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The ensemble of fuzzy clustering can address the problems presented in the base clustering, such as fluctuations in results due to random initialization and performance degradation due to outliers. However, the performance of fuzzy clustering ensembles is still hampered by some challenges that include misaligned membership matrices, loss of information in the cosimilarity matrix, large storage space, unstable ensemble results due to an additional reclustering, the need for original data information for assistance, etc. To address these issues, we propose a parameter-free robust ensemble framework for fuzzy clustering. After obtaining the set of membership matrices, we cascade these membership matrices and mine the latent spectral matrix of the raw data. Benefiting from this step, we obtain global features of the dataset without knowing the specific data. Then, our framework uses transition matrices to solve the alignment problem, avoiding the storage of large-scale matrices. Most importantly, we introduce a robust weighted mechanism in the optimization model, where each base clustering is adaptively adjusted and the effect of outliers is suppressed by a robust function. In addition, the model yields the results as a membership matrix, which produces the exact partition results directly without any subsequent clustering operations. Finally, since our model is a parameter-free model, the setting of hyperparameters is avoided and the applicability of the model is improved as well. The effective algorithm of the optimization model is derived and its time complexity and convergence are analyzed. The results of competitive experiments on benchmark data show that the proposed ensemble framework is effective compared to state-of-the-art methods.

Kernel clustering has the ability to get the inherent nonlinear structure of the data. But the high computational complexity and the unknown representation of the kernel space make it unavailable for the data clustering in distributed peer-to-peer (P2P) networks. To solve this issue, we propose a new series of random feature-based collaborative kernel clustering algorithms in this article. In the most basic algorithm, each node in a distributed P2P network first maps its data into a low-dimensional random feature space with the approximation of the given kernel by using the random Fourier feature mapping method. Then, each node independently searches the clusters with its local data and the collaborative knowledge from its neighbor nodes, and the distributed clustering is performed among all network nodes until reaching the global consensus result, i.e., all nodes have the same cluster centers. In addition, an improved version is designed with assignment of feature weights, which is optimized by the maximum-entropy technique to extract important features for the cluster identification. What’s more, to relief the impact of different kernel functions and related parameters on clustering results, the combination of multiple kernels rather than a single kernel is adopted for the low-dimensional approximation, and the optimized weights are assigned to provide the guidance on the choice of the kernels and their parameters and discover significant features at the same time. Experiments on synthetic and real-world datasets show that the proposed methods achieve similar and even better results than the traditional kernel clustering methods on various performance metrics, including the average classification rate, the average normalized mutual information, and the average adjusted rand index. More importantly, the low-dimensional random features approximated to kernels and the distributed clustering mechanism adopted in these methods bring the greatly lower temporal complexity.

In recent years, benefiting from the abilities in implementation of the smooth operation on noises and preservation of the original gradient information on the texture edges, the guided filter (GF)-based fuzzy clustering has achieved inspiring performance in the task of image segmentation. However, different to image pixels, the general data samples do not have the spatial adjacency relations. Current GF-based methods suffer some limitations in general data clustering. To solve this issue, a series of improved GF-based fuzzy clustering algorithms are proposed in this paper for general data analysis. In the most basic algorithm, a new data filtering window is first defined according to the neighbor relationships between data samples, and a pruning mechanism is designed to ensure the symmetry of neighbor samples. Then, the GF-based Fuzzy C-Means algorithm is put forward for the general data clustering. In addition, a weighted version is presented to process high-dimensional data, in which each dimension is assigned a weight, and the entropy regularization method is applied to optimize the weight assignment and highlight the important dimensions on both filtering and clustering. Furthermore, the kernelization of the above methods are realized for the non-linear data. Experimental results on synthetic and real-world datasets demonstrate better performance of the proposed methods in comparison with some existing FCM-type clustering approaches.

