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Fuzzy-based computational simulations of brain functions – preliminary concept

Fuzzy-based computational simulations of brain functions – preliminary concept Research on the computational models of the brain constitutes an important part of the current challenges within computational neuroscience. The current results are not satisfying. Despite the continuous efforts of scientists and clinicians, it is hard to fully explain all the mechanisms of a brain function. Computational models of the brain based on fuzzy logic, including ordered fuzzy numbers, may constitute another breakthrough in the aforementioned area, offering a completing position to the current state of the art. The aim of this paper is to assess the extent to which possible opportunities concerning computational brain models based on fuzzy logic techniques may be exploited both in the area of theoretical and experimental computational neuroscience and in clinical applications, including our own concept. The proposed approach can open a family of novel methods for a more effective and (neuro)biologically reliable brain simulation based on fuzzy logic techniques useful in both basic sciences and applied sciences. Keywords: brain plasticity; computational brain model; computational neuroscience; fuzzy system; neurology. Huge data sets providing a clear and complete picture of different levels of brain organization; Effective, reliable, and accurate predictive tools; Novel hardware and software for brain simulation purposes; Better ways for disease simulation; Development of the novel brain-inspired technologies, significantly influencing clinical practice, social life, and industry; and Recognition of chances and threats for better risk management associated with a wider use of brainderived technologies [1]. Introduction The importance of computational neuroscience was recently emphasized by Henry Markram in his challenges for neuroscience: ­ Big research teams for solving big problems (e.g. Allen Brain Atlas, Blue Brain Project, Human Connectome Project, and Human Brain Project); *Corresponding author: Dariusz Mikolajewski, Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, ul. Kopernika 1, 85-074 Bydgoszcz, Poland, E-mail: darek.mikolajewski@wp.pl; Department of Informatics, Nicolaus Copernicus University, Toru, Poland; and Centre for Modern Interdisciplinary Technologies, Nicolaus Copernicus University, Toru, Poland Piotr Prokopowicz: Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, Bydgoszcz, Poland Research on the computational models of the brain constitutes an important part of the current challenges within computational neuroscience. The computational brain model or the whole family of such models may provide the following: ­ Linking theoretical knowledge and outcomes of experimental studies; ­ Simultaneous description of the brain processes on all levels: molecular, single neuronal, system, and behavioral (within the so-called causal chain); ­ Linking cortical and subcortical processes with processing on the lower levels: brainstem, spine cord, and peripheral; ­ Cheaper and quicker testing of hypotheses, mainly for their selection purposes; ­ Highlighting the most important mechanisms, analysis of their features, and limitations; ­ Simplifying/scaling mechanisms too complex to the direct simulation (or simulate them in changed timescale); and ­ Possibility of various purposeful damages (representations of injuries/lesions) or simulation in the conditions not possible in the real world due to anatomical or ethical causes. Despite the continuous efforts of scientists and clinicians, it is hard to fully explain all the mechanisms of a brain function ("data ladders") [1]. The proper construction and development of brain models requires well-fitting assumptions and usually needs a lot of attempts. Common errors, such as inadequate formulation of scientific questions, improper 100Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions input signals, ways and levels of processing (associated with both structure and function), and lack of realistic assumptions, make this task very really demanding [2, 3]. The aim of this paper is to assess the extent to which possible opportunities concerning computational brain models based on fuzzy logic techniques may be exploited both in the area of theoretical and experimental computational neuroscience and in clinical applications, including our own concept. level of processing, and timescale. Every disorder of the aforementioned mechanisms may cause severe neurological deficits, including perception of sensory signals, generation of motor responses, and decision-making processes. Such influence has to be reflected in computational models of brain function. We should try to measure noise within the nervous system and incorporate it into brain signal processing [7, 8]. Although cortical and subcortical function simulation seem to be well described, lower-level (e.g. brain stem) functions seem be underscored. The main cause may be limited knowledge (brain stem) or reluctance toward computational models as ineffective or difficult to use. There are attempts to change such image of computational neuroscience. A recent paper by D'Angelo et al. showed relative simplicity and usefulness of biologically realistic computational models of cerebellum [3]. The generation of consciousness is regarded as the most complex phenomenon. The perception of own and the environment and the integration of information from multiple signs to a form of unified picture of the world are