This book presents recent research in the field of interaction between computational intelligence and mathematics, ranging from theory to applications. Computational intelligence, or soft computing consists of various bio-inspired methods, especially fuzzy systems, artificial neural networks, evolutionary and memetic algorithms. These research areas were initiated by professionals in various applied fields, such as engineers, economists, and financial and medical experts. Although computational intelligence offered solutions (at least quasi-optimal solutions) for problems with high complexity, vague and undeterministic features, initially little attention was paid to the mathematical models and analysis of the methods successfully applied. A typical example is the extremely successful Mamdani-algorithm, and its modifications and extensions, applied since the mid-1970s, where the first analysis of the simplest cases, showing why this algorithm was so efficient and stable, was not given until the early 1990s. Since the mid-2000s, the authors have organized international conferences annually to focus on the mathematical methodological issues in connection with computational intelligence approaches. These conferences have attracted a large number of submissions with a wide scope of topics and quality. The editors selected several high-quality papers and approached the authors to submit an essentially extended and improved book chapter based on the lectures.This volume is the first contributed book on the subject.

This book presents recent research in the field of interaction between computational intelligence and mathematics. In the current technological age, we face the challenges of tackling very complex problems - in the usual sense, but also in the mathematical and theoretical computer science sense. However, even the most up-to-date results in mathematics, are unable to provide exact solutions of such problems, and no further technical advances will ever make it possible to find general and exact solutions. Constantly developing technologies (including social technologies) necessitate handling very complex problems. This has led to a search for acceptably "good" or precise solutions, which can be achieved by the combination of traditional mathematical techniques and computational intelligence tools, in order to solve the various problems emerging in many different areas to a satisfactory degree. Important funding programs, such as the European Commission's current framework programme for research and innovation - Horizon 2020 - are devoted to the development of new instruments to deal with the current challenges. Without doubt, research topics associated with the interactions between computational intelligence and traditional mathematics play a key role. Presenting contributions from engineers, scientists and mathematicians, this book offers a series of novel solutions for meaningful and real-world problems that connect those research areas.

This three volume set (CCIS 853-855) constitutes the proceedings of the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2017, held in Cadiz, Spain, in June 2018. The 193 revised full papers were carefully reviewed and selected from 383 submissions. The papers are organized in topical sections on advances on explainable artificial intelligence; aggregation operators, fuzzy metrics and applications; belief function theory and its applications; current techniques to model, process and describe time series; discrete models and computational intelligence; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy logic and artificial intelligence problems; fuzzy mathematical analysis and applications; fuzzy methods in data mining and knowledge discovery; fuzzy transforms: theory and applications to data analysis and image processing; imprecise probabilities: foundations and applications; mathematical fuzzy logic, mathematical morphology; measures of comparison and entropies for fuzzy sets and their extensions; new trends in data aggregation; pre-aggregation functions and generalized forms of monotonicity; rough and fuzzy similarity modelling tools; soft computing for decision making in uncertainty; soft computing in information retrieval and sentiment analysis; tri-partitions and uncertainty; decision making modeling and applications; logical methods in mining knowledge from big data; metaheuristics and machine learning; optimization models for modern analytics; uncertainty in medicine; uncertainty in Video/Image Processing (UVIP).

This three volume set (CCIS 853-855) constitutes the proceedings of the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2017, held in Cadiz, Spain, in June 2018. The 193 revised full papers were carefully reviewed and selected from 383 submissions. The papers are organized in topical sections on advances on explainable artificial intelligence; aggregation operators, fuzzy metrics and applications; belief function theory and its applications; current techniques to model, process and describe time series; discrete models and computational intelligence; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy logic and artificial intelligence problems; fuzzy mathematical analysis and applications; fuzzy methods in data mining and knowledge discovery; fuzzy transforms: theory and applications to data analysis and image processing; imprecise probabilities: foundations and applications; mathematical fuzzy logic, mathematical morphology; measures of comparison and entropies for fuzzy sets and their extensions; new trends in data aggregation; pre-aggregation functions and generalized forms of monotonicity; rough and fuzzy similarity modelling tools; soft computing for decision making in uncertainty; soft computing in information retrieval and sentiment analysis; tri-partitions and uncertainty; decision making modeling and applications; logical methods in mining knowledge from big data; metaheuristics and machine learning; optimization models for modern analytics; uncertainty in medicine; uncertainty in Video/Image Processing (UVIP).

This three volume set (CCIS 853-855) constitutes the proceedings of the 17th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2017, held in Cadiz, Spain, in June 2018. The 193 revised full papers were carefully reviewed and selected from 383 submissions. The papers are organized in topical sections on advances on explainable artificial intelligence; aggregation operators, fuzzy metrics and applications; belief function theory and its applications; current techniques to model, process and describe time series; discrete models and computational intelligence; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy logic and artificial intelligence problems; fuzzy mathematical analysis and applications; fuzzy methods in data mining and knowledge discovery; fuzzy transforms: theory and applications to data analysis and image processing; imprecise probabilities: foundations and applications; mathematical fuzzy logic, mathematical morphology; measures of comparison and entropies for fuzzy sets and their extensions; new trends in data aggregation; pre-aggregation functions and generalized forms of monotonicity; rough and fuzzy similarity modelling tools; soft computing for decision making in uncertainty; soft computing in information retrieval and sentiment analysis; tri-partitions and uncertainty; decision making modeling and applications; logical methods in mining knowledge from big data; metaheuristics and machine learning; optimization models for modern analytics; uncertainty in medicine; uncertainty in Video/Image Processing (UVIP).