Categorical data are widely available in many real-world applications, and to discover valuable patterns in such data by clustering is of great importance. However, the lack of a decent quantitative relationship among categorical values makes traditional clustering approaches, which are usually developed for numerical data, perform poorly on categorical datasets. To solve this problem and boost the performance of clustering for categorical data, we propose a novel fuzzy clustering model in this article. At first, by approximating the maximum a posteriori (MAP) estimation of a discrete distribution of data partition, a new fuzzy clustering objective function is designed for categorical data. The Bayesian dissimilarity measure is formulated in this objective to tackle the subtle relationships between categorical values efficiently. Then, to further enhance the performance of clustering, a novel Kullback–Leibler divergence-based graph regularization is integrated into the clustering objective to exploit the prior knowledge on datasets, for example, the information about correlations of data points. The proposed model is solved by the alternative optimization and the experimental results on the synthetic and real-world datasets show that it outperforms the classical and relevant state-of-the-art algorithms. We also present the parameter analysis of our approach, and conduct a comprehensive study on the effectiveness of the Bayesian dissimilarity measure and the KL divergence-based graph regularization.

For a security system built on symmetric-key cryptography algorithms, the substitution box (S-box) plays a crucial role to resist cryptanalysis. In this article, we incorporate quantum chaos and PWLCM chaotic map into a new method of S-box design. The secret key is transformed to generate a six tuple system parameter, which is involved in the generation process of chaotic sequences of two chaotic systems. The output of one chaotic system will disturb the parameters of another chaotic system in order to improve the complexity of encryption sequence. S-box is obtained by XOR operation of the output of two chaotic systems. Over the obtained 500 key-dependent S-boxes, we test the S-box cryptographical properties on bijection, nonlinearity, SAC, BIC, differential approximation probability, respectively. Performance comparison of proposed S-box with those chaos-based one in the literature has been made. The results show that the cryptographic characteristics of proposed S-box has met our design objectives and can be applied to data encryption, user authentication and system access control.

Autonomous systems are an emerging AI technology functioning without human intervention underpinned by the latest advances in intelligence, cognition, computer, and systems sciences. This paper explores the intelligent and mathematical foundations of autonomous systems. It focuses on structural and behavioral properties that constitute the intelligent power of autonomous systems. It explains how system intelligence aggregates from reflexive, imperative, adaptive intelligence to autonomous and cognitive intelligence. A hierarchical intelligence model &#x0028 HIM &#x0029 is introduced to elaborate the evolution of human and system intelligence as an inductive process. The properties of system autonomy are formally analyzed towards a wide range of applications in computational intelligence and systems engineering. Emerging paradigms of autonomous systems including brain-inspired systems, cognitive robots, and autonomous knowledge learning systems are described. Advances in autonomous systems will pave a way towards highly intelligent machines for augmenting human capabilities.

Kernel clustering methods are useful to discover the non-linear structures hidden in data, but they suffer from the difficulty of kernel selection and high computational complexity. In this paper, we propose a novel random feature map-based multiple kernel fuzzy clustering method with all feature weights, in which low-rank randomized features of multiple kernels are generated by random Fourier feature map and Quasi-Monte Carlo feature map, and maximum entropy technique is applied to optimize the weights of all feature attributes. The proposed method is effective to extract important kernel and the important attributes of the kernel so as to achieve good clustering results. What is more, compared with conventional kernel clustering methods, our method is much more time-saving and is available to large data sets. The experiments based on various data sets show the superiority and efficiency of the proposed method.

Uncertain data clustering has been recognized as an essential task in the research of data mining. Many centralized clustering algorithms are extended by defining new distance or similarity measurements to tackle this issue. With the fast development of network applications, these centralized methods show their limitations in conducting data clustering in a large dynamic distributed peer-to-peer network due to the privacy and security concerns or the technical constraints brought by distributive environments. In this paper, we propose a novel distributed uncertain data clustering algorithm, in which the centralized global clustering solution is approximated by performing distributed clustering. To shorten the execution time, the reduction technique is then applied to transform the proposed method into its deterministic form by replacing each uncertain data object with its expected centroid. Finally, the attribute-weight-entropy regularization technique enhances the proposed distributed clustering method to achieve better results in data clustering and extract the essential features for cluster identification. The experiments on both synthetic and real-world data have shown the efficiency and superiority of the presented algorithm.