still far beyond our understanding [9]. Every attempt toward a better understanding of the consciousness and disorders of consciousness (DoCs) is extremely important due to the limited exactness of diagnosis and treatment in patients with DoCs (vegetative state, minimally conscious state, etc.). Early attempts of researchers aiming at calculating integration information within brain-like structures are successful but limited to small numbers of units/ neurons [10, 11]. The computational complexity of measures, such as neural complexity, state-based phi, causal density, and liveliness, causes their limited application. Current computational methods useful in the simulation of postlesional changes (brain reorganization) are also not fully exploited. The most commonly used methods contain Hebbian networks, self-organizing maps (SOMs; Kohonen networks), attractor networks, and unsupervised ontogenic networks. More accurate concepts such as dendritic branching and synaptic plasticity need further computational development. Many approaches, such as liquid state machines (LMSs) [12, 13] and fuzzy-based models of self-organization, need verification. A further development of novel computing technologies may increase our understanding of the severe changes in brain associated with illnesses or injuries, significantly improve early diagnostics, and provide novel approaches, allowing for better prevention and therapy. Changes in signals, their processing, or geometric features of the nervous system may constitute sources of disturbed nervous signal processing. This approach may strengthen the predictive role of computational models. An exploration of existing and novel Key issues ­ current state The development of brain models is affected by the three main approaches: ­ Connectionism, which states that even simplified brain models have to be composed in a way similar to the natural origin; ­ Functionalism, which states that the most important property of the brain constitutes its functional role, described by sensory inputs, causal relations among states, and behavioral outputs; and ­ Hybrid approach. The most commonly used neural simulation environments are based on compartmental neurons such as NEURON [4] and GENESIS [5] and point neurons such as Emergent [6]. Other computational environments for biologically relevant brain simulation are Brian, Catacomb, KInNeSS, MVA Spike, NCS, Nengo, NEST, NSL, P(PSIM), SpikeNet, Topographica, XNBC, and XPP-Aut. Most of such environments are based on biologically relevant single neuron models, such as Hodgkin-Huxlex, FitzHugh-Nagumo, Morris-Lecar, Hindmarsh-Rose, Wilson, Izhikevich, integrate-and-fire, and resonate-and-fire. Despite 60 years of development, none of them is ideal because the true biophysical models of neurons are very complex and cover a huge variety of features. More advanced single neuron models are used in pharmacological studies, where chemical and enzyme kinetics, reaction thermodynamics, or cellular geometry play a crucial role. Noise is also a part of the mechanisms aiming at variability within a real brain; it causes each human unique and each movement unrepeatable. The diversity of noise existing within the nervous system influences information processing and almost all aspects of function and behavior. This influence may cause important favorable effects: stabilization, increased activation, probabilistic differentiation, stochastic fluctuation, etc. The level and range of change caused by noise depend on noise sources and features, Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions101 databases and the use of effective data mining algorithms may provide identification of more accurate predictors useful in clinical applications. The aim is early diagnosis (in Alzheimer's disease), increased exactness of diagnosis, and more effective treatment. Congenital diseases are not beyond our reach: research concerning computational models of distinctive features of autism spectrum disorders (ASD) and attention-deficit hyperactivity disorder (ADHD) showed potential of such efforts [14]. Neurorehabilitation and assistive technology (AT) are regarded as key elements of contemporary acute, postacute, and long-term therapy of patients with neurological conditions. The quick development of neurorehabilitation methods and techniques is partially inhibited by weak evidences [low number of randomized controlled trials (RCTs)] and the lack of full understanding of changes in the brain associated with stimulated recovery. A better understanding of the processes associated with brain plasticity and neural repair is needed for the most efficient artificial (activity-dependent) stimulation of the reorganization of neural networks within the brain. Reliable and accurate experimentally validated models of the neural control of movements, motor learning, functional recovery, and therapy control strategies could change this situation. Computational models can constitute a useful way of the optimization of neurorehabilitation. There is a possibility to work out improved or completely novel forms of neurorehabilitation organization or application, better adapted to the needs of particular patients (focus to patient-tailored rehabilitation). Traditional forms of the therapy of neurological deficits such as neurosurgery, drug therapy, and neurorehabilitation can be supported or replaced by more effective AT solutions. Brain-computer interfaces (BCIs), neuroprostheses (NPs), artificial deep brain stimulation (DBS), and robotic postural interfaces need reliable computational models, allowing for