Other Paradigms

Some of the major paradigms of computational intelligence are gran-ular computing, chaos theory, and artificial immune systems. Grangran-ular computing is an emerging computing paradigm of information process-ing. It concerns the processing of complex information entities called information granules, which arise in the process of data abstraction and derivation of knowledge from information. Chaos theory is a developing scientific discipline, which is focused on the study of nonlinear systems.

The specific example of a relatively new CI paradigm is the Artificial Immune System (AIS), which is a computational pattern recognition technique, based on how white blood cells in the human immune system detect pathogens that do not belong to the body. Instead of building an explicit model of the available training data, AIS builds an implicit classifier that models everything else but the training data, making it suited to detecting anomalous behavior in systems. Thus, AIS is well suited for applications in anti-virus software, intrusion detection systems, and fraud detection in the financial sector.

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Further, fields such as Artificial Life (ALife), robotics (especially multi-agent systems) and bioinformatics are application areas for CI techniques. Alternatively, it can be argued that those fields are a breed-ing ground for tomorrow’s CI ideas. For example, evolutionary com-puting techniques have been successfully employed in bioinformatics to decipher genetic sequences. Hand in hand with that comes a deeper understanding of the biological evolutionary process and improved evo-lutionary algorithms.

As another example, consider RoboCup, a project with a very ambi-tious goal. The challenge is to produce a team of autonomous humanoid robots that will be able to beat the human world championship team in soccer by the year 2050. This is obviously an immense undertaking that will require drawing on many disciplines. The mechanical engineering aspects are only one of the challenges standing in the way of meeting this goal. Controlling the robots is quite another. Swarm robotics, an ex-tension of swarm intelligence into robotics, is a new paradigm in CI that may hold some of the answers. In the mean time, simulated RoboCup challenges, which are held annually, will have to suffice.

1.7.1 Granular Computing

Uncertainty processing paradigms can be considered as conceptual frames. Information granule is a conceptual frame of fundamental enti-ties considered to be of importance in a problem formulation. That con-ceptual frame is a place where generic concepts, important for some ab-straction level, processing, or transfer of results in outer environment, are formulated. Information granule can be considered as knowledge repre-sentation and knowledge processing components. Granularity level (size) of information granules is important for a problem description and for a problem-solving strategy. Soft computing can be viewed in the con-text of computational frame based on information granules, and referred to as granular computing. Essential common features of problems are identified in granular computing, and those features are represented by granularity.

Granular computing has the ability to process information granules, and to interact with other granular or numerical world, eliciting needed granular information and giving results of granular evaluations. Granu-lar computing enables abstract formal theories of sets, probability, fuzzy sets, rough sets, and maybe others, to be considered in the same context, noticing basic common features of those formalisms, providing one more computing level, higher from soft computing, through synergy of con-sidered approaches. Since several computing processes can be present in the same time, with possible mutual communication, a distributed

pro-Computational Intelligence 19 cessing model can be conceived. In that model every process, or agent, Figure 1.4, is treated as a single entity.

FIGURE 1.4: An Agent

Every agent, as shown in Figure 1.5, acts in its own granular comput-ing environment and communicates with other agents.

FIGURE 1.5: Granular computing implemented by agents

A formal concept of granular computing can be expressed by four-tuple

<X,F,A,C >, where: X - is universe of discourse, F - is formal granulation frame, A is a collecgranulation of generic informagranulation granules, and, C -is a relevant communication mechan-ism. Granular computing becomes a layer of computational intelligence, a level of abstraction above soft

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puting. Granular computing synergically complements different aspects of representing, learning, and optimization. A role of granular comput-ing in development of intelligent systems, and so of computcomput-ing systems can be significant, as in knowledge integration, and also in development of computing systems more adapted to user, linguistic, and biologically motivated.