Cognitive Computing (CC) is a contemporary field of studies on intelligent computing methodologies and brain-inspired mechanisms of cognitive systems, cognitive machine learning and cognitive robotics. The IEEE conference ICCI*CC'17 on Cognitive Informatics and Cognitive Computing was focused on the theme of neurocomputation, cognitive machine learning and brain-inspired systems. This article reports the plenary panel (Part II) in IEEE ICCI*CC'17 at Oxford University. The summary is contributed by distinguished panelists who are part of the world's renowned scholars in the transdisciplinary field of cognitive computing.

Cognitive consumer electronics (CE), the fastest-growing sector worldwide that is driven by machine intelligence and cognitive systems, is triggered and enabled by audio- and video-capturing devices, smart sensors, health- and fitness-monitoring devices, security and education electronics, and intelligent systems. Smart consumer sensors and cognitive systems are synergized through the Internet of Things (IoT) for optimal information sharing, communication, real-time updates, data analytics, and enhanced support for decision making. Biometric-based devices, originally intended for large-scale applications in airports, border controls, disaster zones, or refugee migration zones, are enabling a wide range of applications in commercial and consumer sectors as standalone systems or with interconnected sensor networks. This article introduces the applications of Microsoft Kinect in cognitive systems for smart CE, and, using Kinect sensors, a human-behavior cognition technology is presented for gesture and activity recognition. As a novel front end of pervasive cognitive systems, the challenges and applications of a Kinect sensor-based system will be explored in CE, such as smart automobiles, health care, surveillance, and activity recognition.

Cognitive Informatics (CI) is a contemporary field of basic studies on the brain, computational intelligence theories and underpinning denotational mathematics. Its applications include cognitive systems, cognitive computing, cognitive machine learning and cognitive robotics. IEEE ICCI*CC'17 on Cognitive Informatics and Cognitive Computing was focused on the theme of neurocomputation, cognitive machine learning and brain-inspired systems. This paper reports the plenary panel (Part I) at IEEE ICCI*CC'17 held at Oxford University. The summary is contributed by invited keynote speakers and distinguished panelists who are part of the world's renowned scholars in the transdisciplinary field of CI and cognitive computing.

Music emotions recognition (MER) is a challenging field of studies addressed in multiple disciplines such as musicology, cognitive science, physiology, psychology, arts and affective computing. In this article, music emotions are classified into four types known as those of pleasing, angry, sad and relaxing. MER is formulated as a classification problem in cognitive computing where 548 dimensions of music features are extracted and modeled. A set of classifications and machine learning algorithms are explored and comparatively studied for MER, which includes Support Vector Machine (SVM), k-Nearest Neighbors (KNN), Neuro-Fuzzy Networks Classification (NFNC), Fuzzy KNN (FKNN), Bayes classifier and Linear Discriminant Analysis (LDA). Experimental results show that the SVM, FKNN and LDA algorithms are the most effective methodologies that obtain more than 80% accuracy for MER.

Cognitive knowledge learning (CKL) is a fundamental methodology for cognitive robots and machine learning. Traditional technologies for machine learning deal with object identification, cluster classification, pattern recognition, functional regression and behavior acquisition. A new category of CKL is presented in this paper embodied by the Algorithm of Cognitive Concept Elicitation (ACCE). Formal concepts are autonomously generated based on collective intension (attributes) and extension (objects) elicited from informal descriptions in dictionaries. A system of formal concept generation by cognitive robots is implemented based on the ACCE algorithm. Experiments on machine learning for knowledge acquisition reveal that a cognitive robot is able to learn synergized concepts in human knowledge in order to build its own knowledge base. The machine–generated knowledge base demonstrates that the ACCE algorithm can outperform human knowledge expressions in terms of relevance, accuracy, quantification and cohesiveness.

Big data are pervasively generated by human cognitive processes, formal inferences, and system quantifications. This paper presents the cognitive foundations of big data systems towards big data science. The key perceptual model of big data systems is the recursively typed hyperstructure (RTHS). The RTHS model reveals the inherited complexities and unprecedented difficulty in big data engineering. This finding leads to a set of mathematical and computational models for efficiently processing big data systems. The cognitive relationship between data, information, knowledge, and intelligence is formally described.