improving the chances for therapeutic success and avoiding misdiagnosis or false effects. Many general mechanisms of the brain processes in both healthy people and people with neurological conditions may arise from proper or disturbed brain dynamics. Methods of multidimensional scaling (MDS), including fuzzy symbolic dynamics (FSD) [15­17], are useful in these attempts. Attractor analysis needs a deeper insight into the complexity of basis of solutions and brain subnet states. Such analysis is still limited and requires deep knowledge concerning the brain areas involved in particular mechanisms (e.g. possible number of interacting subnets and general rules of operation). There is a necessity for a further common effort of both medical staff and engineers. The unified strategy should incorporate not only improved databases but also whole technical-assisted problem-solving approaches (i.e. hypermodels of pathogenic mechanism) in everyday clinical practice. Novel approach of the fuzzy nature of brain processes Computational models of the brain based on fuzzy logic may constitute another breakthrough in the aforementioned area, offering a completing position to the current state of the art. A great part of our knowledge about the functions of the brain is vague and imprecise. Thus, a fuzzy logic seems a good direction when we look for tools in modeling such object. Although fuzzy techniques are used in object recognition and linguistic property modeling [18], evidence concerning their use in brain simulations is weak. There is a need for novel, more effective approach, providing a better, clear, and easy understanding of processes underlying brain function. Novel integrated approach Attempts to describe a simplified brain function in the form of mathematical equations are difficult. As mentioned before, brain function arises from complex behaviors of units on the lower level (neurons, synapses, etc.). It makes this situation similar rather to multiagent architecture. However, a cascade of fuzzy logic systems may provide another insight into the behavior of the particular subsystems or mechanisms, allowing for easy configuration and use of complicated sets of semirealistic features. Basic fuzzy technologies A conception of the fuzzy system is a great tool for modeling situations described by imprecise or incomplete information. Its important element is a linguistic variable idea [19], which allows the transfer of any universes with the crisp values into universes with the fuzzy sets. As a result, we can operate on linguistic values such as many, few, and average. Mamdani-type fuzzy systems [20] use linguistic variables as inputs and outputs. This type of fuzzy system attracted a considerable interest of designers of control systems especially for two reasons. First is the ability to effective model nonlinear systems, and the second more important for this paper is an explanation of the system 102Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions in an understandable way for humans. This feature can be called the "transparency", which is definitely lacking in artificial neural networks or strictly traditional mathematical modeling. The fuzzy modeling of brain functions is a compromise between the highly precise mathematical model and the neural model based on biological structure. As already noticed in Ref. [21], there is a potential for combining the fuzzy systems (fuzzy controllers) in a hierarchical structure. Although, in this publication, we do not focus on the problem of fuzzy control, the idea of a cascade connecting singular fuzzy systems is especially valuable in modeling the functional structure of the brain. It was already mentioned in this paper that the brain can be modeled as a multiagent system, where individual agents (or group of agents) correspond to the specified functions of the brain. It is noteworthy that, in place of agents represented by the complex mathematical models or due to the difficulty in analyzing and defining the artificial neural networks, we can use fuzzy systems. Their cascade connection allows for linguistic values reflecting even more complex relationships. Such constructions are similar to fuzzy networks [22]; however, we propose some particular changes. Figure 1:FIB from fuzzy system. Strict fuzzy processing Processing of information using a fuzzy system usually begins with an operation of fuzzyfication and ends with defuzzyfication. Fuzzyfication, in general, is the conversion of a crisp value into fuzzyfication and defuzzyfication and vice versa. This operation can be done in many different ways. A proper choice of them (especially the defuzzyfication method) often has a significant impact on the correctness and effectiveness of the whole model. Furthermore, the change of fuzzy value into a crisp one is the replacement of a complex value with a simpler one. Such action usually involves some approximation or rounding, so it introduces an additional error into the results. The repetition of such actions is not recommended, especially when the output value of one stage will be the input value for another. If we want to model more complex structures such as the brain using fuzzy values, the exclusion of the fuzzyfication and defuzzyfication operations outside the base system is recommended. For future analysis, we will call a fuzzy system without fuzzyfication and defuzzyfication stages as the fuzzy inference block (FIB). Its idea is presented in Figure 1. Such element is a conceptual base for a cascade modeling complex relations described linguistically. Figure 2:CFCM. Figure 2 