1.7.2 Chaos Theory

Chaos Theory is amongst the youngest of the sciences, and has rock-eted from its isolated roots in the seventies to become one of the most captivating fields in existence. This theory is applied in the research on several physical systems, and also implemented in areas such as image compression, fluid dynamics, Chaos science assures to continue to yield absorbing scientific information which may shape the face of science in the future. The acceptable definition of chaos theory states, Chaos The-ory is the qualitative study of unstable aperiodic behavior in determinis-tic nonlinear systems. The behavior of chaos is complex, nonlinear, and dynamic complex implies aperiodic (is simply the behavior that never re-peats), nonlinear implies recursion and higher mathematical algorithms, and dynamic implies non-constant and non-periodic (time variables).

Thus, Chaos Theory is the study of forever changing complex systems based on mathematical concepts of recursion, whether in form of a recur-sive process or a set of differential equations modeling a physical system.

Newhouse’s definition states, A bounded deterministic dynamical sys-tem with at least one positive Liaponov exponent is a chaotic syssys-tem;

a chaotic signal is an observation of a chaotic system. The presence of a positive Liaponov exponent causes trajectories that are initially close to each other to separate exponentially. This, in turn, implies sensitive dependence of the dynamics on initial conditions, which is one of the most important characteristics of chaotic systems. What is so incredible about Chaos Theory is that unstable aperiodic behavior can be found in mathematically simple systems. Lorenz proved that the complex, dy-namical systems show order, but they never repeat. Our world is a best example of chaos, since it is classified as a dynamical, complex system, our lives, our weather, and our experiences never repeat; however, they should form patterns.

Chaotic behavior has been observed in the laboratory in a variety of systems including electrical and electronic circuits, lasers, oscillat-ing chemical reactions, fluid dynamics, and mechanical and magneto-mechanical devices. Observations of chaotic behavior in nature include the dynamics of satellites in the solar system, the time evolution of the magnetic field of celestial bodies, population growth in ecology, the

dy-Computational Intelligence 21 namics of the action potentials in neurons, and molecular vibrations. Ev-eryday examples of chaotic systems include weather and climate. There is some controversy over the existence of chaotic dynamics in the plate tectonics and in economics.

Systems that exhibit mathematical chaos are settled and thus orderly in some sense; this technical use of the word chaos is at odds with common parlance, which suggests complete disorder. A related field of physics called quantum chaos theory studies systems that follow the laws of quantum mechanics. Recently, another field, called relativistic chaos, has emerged to describe systems that follow the laws of general relativity.

As well as being orderly in the sense of being deterministic, chaotic systems usually have well defined statistics. For example, the Lorenz system pictured is chaotic, but has a clearly defined structure. Bounded chaos is a useful term for describing models of disorder.

Chaos theory is applied in many scientific disciplines: mathematics, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, and robotics.

Chaos theory is also currently being applied to medical studies of epilepsy, specifically to the prediction of seemingly random seizures by observing initial conditions.

1.7.3 Artificial Immune Systems

The biological immune system is a highly parallel, distributed, and adaptive system. It uses learning, memory, and associative retrieval to solve recognition and classification tasks. In particular, it learns to rec-ognize relevant patterns, remembers patterns that have been seen previ-ously, and uses combinatorics to construct pattern detectors efficiently.

These remarkable information processing abilities of the immune system provide important aspects in the field of computation. This emerging field is sometimes referred to as Immunological Computation, Immuno-computing, or Artificial Immune Systems (AIS). Although it is still rela-tively new, AIS, having a strong relationship with other biology-inspired computing models, and computational biology, is establishing its unique-ness and effectiveunique-ness through the zealous efforts of researchers around the world.

An artificial immune system (AIS) is a type of optimization algo-rithm inspired by the principles and processes of the vertebrate immune system. The algorithms typically exploit the immune system’s charac-teristics of learning and memory to solve a problem. They are coupled to artificial intelligence and closely related to genetic algorithms.

Processes simulated in AIS include pattern recognition, hypermuta-tion and clonal selechypermuta-tion for B cells, negative selechypermuta-tion of T cells, affinity

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maturation, and immune network theory.