Basic studies in denotational mathematics and mathematical engineering have led to the theory of abstract intelligence (aI), which is a set of mathematical models of natural and computational intelligence in cognitive informatics (CI) and cognitive computing (CC). Abstract intelligence triggers the recent breakthroughs in cognitive systems such as cognitive computers, cognitive robots, cognitive neural networks, and cognitive learning. This paper reports a set of position statements presented in the plenary panel (Part II) of IEEE ICCI*CC'16 on Cognitive Informatics and Cognitive Computing at Stanford University. The summary is contributed by invited panelists who are part of the world's renowned scholars in the transdisciplinary field of CI and CC.

Music emotion recognition (MER) is a challenging field of studies that has been addressed in multiple disciplines such as cognitive science, physiology, psychology, musicology, and arts. In this paper, music emotions are modeled as a set of continuous variables composed of valence and arousal (VA) values based on the Valence-Arousal model. MER is formulated as a regression problem where 548 dimensions of music features were extracted and selected. A wide range of methods including multivariate adaptive regression spline, support vector regression (SVR), radial basis function, random forest regression (RFR), and regression neural networks are adopted to recognize music emotions. Experimental results show that these regression algorithms have led to good regression effect for MER. The optimal R2 statistics and VA values are 29.3% and 62.5%, respectively, which are obtained by the RFR and SVR algorithms in the relief feature space.

The theme of IEEE ICCI*CC'16 on Cognitive Informatics (CI) and Cognitive Computing (CC) was on cognitive computers, big data cognition, and machine learning. CI and CC are a contemporary field not only for basic studies on the brain, computational intelligence theories, and denotational mathematics, but also for engineering applications in cognitive systems towards deep learning, deep thinking, and deep reasoning. This paper reports a set of position statements presented in the plenary panel (Part I) in IEEE ICCI*CC'16 at Stanford University. The summary is contributed by invited panelists who are part of the world's renowned scholars in the transdisciplinary field of CI and CC.

Knowledge learning is the sixth and the most fundamental category of machine learning mimicking the brain. It is recognized that the semantic space of machine knowledge is a hierarchical concept network (HCN), which can be rigorously represented by formal concepts in concept algebra and semantic algebra. This paper presents theories and algorithms of hierarchical concept classification by quantitative semantic analysis based on machine learning. Semantic equivalence between formal concepts is rigorously measured by an Algorithm of Concept Equivalence Analysis (ACEA). The semantic hierarchy among formal concepts is quantitatively determined by an Algorithm of Relational Semantic Classification (ARSC). Experiments applying Algorithms ACEA and ARSC on a set of formal concepts have been successfully conducted, which demonstrate a deep machine understanding of formal concepts and quantitative relations in the hierarchical semantic space by machine learning beyond human empirical perspectives.

Knowledge is one of the fundamental cognitive objects in the brain among those of data, information, and intelligence. Knowledge can be classified into two main categories, i.e., conceptual knowledge for knowing to-be and behavioral knowledge for knowing to-do, particularly the former. This paper presents a basic study on a mathematical theory of knowledge towards knowledge science. The taxonomy and cognitive foundations of knowledge are explored, which reveal that the basic cognitive structure of conceptual knowledge is a formal concept and that of behavioral knowledge is a formal process. Mathematical models of knowledge are created in order to enable formal representation and rigorous manipulation of knowledge. A set of formal principles and properties of knowledge is elicited and elaborated towards the development of knowledge science and cognitive knowledge systems. It is discovered that the basic unit of knowledge is a binary relation, shortly bir, as a counterpart of bit (a binary digit) for information and data.

Basic studies in system science explore the theories, principles, and properties of abstract and concrete systems as well as their applications in system engineering. Systems are the most complicated entities and phenomena in abstract, physical, information, cognitive, brain, and social worlds across a wide range of science and engineering disciplines. The mathematical model of a general system is embodied as a hyperstructure of the abstract system. The theoretical framework of system science is formally described by a set of algebraic operations on abstract systems known as system algebra. A set of abstract structures, properties, behaviors, and principles is rigorously formalized in contemporary system theories. Applications of the formal theories of system science in system engineering, intelligent engineering, cognitive informatics, cognitive robotics, software engineering, cognitive linguistics, and cognitive computing are demonstrated, which reveals how system structural and behavioral complexities may be efficiently reduced in system representation, modeling, analysis, synthesis, inference, and implementation.