presents an example of some complicated dependencies modeled by FIBs. For purposes of this paper, we can call such construction complex fuzzy cascade model (CFCM). It is worth noting that every FIB can represent one agent from the multiagent architecture. With this approach, we can describe even more complex structures. It is easy to imagine that, in place of single FIBs, we can insert the CFCM; thus, we introduce a kind of recursion in the CFCM, where only the lowest level relates directly to FIBs. Still, despite the high complexity of the model, we describe relations at various stages linguistically. Important issue However, the idea of CFCM with FIBs seems quite good for the linguistic modeling of complex relations. There can arise some problems. The classical methods for fuzzy Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions103 models often produce fuzzy answer sets, which are much fragmented, not normal, and not convex. Such results formally still are fuzzy sets, but their forward processing without defuzzyfication could be questionable. The above-mentioned problems do not occur if we use the ordered fuzzy number (OFN) model [23­26]. It is quite a recent proposition for modeling the calculations on imprecise values in a similar way as the fuzzy numbers. There are proposed special methods for OFNs to use them in fuzzy systems [27­29]. An important advantage of this method is that we get a kind of fuzzy number on each step of processing data. Thus, a further use of such result is easy and fluent without defuzzyfication and then fuzzyfication again. reliable brain simulation based on fuzzy logic techniques useful in both basic sciences and applied sciences. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission. Research funding: None declared. Employment or leadership: None declared. Honorarium: None declared. Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication. Limitations of the proposed approach Current models need additional validation toward the effective replication of natural processes. They are abstract networks proving only the basic principles of brain circuit functioning due to the lack of spiking neurons and hard implementation of the biological properties of neurons and synapses. However, such solutions implementing brain mechanisms in the form of relatively abstract computational principles may be useful on system levels, where scaling is not fully possible, and biologically relevant networks are too complicated to simulate. Such simple models are less time-consuming and proper for the testing of the preliminary hypotheses. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bio-Algorithms and Med-Systems de Gruyter

Fuzzy-based computational simulations of brain functions – preliminary concept

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de Gruyter
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1895-9091
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Abstract

Research on the computational models of the brain constitutes an important part of the current challenges within computational neuroscience. The current results are not satisfying. Despite the continuous efforts of scientists and clinicians, it is hard to fully explain all the mechanisms of a brain function. Computational models of the brain based on fuzzy logic, including ordered fuzzy numbers, may constitute another breakthrough in the aforementioned area, offering a completing position to the current state of the art. The aim of this paper is to assess the extent to which possible opportunities concerning computational brain models based on fuzzy logic techniques may be exploited both in the area of theoretical and experimental computational neuroscience and in clinical applications, including our own concept. The proposed approach can open a family of novel methods for a more effective and (neuro)biologically reliable brain simulation based on fuzzy logic techniques useful in both basic sciences and applied sciences. Keywords: brain plasticity; computational brain model; computational neuroscience; fuzzy system; neurology. Huge data sets providing a clear and complete picture of different levels of brain organization; Effective, reliable, and accurate predictive tools; Novel hardware and software for brain simulation purposes; Better ways for disease simulation; Development of the novel brain-inspired technologies, significantly influencing clinical practice, social life, and industry; and Recognition of chances and threats for better risk management associated with a wider use of brainderived technologies [1]. Introduction The importance of computational neuroscience was recently emphasized by Henry Markram in his challenges for neuroscience: ­ Big research teams for solving big problems (e.g. Allen Brain Atlas, Blue Brain Project, Human Connectome Project, and Human Brain Project); *Corresponding author: Dariusz Mikolajewski, Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, ul. Kopernika 1, 85-074 Bydgoszcz, Poland, E-mail: darek.mikolajewski@wp.pl; Department of Informatics, Nicolaus Copernicus University, Toru, Poland; and Centre for Modern Interdisciplinary Technologies, Nicolaus Copernicus University, Toru, Poland Piotr Prokopowicz: Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, Bydgoszcz, Poland Research on the computational models of the brain constitutes an important part of the current challenges within computational neuroscience. The computational brain model or the whole family of such models may provide the following: ­ Linking theoretical knowledge and outcomes of experimental studies; ­ Simultaneous description of the brain processes on all levels: molecular, single neuronal, system, and behavioral (within the so-called causal chain); ­ Linking cortical and subcortical processes with processing on the lower levels: brainstem, spine cord, and peripheral; ­ Cheaper and quicker testing of hypotheses, mainly for their selection purposes; ­ Highlighting the most important mechanisms, analysis of their features, and limitations; ­ Simplifying/scaling mechanisms too complex to the direct simulation (or simulate them in changed timescale); and ­ Possibility of various purposeful damages (representations of injuries/lesions) or simulation in the conditions not possible in the real world due to anatomical or ethical causes. Despite the continuous efforts of scientists and clinicians, it is hard to fully explain all the mechanisms of a brain function ("data ladders") [1]. The proper construction and development of brain models requires well-fitting assumptions and usually needs a lot of attempts. Common errors, such as inadequate formulation of scientific questions, improper 100Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions input signals, ways and levels of processing (associated with both structure and function), and lack of realistic assumptions, make this task very really demanding [2, 3]. The aim of this paper is to assess the extent to which possible opportunities concerning computational brain models based on fuzzy logic techniques may be exploited both in the area of theoretical and experimental computational neuroscience and in clinical applications, including our own concept. level of processing, and timescale. Every disorder of the aforementioned mechanisms may cause severe neurological deficits, including perception of sensory signals, generation of motor responses, and decision-making processes. Such influence has to be reflected in computational models of brain function. We should try to measure noise within the nervous system and incorporate it into brain signal processing [7, 8]. Although cortical and subcortical function simulation seem to be well described, lower-level (e.g. brain stem) functions seem be underscored. The main cause may be limited knowledge (brain stem) or reluctance toward computational models as ineffective or difficult to use. There are attempts to change such image of computational neuroscience. A recent paper by D'Angelo et al. showed relative simplicity and usefulness of biologically realistic computational models of cerebellum [3]. The generation of consciousness is regarded as the most complex phenomenon. The perception of own and the environment and the integration of information from multiple signs to a form of unified picture of the world are still far beyond our understanding [9]. Every attempt toward a better understanding of the consciousness and disorders of consciousness (DoCs) is extremely important due to the limited exactness of diagnosis and treatment in patients with DoCs (vegetative state, minimally conscious state, etc.). Early attempts of researchers aiming at calculating integration information within brain-like structures are successful but limited to small numbers of units/ neurons [10, 11]. The computational complexity of measures, such as neural complexity, state-based phi, causal density, and liveliness, causes their limited application. Current computational methods useful in the simulation of postlesional changes (brain reorganization) are also not fully exploited. The most commonly used methods contain Hebbian networks, self-organizing maps (SOMs; Kohonen networks), attractor networks, and unsupervised ontogenic networks. More accurate concepts such as dendritic branching and synaptic plasticity need further computational development. Many approaches, such as liquid state machines (LMSs) [12, 13] and fuzzy-based models of self-organization, need verification. A further development of novel computing technologies may increase our understanding of the severe changes in brain associated with illnesses or injuries, significantly improve early diagnostics, and provide novel approaches, allowing for better prevention and therapy. Changes in signals, their processing, or geometric features of the nervous system may constitute sources of disturbed nervous signal processing. This approach may strengthen the predictive role of computational models. An exploration of existing and novel Key issues ­ current state The development of brain models is affected by the three main approaches: ­ Connectionism, which states that even simplified brain models have to be composed in a way similar to the natural origin; ­ Functionalism, which states that the most important property of the brain constitutes its functional role, described by sensory inputs, causal relations among states, and behavioral outputs; and ­ Hybrid approach. The most commonly used neural simulation environments are based on compartmental neurons such as NEURON [4] and GENESIS [5] and point neurons such as Emergent [6]. Other computational environments for biologically relevant brain simulation are Brian, Catacomb, KInNeSS, MVA Spike, NCS, Nengo, NEST, NSL, P(PSIM), SpikeNet, Topographica, XNBC, and XPP-Aut. Most of such environments are based on biologically relevant single neuron models, such as Hodgkin-Huxlex, FitzHugh-Nagumo, Morris-Lecar, Hindmarsh-Rose, Wilson, Izhikevich, integrate-and-fire, and resonate-and-fire. Despite 60 years of development, none of them is ideal because the true biophysical models of neurons are very complex and cover a huge variety of features. More advanced