Quaternion Neuro-Fuzzy Learning Algorithm for Fuzzy Rule Generation

Abstract—In order to generate or tune fuzzy rules, Neuro- Fuzzy learning algorithms with Gaussian type membership functions based on gradient-descent method are well known. In this paper, we propose a new learning approach, the Quaternion Neuro-Fuzzy learning algorithm. This method is an extension of the conventional method to four-dimensional space by using a quaternion neural network that maps quaternion to real values. Input, antecedent membership functions and consequent singletons are quaternion, and output is real. Four-dimensional input can be better represented by quaternion than by real values. We compared it with the conventional method by several function identification problems, and revealed that the proposed method outperformed the counterpart: The number of rules was reduced to 5 from 625, the number of epochs by one fortieth, and error by one tenth in the best cases.The Second International Conference on Robot, Vision and Signal Processing December 10-12, 2013 Kitakyushu, Japa

Selected aspects of complex, hypercomplex and fuzzy neural networks

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.Comment: 46 page

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Inverse Kinematic Analysis of Robot Manipulators

An important part of industrial robot manipulators is to achieve desired position and orientation of end effector or tool so as to complete the pre-specified task. To achieve the above stated goal one should have the sound knowledge of inverse kinematic problem. The problem of getting inverse kinematic solution has been on the outline of various researchers and is deliberated as thorough researched and mature problem. There are many fields of applications of robot manipulators to execute the given tasks such as material handling, pick-n-place, planetary and undersea explorations, space manipulation, and hazardous field etc. Moreover, medical field robotics catches applications in rehabilitation and surgery that involve kinematic, dynamic and control operations. Therefore, industrial robot manipulators are required to have proper knowledge of its joint variables as well as understanding of kinematic parameters. The motion of the end effector or manipulator is controlled by their joint actuator and this produces the required motion in each joints. Therefore, the controller should always supply an accurate value of joint variables analogous to the end effector position. Even though industrial robots are in the advanced stage, some of the basic problems in kinematics are still unsolved and constitute an active focus for research. Among these unsolved problems, the direct kinematics problem for parallel mechanism and inverse kinematics for serial chains constitute a decent share of research domain. The forward kinematics of robot manipulator is simpler problem and it has unique or closed form solution. The forward kinematics can be given by the conversion of joint space to Cartesian space of the manipulator. On the other hand inverse kinematics can be determined by the conversion of Cartesian space to joint space. The inverse kinematic of the robot manipulator does not provide the closed form solution. Hence, industrial manipulator can achieve a desired task or end effector position in more than one configuration. Therefore, to achieve exact solution of the joint variables has been the main concern to the researchers. A brief introduction of industrial robot manipulators, evolution and classification is presented. The basic configurations of robot manipulator are demonstrated and their benefits and drawbacks are deliberated along with the applications. The difficulties to solve forward and inverse kinematics of robot manipulator are discussed and solution of inverse kinematic is introduced through conventional methods. In order to accomplish the desired objective of the work and attain the solution of inverse kinematic problem an efficient study of the existing tools and techniques has been done. A review of literature survey and various tools used to solve inverse kinematic problem on different aspects is discussed. The various approaches of inverse kinematic solution is categorized in four sections namely structural analysis of mechanism, conventional approaches, intelligence or soft computing approaches and optimization based approaches. A portion of important and more significant literatures are thoroughly discussed and brief investigation is made on conclusions and gaps with respect to the inverse kinematic solution of industrial robot manipulators. Based on the survey of tools and techniques used for the kinematic analysis the broad objective of the present research work is presented as; to carry out the kinematic analyses of different configurations of industrial robot manipulators. The mathematical modelling of selected robot manipulator using existing tools and techniques has to be made for the comparative study of proposed method. On the other hand, development of new algorithm and their mathematical modelling for the solution of inverse kinematic problem has to be made for the analysis of quality and efficiency of the obtained solutions. Therefore, the study of appropriate tools and techniques used for the solution of inverse kinematic problems and comparison with proposed method is considered. Moreover, recommendation of the appropriate method for the solution of inverse kinematic problem is presented in the work. Apart from the forward kinematic analysis, the inverse kinematic analysis is quite complex, due to its non-linear formulations and having multiple solutions. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Artificial neural network (ANN) can be gainfully used to yield the desired results. Therefore, in the present work several models of artificial neural network (ANN) are used for the solution of the inverse kinematic problem. This model of ANN does not rely on higher mathematical formulations and are adept to solve NP-hard, non-linear and higher degree of polynomial equations. Although intelligent approaches are not new in this field but some selected models of ANN and their hybridization has been presented for the comparative evaluation of inverse kinematic. The hybridization scheme of ANN and an investigation has been made on accuracies of adopted algorithms. On the other hand, any Optimization algorithms which are capable of solving various multimodal functions can be implemented to solve the inverse kinematic problem. To overcome the problem of conventional tool and intelligent based method the optimization based approach can be implemented. In general, the optimization based approaches are more stable and often converge to the global solution. The major problem of ANN based approaches are its slow convergence and often stuck in local optimum point. Therefore, in present work different optimization based approaches are considered. The formulation of the objective function and associated constrained are discussed thoroughly. The comparison of all adopted algorithms on the basis of number of solutions, mathematical operations and computational time has been presented. The thesis concludes the summary with contributions and scope of the future research work

Machine learning methods for sign language recognition: a critical review and analysis.