A recent discovery in computer and software sciences is that information in general is a deterministic abstract quantity rather than a probability-based property of the nature. Information is a general form of abstract objects represented by symbolical, mathematical, communication, computing, and cognitive systems. Therefore, information science is one of the contemporary scientific disciplines collectively known as abstract sciences such as system, information, cybernetics, cognition, knowledge, and intelligence sciences. This paper presents the cognitive foundations, mathematical models, and formal properties of information towards an extended theory of information science. From this point of view, information is classified into the categories of classic, computational, and cognitive information in the contexts of communication, computation, and cognition, respectively. Based on the three generations of information theories, a coherent framework of contemporary information is introduced, which reveals the nature of information and the fundamental principles of information science and engineering.

Cognitive robots are brain-inspired robots that are capable of inference, perception, and learning mimicking the cognitive mechanisms of the brain. Cognitive learning theories and methodologies for knowledge and behavior acquisition are centric in cognitive robotics. This paper explores the cognitive foundations and denotational mathematical means of cognitive learning engines (CLE) and cognitive knowledge bases (CKB) for cognitive robots. The architectures and functions of CLE are formally presented. A content-addressed knowledge base access methodology for CKB is rigorously elaborated. The CLE and CKB methodologies are not only designed to explain the mechanisms of human knowledge acquisition and learning, but also applied in the development of cognitive robots, cognitive computers, and knowledge-based systems.

Cognitive Informatics (CI) is a contemporary multidisciplinary field spanning across computer science, information science, cognitive science, brain science, intelligence science, knowledge science, cognitive linguistics, and cognitive philosophy. Cognitive Computing (CC) is a novel paradigm of intelligent computing methodologies and systems based on CI that implements computational intelligence by autonomous inferences and perceptions mimicking the mechanisms of the brain. This paper reports a set of position statements presented in the plenary panel of IEEE ICCI*CC'14 on Cognitive Informatics and Cognitive Computing. The summary is contributed by invited panelists who are part of the world's renowned researchers and scholars in the transdisciplinary field of cognitive informatics and cognitive computing.

To investigate the effect of different heat-stimulating time lengths on lower back pain.

Relations are one of the most important conceptual models and mathematical entities in logic, discrete mathematics, computer science, software science, system science, and formal semantics. However, some fundamental and indispensable operations on formal relations were overlooked in traditional studies. This paper presents an extended relation theory with a set of novel algebraic operators on relations beyond classic operations. The algebraic operators on formal relations known as the incremental union and decremental disunion are formally elaborated. The property of relational gains is mathematically modeled, which explains the dynamic mechanism of relations generated by associations of static sets of objects in physical or abstract systems.

Big data are products of human collective intelligence that are exponentially increasing in all facets of quantity, complexity, semantics, distribution, and processing costs in computer science, cognitive informatics, web-based computing, cloud computing, and computational intelligence. This paper presents fundamental big data analysis and mining technologies in the domain of social networks as a typical paradigm of big data engineering. A key principle of computational sociology known as the characteristic opinion equilibrium is revealed in social networks and electoral systems. A set of numerical and fuzzy models for collective opinion analyses is formally presented. Fuzzy data mining methodologies are rigorously described for collective opinion elicitation and benchmarking in order to enhance the conventional counting and statistical methodologies for big data analytics.

Humor is an advanced emotional and cognitive ability of mankind that involves complex semantic inference and deep passionate appreciation. This paper presents the cognitive foundations of amusement and a general theory of humor based on the recent advances in cognitive informatics, cognitive linguistics, cognitive computing, and fuzzy causal analyses. A theory of fuzzy false causation (FFC) is introduced that reveals humor and jokes as false causations in fuzzy causal inferences. Base on the FFC theory, a general pattern of humor (GPH) is formalized for analyzing the settings and appreciations of a set of sample jokes. A formal measurement of the degree of amusement in jokes and humor is quantitatively described towards the rational explanation of jokes based on cognitive affective assessment. The formal models of humor and jokes enable machines for humor comprehension and appreciation in artificial intelligence, cognitive computing, computational intelligence, and cognitive robots.

