approach. This work was
supported by the Polish National Science Centre (NCN) grants DEC-2011/01/D
/ST6/ 06981, DEC-2013/09/B/ST6/01568 and by the Polish National Centre for Research and Development (NCBiR) grant.

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