Sign language is an essential tool to bridge the communication gap between normal and hearing-impaired people. However, the diversity of over 7000 present-day sign languages with variability in motion position, hand shape, and position of body parts making automatic sign language recognition (ASLR) a complex system. In order to overcome such complexity, researchers are investigating better ways of developing ASLR systems to seek intelligent solutions and have demonstrated remarkable success. This paper aims to analyse the research published on intelligent systems in sign language recognition over the past two decades. A total of 649 publications related to decision support and intelligent systems on sign language recognition (SLR) are extracted from the Scopus database and analysed. The extracted publications are analysed using bibliometric VOSViewer software to (1) obtain the publications temporal and regional distributions, (2) create the cooperation networks between affiliations and authors and identify productive institutions in this context. Moreover, reviews of techniques for vision-based sign language recognition are presented. Various features extraction and classification techniques used in SLR to achieve good results are discussed. The literature review presented in this paper shows the importance of incorporating intelligent solutions into the sign language recognition systems and reveals that perfect intelligent systems for sign language recognition are still an open problem. Overall, it is expected that this study will facilitate knowledge accumulation and creation of intelligent-based SLR and provide readers, researchers, and practitioners a roadmap to guide future direction

Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Sciences), Vol. IV

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors - all collected in the previous three decades (1980-2010) – but most of them are from the last decade (2000-2010), some of them being lost and found, yet others are extended, diversified, improved versions. This is an eclectic tome of 800 pages with papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory, information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics. It was my preoccupation and collaboration as author, co-author, translator, or cotranslator, and editor with many scientists from around the world for long time. Many topics from this book are incipient and need to be expanded in future explorations

Development of advanced autonomous learning algorithms for nonlinear system identification and control

Identification of nonlinear dynamical systems, data stream analysis, etc. is usually handled by autonomous learning algorithms like evolving fuzzy and evolving neuro-fuzzy systems (ENFSs). They are characterized by the single-pass learning mode and open structure-property. Such features enable their effective handling of fast and rapidly changing natures of data streams. The underlying bottleneck of ENFSs lies in its design principle, which involves a high number of free parameters (rule premise and rule consequent) to be adapted in the training process. This figure can even double in the case of the type-2 fuzzy system. From this literature gap, a novel ENFS, namely Parsimonious Learning Machine (PALM) is proposed in this thesis. To reduce the number of network parameters significantly, PALM features utilization of a new type of fuzzy rule based on the concept of hyperplane clustering, where it has no rule premise parameters. PALM is proposed in both type-1 and type-2 fuzzy systems where all of them characterize a fully dynamic rule-based system. Thus, it is capable of automatically generating, merging, and tuning the hyperplane-based fuzzy rule in a single-pass manner. Moreover, an extension of PALM, namely recurrent PALM (rPALM), is proposed and adopts the concept of teacher-forcing mechanism in the deep learning literature. The efficacy of both PALM and rPALM have been evaluated through numerical study with data streams and to identify nonlinear unmanned aerial vehicle system. The proposed models showcase significant improvements in terms of computational complexity and the number of required parameters against several renowned ENFSs while attaining comparable and often better predictive accuracy. The ENFSs have also been utilized to develop three autonomous intelligent controllers (AICons) in this thesis. They are namely Generic (G) controller, Parsimonious controller (PAC), and Reduced Parsimonious Controller (RedPAC). All these controllers start operating from scratch with an empty set of fuzzy rules, and no offline training is required. To cope with the dynamic behavior of the plant, these controllers can add, merge or prune the rules on demand. Among three AICons, the G-controller is built by utilizing an advanced incremental learning machine, namely Generic Evolving Neuro-Fuzzy Inference System. The integration of generalized adaptive resonance theory provides a compact structure of the G-controller. Consequently, the faster evolution of structure is witnessed, which lowers its computational cost. Another AICon namely, PAC is rooted with PALM's architecture. Since PALM has a dependency on user-defined thresholds to adapt the structure, these thresholds are replaced with the concept of bias- variance trade-off in PAC. In RedPAC, the network parameters have further reduced in contrast with PALM-based PAC, where the number of consequent parameters has reduced to one parameter per rule. These AICons work with very minor expert domain knowledge and developed by incorporating the sliding mode control technique. In G-controller and RedPAC, the control law and adaptation laws for the consequent parameters are derived from the SMC algorithm to establish a stable closed-loop system, where the stability of these controllers are guaranteed by using the Lyapunov function and the uniform asymptotic convergence of tracking error to zero is witnessed through the implication of an auxiliary robustifying control term. While using PAC, the boundedness and convergence of the closed-loop control system's tracking error and the controller's consequent parameters are confirmed by utilizing the LaSalle-Yoshizawa theorem. Their efficacy is evaluated by observing various trajectory tracking performance of unmanned aerial vehicles. The accuracy of these controllers is comparable or better than the benchmark controllers where the proposed controllers incur significantly fewer parameters to attain similar or better tracking performance