A cognitive knowledge base (CKB) is a novel structure of intelligent knowledge base that represents and manipulates knowledge as a dynamic concept network mimicking human knowledge processing. The essence of CKB is the denotational mathematical model of formal concept that is dynamically associated to other concepts in a CKB beyond conventional rule-based or ontology-based knowledge bases. This paper presents a formal CKB and autonomous knowledge manipulation system based on recent advances in neuroinformatics, concept algebra, semantic algebra, and cognitive computing. An item knowledge in CKB is represented by a formal concept, while the entire knowledge base is embodied by a dynamic concept network. The CKB system is manipulated by algorithms of knowledge acquisition and retrieval on the basis of concept algebra. CKB serves as a kernel of cognitive learning engines for cognitive robots and machine learning systems. CKB plays a central role not only in explaining the mechanisms of human knowledge acquisition and learning, but also in the development of cognitive robots, cognitive learning engines, and knowledge-based systems.

Eyes as the unique organ possess intensively direct connections to the brain and dynamically perceptual accessibility to the mind. This paper analyzes the cognitive mechanisms of eyes not only as the sensory of vision, but also the browser of internal memory in thinking and perception. The browse function of eyes is created by abstract conditioning of the eye's tracking pathway for accessing internal memories, which enables eye movements to function as the driver of the perceptive thinking engine of the brain. The dual mechanisms of the eyes as both the external sensor of the brain and the internal browser of the mind are explained based on evidences and cognitive experiences in cognitive informatics, neuropsychology, cognitive science, and brain science. The finding on the experiment's internal browsing mechanism of eyes reveals a crucial role of eyes interacting with the brain for accessing internal memory and the cognitive knowledge base in thinking, perception, attention, consciousness, learning, memorization, and inference.

Concept algebra (CA) is a denotational mathematics for formal knowledge manipulation and natural language processing. In order to explicitly demonstrate the mathematical models of formal concepts and their algebraic operations in CA, a simulation and visualization software is developed in the MATLAB environment known as the Visual Simulator of Concept Algebra (VSCA). This paper presents the design and implementation of VSCA and the theories underpinning its development. Visual simulations for the sets of reproductive and compositional operations of CA are demonstrated by real-world examples throughout the elaborations of CA and VSCA.

To evaluate the effect on acne vulgaris of pricking-bloodletting cupping at Dazhui (GV 14) under acupuncture anesthesia, and establish whether providing anesthesia to the treatment area by manipulating Hegu (LI 4) and Quchi (LI 11) might have an additional therapeutic benefit.

The human sensory system is a perfect natural real-time distributed system. It transforms physical and chemical stimuli of the external environment into electronic neural signals by specialized sensory receptors. This paper presents a comprehensive framework of the human sensory system as well as its cognitive and theoretical foundations. A set of primary and perceptual sensory and neural receptors is formally modeled and analyzed. Sensory neural interfaces and interactions to the central and peripheral nervous systems of the brain and associated memories are systematically described. This work is a part of a strategic project towards the development of cognitive computers and cognitive robots.

Cognitive Informatics (CI) is a contemporary multidisciplinary field spanning across computer science, information science, cognitive science, brain science, intelligence science, knowledge science, cognitive linguistics, and cognitive philosophy. CI aims to investigate the internal information processing mechanisms and processes of the brain, the underlying abstract intelligence theories and denotational mathematics, and their engineering applications in cognitive computing and computational intelligence. This paper reports a set of eleven position statements presented in the plenary panel of IEEE ICCI*CC’13 on Cognitive Computers and Knowledge Processors contributed from invited panelists who are part of the world’s renowned researchers and scholars in the field of cognitive informatics and cognitive computing.