single neuron models are used in pharmacological studies, where chemical and enzyme kinetics, reaction thermodynamics, or cellular geometry play a crucial role. Noise is also a part of the mechanisms aiming at variability within a real brain; it causes each human unique and each movement unrepeatable. The diversity of noise existing within the nervous system influences information processing and almost all aspects of function and behavior. This influence may cause important favorable effects: stabilization, increased activation, probabilistic differentiation, stochastic fluctuation, etc. The level and range of change caused by noise depend on noise sources and features, Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions101 databases and the use of effective data mining algorithms may provide identification of more accurate predictors useful in clinical applications. The aim is early diagnosis (in Alzheimer's disease), increased exactness of diagnosis, and more effective treatment. Congenital diseases are not beyond our reach: research concerning computational models of distinctive features of autism spectrum disorders (ASD) and attention-deficit hyperactivity disorder (ADHD) showed potential of such efforts [14]. Neurorehabilitation and assistive technology (AT) are regarded as key elements of contemporary acute, postacute, and long-term therapy of patients with neurological conditions. The quick development of neurorehabilitation methods and techniques is partially inhibited by weak evidences [low number of randomized controlled trials (RCTs)] and the lack of full understanding of changes in the brain associated with stimulated recovery. A better understanding of the processes associated with brain plasticity and neural repair is needed for the most efficient artificial (activity-dependent) stimulation of the reorganization of neural networks within the brain. Reliable and accurate experimentally validated models of the neural control of movements, motor learning, functional recovery, and therapy control strategies could change this situation. Computational models can constitute a useful way of the optimization of neurorehabilitation. There is a possibility to work out improved or completely novel forms of neurorehabilitation organization or application, better adapted to the needs of particular patients (focus to patient-tailored rehabilitation). Traditional forms of the therapy of neurological deficits such as neurosurgery, drug therapy, and neurorehabilitation can be supported or replaced by more effective AT solutions. Brain-computer interfaces (BCIs), neuroprostheses (NPs), artificial deep brain stimulation (DBS), and robotic postural interfaces need reliable computational models, allowing for improving the chances for therapeutic success and avoiding misdiagnosis or false effects. Many general mechanisms of the brain processes in both healthy people and people with neurological conditions may arise from proper or disturbed brain dynamics. Methods of multidimensional scaling (MDS), including fuzzy symbolic dynamics (FSD) [15­17], are useful in these attempts. Attractor analysis needs a deeper insight into the complexity of basis of solutions and brain subnet states. Such analysis is still limited and requires deep knowledge concerning the brain areas involved in particular mechanisms (e.g. possible number of interacting subnets and general rules of operation). There is a necessity for a further common effort of both medical staff and engineers. The unified strategy should incorporate not only improved databases but also whole technical-assisted problem-solving approaches (i.e. hypermodels of pathogenic mechanism) in everyday clinical practice. Novel approach of the fuzzy nature of brain processes Computational models of the brain based on fuzzy logic may constitute another breakthrough in the aforementioned area, offering a completing position to the current state of the art. A great part of our knowledge about the functions of the brain is vague and imprecise. Thus, a fuzzy logic seems a good direction when we look for tools in modeling such object. Although fuzzy techniques are used in object recognition and linguistic property modeling [18], evidence concerning their use in brain simulations is weak. There is a need for novel, more effective approach, providing a better, clear, and easy understanding of processes underlying brain function. Novel integrated approach Attempts to describe a simplified brain function in the form of mathematical equations are difficult. As mentioned before, brain function arises from complex behaviors of units on the lower level (neurons, synapses, etc.). It makes this situation similar rather to multiagent architecture. However, a cascade of fuzzy logic systems may provide another insight into the behavior of the particular subsystems or mechanisms, allowing for easy configuration and use of complicated sets of semirealistic features. Basic fuzzy technologies A conception of the fuzzy system is a great tool for modeling situations described by imprecise or incomplete information. Its important element is a linguistic variable idea [19], which allows the transfer of any universes with the crisp values into universes with the fuzzy sets. As a result, we can operate on linguistic values such as many, few, and average. Mamdani-type fuzzy systems [20] use linguistic variables as inputs and outputs. This type of fuzzy system attracted a considerable interest of designers of control systems especially for two reasons. First is the ability to effective model nonlinear systems, and the