The Encyclopedia of Neutrosophic Researchers - vol. 1

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

The Encyclopedia of Neutrosophic Researchers - vol. 3

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

Hybrid intelligent parameter tuning approach for COVID-19 time series modeling and prediction

A novel hybrid intelligent approach for tuning the parameters of Interval Type-2 Intuitionistic Fuzzy Logic System (IT2IFLS) is introduced for the modeling and prediction of coronavirus disease 2019 (COVID-19) time series. COVID-19 is known to be a virus caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARSCoV-2) with a huge negative impact on human, work and world economy. Globally, more than 100 million people have been infected with over two million deaths and it is not certain when the pandemic will end. Predicting the trend of the COVID-19 therefore becomes an important and challenging task. Many approaches ranging from statistical approaches to machine learning methods have been formulated and applied for the prediction of the disease. In this work, the sliding mode control learning algorithm is used to adjust the parameters of the antecedent parts of  IT2IFLS system while the gradient descent backpropagation is adopted to tune the consequent parameters in a hybrid manner. The results of the hybrid intelligent learning model are compared with results of single learning models using sliding mode control and gradient descent algorithms and found to provide good performance in terms of Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) especially in noisy environments. The type-2 hybrid model also outperforms its type-1 counterparts in the different problem instances

Data Science: Measuring Uncertainties

With the increase in data processing and storage capacity, a large amount of data is available. Data without analysis does not have much value. Thus, the demand for data analysis is increasing daily, and the consequence is the appearance of a large number of jobs and published articles. Data science has emerged as a multidisciplinary field to support data-driven activities, integrating and developing ideas, methods, and processes to extract information from data. This includes methods built from different knowledge areas: Statistics, Computer Science, Mathematics, Physics, Information Science, and Engineering. This mixture of areas has given rise to what we call Data Science. New solutions to the new problems are reproducing rapidly to generate large volumes of data. Current and future challenges require greater care in creating new solutions that satisfy the rationality for each type of problem. Labels such as Big Data, Data Science, Machine Learning, Statistical Learning, and Artificial Intelligence are demanding more sophistication in the foundations and how they are being applied. This point highlights the importance of building the foundations of Data Science. This book is dedicated to solutions and discussions of measuring uncertainties in data analysis problems

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Multiple-Criteria Decision Making

Decision-making on real-world problems, including individual process decisions, requires an appropriate and reliable decision support system. Fuzzy set theory, rough set theory, and neutrosophic set theory, which are MCDM techniques, are useful for modeling complex decision-making problems with imprecise, ambiguous, or vague data.This Special Issue, “Multiple Criteria Decision Making”, aims to incorporate recent developments in the area of the multi-criteria decision-making field. Topics include, but are not limited to:- MCDM optimization in engineering;- Environmental sustainability in engineering processes;- Multi-criteria production and logistics process planning;- New trends in multi-criteria evaluation of sustainable processes;- Multi-criteria decision making in strategic management based on sustainable criteria

The Encyclopedia of Neutrosophic Researchers, 5th Volume

Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements. There are about 7,000 neutrosophic researchers, within 89 countries around the globe, that have produced about 4,000 publications and tenths of PhD and MSc theses, within more than two decades. This is the fifth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation, with an introduction contains a short history of neutrosophics, together with links to the main papers and books

Interval type-2 Atanassov-intuitionistic fuzzy logic for uncertainty modelling

This thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark a shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzzy set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess this thesis investigates a new paradigm for uncertainty modelling by employing a new class of type-2 fuzzy logic system that utilises fuzzy sets with membership and non-membership functions that are intervals. Fuzzy logic systems, employing type-1 fuzzy sets, that mark shift from computing with numbers towards computing with words have made remarkable impacts in the field of artificial intelligence. Fuzzy logic systems of type-2, a generalisation of type-1 fuzzy logic systems that utilise type-2 fuzzy sets, have created tremendous advances in uncertainty modelling. The key feature of the type-2 fuzzy logic systems, with particular reference to interval type-2 fuzzy logic systems, is that the membership functions of interval type-2 fuzzy sets are themselves fuzzy. These give interval type-2 fuzzy logic systems an advantage over their type-1 counterparts which have precise membership functions. Whilst the interval type-2 fuzzy logic systems are effective in modelling uncertainty, they are not able to adequately handle an indeterminate/neutral characteristic of a set, because interval type-2 fuzzy sets are only specified by membership functions with an implicit assertion that the non-membership functions are complements of the membership functions (lower or upper). In a real life scenario, it is not necessarily the case that the non-membership function of a set is complementary to the membership function. There may be some degree of hesitation arising from ignorance or a complete lack of interest concerning a particular phenomenon. Atanassov intuitionistic fuzzy set, another generalisation of the classical fuzzy set, captures this thought process by simultaneously defining a fuzzy set with membership and non-membership functions such that the sum of both membership and non-membership functions is less than or equal to 1. In this thesis, the advantages of both worlds (interval type-2 fuzzy set and Atanassov intuitionistic fuzzy set) are explored and a new and enhanced class of interval type-2 fuzz set namely, interval type-2 Atanassov intuitionistic fuzzy set, that enables hesitation, is introduced. The corresponding fuzzy logic system namely, interval type-2 Atanassov intuitionistic fuzzy logic system is rigorously and systematically formulated. In order to assess the viability and efficacy of the developed framework, the possibilities of the optimisation of the parameters of this class of fuzzy systems are rigorously examined. First, the parameters of the developed model are optimised using one of the most popular fuzzy logic optimisation algorithms such as gradient descent (first-order derivative) algorithm and evaluated on publicly available benchmark datasets from diverse domains and characteristics. It is shown that the new interval type-2 Atanassov intuitionistic fuzzy logic system is able to handle uncertainty well through the minimisation of the error of the system compared with other approaches on the same problem instances and performance criteria. Secondly, the parameters of the proposed framework are optimised using a decoupledextended Kalman filter (second-order derivative) algorithm in order to address the shortcomings of the first-order gradient descent method. It is shown statistically that the performance of this new framework with fuzzy membership and non-membership functions is significantly better than the classical interval type-2 fuzzy logic systems which have only the fuzzy membership functions, and its type-1 counterpart which are specified by single membership and non-membership functions. The model is also assessed using a hybrid learning of decoupled extended Kalman filter and gradient descent methods. The proposed framework with hybrid learning algorithm is evaluated by comparing it with existing approaches reported in the literature on the same problem instances and performance metrics. The simulation results have demonstrated the potential benefits of using the proposed framework in uncertainty modelling. In the overall, the fusion of these two concepts (interval type-2 fuzzy logic system and Atanassov intuitionistic fuzzy logic system) provides a synergistic capability in dealing with imprecise and vague information