Intelligent knowledge base theories and technologies are fundamentally centric in machine learning and cognitive robotics. This paper presents the design of a formal knowledge retrieval system (FKTS) for intelligent knowledge base modeling and manipulations based on concept algebra. In order to rigorously design and implement FKTS, real-time process algebra (RTPA) is adopted to formally describe the architectures and behaviors of FKTS. The architectural model of FKTS in the form of a set of unified structure models (USMs) is rigorously described. On the basis of USMs, functional models of FKTS are hierarchically refined by a set of unified process models (UPMs). The UPMs of FFTS are divided into two subsystems known as those of the knowledge visualization and knowledge base retrieval subsystems where the content-addressed searching mechanism is implemented in knowledge bases manipulations. The FKTS system is design and implemented as a part of the cognitive learning engine (CLE) for cognitive computers and cognitive robots.

The human brain is a superbly marvelous and extremely complicated neurophysiological structure for generating natural intelligence that transforms cognitive information into colorful behaviors. The brain is the most complex and interesting objects in nature that requires rigorous scientific investigations by multidisciplinary methodologies and via transdisciplinary approaches where only low-level studies could not explain it. A fundamental problem and difficulty in contemporary brain science is the indistinguishable confusion of the cognitive mechanisms and neurophysiological structures of the kernel brain and its memories. This paper presents a set of formal neuroinformatics models of memory and a rigorous mapping between the cognitive functions of memory and their neurophysiological structures. The neurophysiological foundations of memory are rigorously described based on comprehensive cognitive models of memory. The cognitive architecture of human memory and its relationship to the intelligence power of the brain are logically analyzed. The cognitive roles of memory allocated in both cerebrum and cerebellum are revealed by mapping the functional models of memory onto corresponding neurophysiological structures of the brain. As a result, fundamental properties of memory and knowledge as well as their neurophysiological forms in the brain are systematically explained.

Attention is a complex mental function of humans in order to capture and serve the basic senses of vision, hearing, touch, smell, and taste, as well as internal motivations and perceptions. This paper presents a formal model and a cognitive process for rigorously explaining human attentions. Cognitive foundations of attentions and their relationships with consciousness and other perception processes are explored. The closed loop of attentions is identified that encompasses event capture and behavior reaction. Events for attention are classified into the categories of external stimuli and internal motivations. Behaviors as corresponding responses of attentions encompass recurrent, temporary, and reflex actions. Mathematical models of attentions are created as a foundation for rigorously describing the cognitive process of attentions in denotational mathematics. A wide range of applications of the unified attention model are identified in cognitive informatics, cognitive computing, and computational intelligence toward the mimic and simulation of human attention and perception in cognitive computers, cognitive robotics, and cognitive systems.

Consciousness is the sense of self and the sign of life in natural intelligence. One of the profound myths in cognitive informatics, psychology, brain science, and computational intelligence is how consciousness is generated by physiological organs and neural networks in the bran. This paper presents a formal model and a cognitive process of consciousness in order to explain how abstract consciousness is generated and what its cognitive mechanisms are. The hierarchical levels of consciousness are explored from the facets of neurology, physiology, and computational intelligence. A rigorous mathematical model of consciousness is created that elaborates the nature of consciousness. The cognitive process of consciousness is formally described using denotational mathematics. It is recognized that consciousness is a set of real-time mental information about bodily and emotional status of an individual stored in the cerebellums known as the Conscious Status Memory (CSM) and is processed/interpreted by the thalamus. The abstract intelligence model of consciousness can be applied in cognitive informatics, cognitive computing, and computational intelligence toward the mimicry and simulation of human perception and awareness of the internal states, external environment, and their interactions in reflexive, perceptive, cognitive, and instructive intelligence.

The Telephone Switching Systems (TSS) is a typical real-time system that is highly complicated in design and implementation. In order to deal with the extreme complexity in real-world settings, a suitable and efficient mathematical means is required beyond any programming language. To this purpose, an efficient and precise denotational mathematics known as the Real-Time Process Algebra (RTPA) and the RTPA methodology for system modeling are introduced. Empirical experimental results are reported in this paper on the implementation of TSS based on formal models of the system in RTPA. Three phases of experiments are designed on TSS conceptual modeling, system interface design, and programming implementation and testing. All groups in the experiments with 7 to 8 members have been able to efficiently understood, design, and implement the TSS system in a simplified version in four weeks, which has been estimated as a 10+ person-year project in the industry. The efficiency and expressiveness of RTPA are empirically demonstrated base on the case studies in the experiments.