second more important for this paper is an explanation of the system 102Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions in an understandable way for humans. This feature can be called the "transparency", which is definitely lacking in artificial neural networks or strictly traditional mathematical modeling. The fuzzy modeling of brain functions is a compromise between the highly precise mathematical model and the neural model based on biological structure. As already noticed in Ref. [21], there is a potential for combining the fuzzy systems (fuzzy controllers) in a hierarchical structure. Although, in this publication, we do not focus on the problem of fuzzy control, the idea of a cascade connecting singular fuzzy systems is especially valuable in modeling the functional structure of the brain. It was already mentioned in this paper that the brain can be modeled as a multiagent system, where individual agents (or group of agents) correspond to the specified functions of the brain. It is noteworthy that, in place of agents represented by the complex mathematical models or due to the difficulty in analyzing and defining the artificial neural networks, we can use fuzzy systems. Their cascade connection allows for linguistic values reflecting even more complex relationships. Such constructions are similar to fuzzy networks [22]; however, we propose some particular changes. Figure 1:FIB from fuzzy system. Strict fuzzy processing Processing of information using a fuzzy system usually begins with an operation of fuzzyfication and ends with defuzzyfication. Fuzzyfication, in general, is the conversion of a crisp value into fuzzyfication and defuzzyfication and vice versa. This operation can be done in many different ways. A proper choice of them (especially the defuzzyfication method) often has a significant impact on the correctness and effectiveness of the whole model. Furthermore, the change of fuzzy value into a crisp one is the replacement of a complex value with a simpler one. Such action usually involves some approximation or rounding, so it introduces an additional error into the results. The repetition of such actions is not recommended, especially when the output value of one stage will be the input value for another. If we want to model more complex structures such as the brain using fuzzy values, the exclusion of the fuzzyfication and defuzzyfication operations outside the base system is recommended. For future analysis, we will call a fuzzy system without fuzzyfication and defuzzyfication stages as the fuzzy inference block (FIB). Its idea is presented in Figure 1. Such element is a conceptual base for a cascade modeling complex relations described linguistically. Figure 2:CFCM. Figure 2 presents an example of some complicated dependencies modeled by FIBs. For purposes of this paper, we can call such construction complex fuzzy cascade model (CFCM). It is worth noting that every FIB can represent one agent from the multiagent architecture. With this approach, we can describe even more complex structures. It is easy to imagine that, in place of single FIBs, we can insert the CFCM; thus, we introduce a kind of recursion in the CFCM, where only the lowest level relates directly to FIBs. Still, despite the high complexity of the model, we describe relations at various stages linguistically. Important issue However, the idea of CFCM with FIBs seems quite good for the linguistic modeling of complex relations. There can arise some problems. The classical methods for fuzzy Prokopowicz and Mikolajewski: Fuzzy-based simulations of brain functions103 models often produce fuzzy answer sets, which are much fragmented, not normal, and not convex. Such results formally still are fuzzy sets, but their forward processing without defuzzyfication could be questionable. The above-mentioned problems do not occur if we use the ordered fuzzy number (OFN) model [23­26]. It is quite a recent proposition for modeling the calculations on imprecise values in a similar way as the fuzzy numbers. There are proposed special methods for OFNs to use them in fuzzy systems [27­29]. An important advantage of this method is that we get a kind of fuzzy number on each step of processing data. Thus, a further use of such result is easy and fluent without defuzzyfication and then fuzzyfication again. reliable brain simulation based on fuzzy logic techniques useful in both basic sciences and applied sciences. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission. Research funding: None declared. Employment or leadership: None declared. Honorarium: None declared. Competing interests: The funding organization(s) played no role in the study design; in the collection, analysis, and interpretation of data; in the writing of the report; or in the decision to submit the report for publication. Limitations of the proposed approach Current models need additional validation toward the effective replication of natural processes. They are abstract networks proving only the basic principles of brain circuit functioning due to the lack of spiking neurons and hard implementation of the biological properties of neurons and synapses. However, such solutions implementing brain mechanisms in the form of relatively abstract computational principles may be useful on system levels, where scaling is not fully possible, and biologically relevant networks are too complicated to simulate. Such simple models are less time-consuming and proper for the testing of the preliminary hypotheses.

Journal

Bio-Algorithms and Med-Systemsde Gruyter

Published: Sep 1, 2016

References