Emotions are one of the important subconscious mechanisms that influence human behaviors, attentions, and decision making. The emotion process helps to determine how humans perceive their internal status and needs in order to form consciousness of an individual. Emotions have been studied from multidisciplinary perspectives and covered a wide range of empirical and psychological topics, such as understanding the emotional processes, creating cognitive and computational models of emotions, and applications in computational intelligence. This paper presents a comprehensive survey of cognitive and computational models of emotions resulted from multidisciplinary studies. It explores how cognitive models serve as the theoretical basis of computational models of emotions. The mechanisms underlying affective behaviors are examined as important elements in the design of these computational models. A comparative analysis of current approaches is elaborated based on recent advances towards a coherent cognitive computational model of emotions, which leads to the machine simulated emotions for cognitive robots and autonomous agent systems in cognitive informatics and cognitive computing.

Graphs are one of the most fundamental and widely used non-linear hierarchical structures of linked nodes. Problems in sciences and engineering can be formulated and solved by the graph model. This paper develops a comprehensive design pattern of formal digraphs using the Doubly-Linked List (DLL) architecture. The most complicated form of graphs known as the weighted digraph is selected as a general graph model, based on it simple graphs such as nondirected and/or nonweighted ones can be easily derived and tailored. A rigorous denotational mathematics, Real-Time Process Algebra (RTPA), is adopted, which allows both architectural and behavioral models of digraphs to be rigorously designed and implemented in a top-down approach. The architectural models of digraphs are created using RTPA architectural modeling methodologies known as the Unified Data Models (UDMs). The physical model of digraphs is implemented using nodes of DLL dynamically created in the memory. The behavioral models of digraphs are specified and refined by a set of 18 Unified Process Models (UPMs) in three categories namely the management operations, traversal operations, and node manipulation operations. This work has been applied in a number of real-time and nonreal-time system designs and specifications such as a Real-Time Operating System (RTOS+), graph-based and tree-based applications, and the ADT library for an RTPA-based automatic code generation tool.

Inference as the basic mechanism of thought is abilities gifted to human beings, which is a cognitive process that creates rational causations between a pair of cause and effect based on empirical arguments, formal reasoning, and/or statistical norms. It’s recognized that a coherent theory and mathematical means are needed for dealing with formal causal inferences. Presented is a novel denotational mathematical means for formal inferences known as Inference Algebra (IA) and structured as a set of algebraic operators on a set of formal causations. The taxonomy and framework of formal causal inferences of IA are explored in three categories: a) Logical inferences; b) Analytic inferences; and c) Hybrid inferences. IA introduces the calculus of discrete causal differential and formal models of causations. IA enables artificial intelligence and computational intelligent systems to mimic human inference abilities by cognitive computing. A wide range of applications of IA are identified and demonstrated in cognitive informatics and computational intelligence towards novel theories and technologies for machine-enabled inferences and reasoning. This work is presented in two parts. The inference operators of IA as well as their extensions and applications will be presented in this paper; while the structure of formal inference, the framework of IA, and the mathematical models of formal causations has been published in the first part of the paper in IJCINI 5(4).

Inference as the basic mechanism of thought is one of the gifted abilities of human beings. It is recognized that a coherent theory and mathematical means are needed for dealing with formal causal inferences. This paper presents a novel denotational mathematical means for formal inferences known as Inference Algebra (IA). IA is structured as a set of algebraic operators on a set of formal causations. The taxonomy and framework of formal causal inferences of IA are explored in three categories: a) Logical inferences on Boolean, fuzzy, and general logic causations; b) Analytic inferences on general functional, correlative, linear regression, and nonlinear regression causations; and c) Hybrid inferences on qualification and quantification causations. IA introduces a calculus of discrete causal differential and formal models of causations; based on them nine algebraic inference operators of IA are created for manipulating the formal causations. IA is one of the basic studies towards the next generation of intelligent computers known as cognitive computers. A wide range of applications of IA are identified and demonstrated in cognitive informatics and computational intelligence towards novel theories and technologies for machine-enabled inferences and reasoning.