This book presents recent research in the field of interaction between computational intelligence and mathematics, ranging from theory to applications. Computational intelligence, or soft computing consists of various bio-inspired methods, especially fuzzy systems, artificial neural networks, evolutionary and memetic algorithms. These research areas were initiated by professionals in various applied fields, such as engineers, economists, and financial and medical experts. Although computational intelligence offered solutions (at least quasi-optimal solutions) for problems with high complexity, vague and undeterministic features, initially little attention was paid to the mathematical models and analysis of the methods successfully applied. A typical example is the extremely successful Mamdani-algorithm, and its modifications and extensions, applied since the mid-1970s, where the first analysis of the simplest cases, showing why this algorithm was so efficient and stable, was not given until the early 1990s. Since the mid-2000s, the authors have organized international conferences annually to focus on the mathematical methodological issues in connection with computational intelligence approaches. These conferences have attracted a large number of submissions with a wide scope of topics and quality. The editors selected several high-quality papers and approached the authors to submit an essentially extended and improved book chapter based on the lectures.This volume is the first contributed book on the subject.

This book constitutes the refereed proceedings of the 23rd Australasian Joint Conference on Rough Sets and Intelligent Systems Paradigms, RSEISP 2014, held in Granada and Madrid, Spain, in July 2014. RSEISP 2014 was held along with the 9th International Conference on Rough Sets and Current Trends in Computing, RSCTC 2014, as a major part of the 2014 Joint Rough Set Symposium, JRS 2014. JRS 2014 received 40 revised full papers and 37 revised short papers which were carefully reviewed and selected from 120 submissions and presented in two volumes. This volume contains the papers accepted for the conference RSEISP 2014, as well as the three invited papers presented at the conference. The papers are organized in topical sections on plenary lecture and tutorial papers; foundations of rough set theory; granular computing and covering-based rough sets; applications of rough sets; induction of decision rules - theory and practice; knowledge discovery; spatial data analysis and spatial databases; information extraction from images.

Complex problems and systems, which prevail in the real world, cannot often be tackled and solved either by traditional methods offered by mathematics or even the traditional computer science (CS) and and artificial intelligence (AI)..). What is the way out of this dilemma? Advanced methodologies, and tools and techniques, "mimicking" human reasoning or the behavior of animals, animal populations or certain parts of the living bod, based on traditional computer science science and the initial approaches of artificial intelligence are often referred to as biologically inspired methods, or often computational intelligence (CI). Computational intelligence offers effective and efficient solutions to many "unsolvable" problems problems. However, it is far from being a ready to use and complete collection of approaches, and is rather a continuously developing field without clear borders. The emerging new models and algorithms of computational intelligence are deeply rooted in the vast apparatus of traditional mathematics. Thus, the investigation of connections and synergy between mathematics and computational intelligence is an eminent goal which is periodically pursued by a group of mathematicians and computational intelligence researchers who regularly attand the annual European Symposia on Computational Intelligence and Mathematics (ESCIM). Some relevant papers from the last ESCIM-2020 are included in this volume.

This book collects the final versions of the highest quality papers presented at the conference 11th European Symposium on Computational Intelligence and Mathematics held on October 2-5, 2019, in Toledo (Spain). The conjugation of computational sciences with different mathematical tools is essential in order to solve different challenges that arise in a wide-ranging knowledge areas. Nowadays, many promising research lines are being developed in this direction from the theoretical and applicational perspectives. In this publication, computational intelligence and mathematics are combined in interesting research works that aim to give answers to complex real problems. Moreover, the technical program of this conference included four excellent keynote speeches, given by Prof. Jose Luis Verdegay (Guidelines to solve Decision Making Problems), Prof. Joao Paulo Carvalho (Recommender Systems: Using Fuzzy Fingerprints for ``Proper'' Recommendations), Dr. Andreja Tepavcevic (Special lattice valued structures and approximate solutions of linear equations), and Prof. Juan Moreno-Garcia (Generating linguistic descriptions using Linguistic Petri Nets).

The recent book of the series continues the collection of articles dealing with the important and efficient combination of traditional and novel mathematical approaches with various computational intelligence techniques, with a stress of fuzzy systems, and fuzzy logic. Complex systems are theoretically intractable, as the need of time and space resources (e.g., computer capacity) exceed any implementable extent. How is it possible that in the practice, such problems are usually manageable with an acceptable quality by human experts? They apply expert domain knowledge and various methods of approximate modeling and corresponding algorithms. Computational intelligence is the mathematical tool box that collects techniques which are able to model such human interaction, while (new) mathematical approaches are developed and used everywhere where the complexity of the sub-task allows it. The innovative approaches in this book give answer to many questions on how to solve "unsolvable" problems.

Complex problems and systems, which prevail in the real world, cannot often be tackled and solved either by traditional methods offered by mathematics or even the traditional computer science (CS) and and artificial intelligence (AI)..). What is the way out of this dilemma? Advanced methodologies, and tools and techniques, "mimicking" human reasoning or the behavior of animals, animal populations or certain parts of the living bod, based on traditional computer science science and the initial approaches of artificial intelligence are often referred to as biologically inspired methods, or often computational intelligence (CI). Computational intelligence offers effective and efficient solutions to many "unsolvable" problems problems. However, it is far from being a ready to use and complete collection of approaches, and is rather a continuously developing field without clear borders. The emerging new models and algorithms of computational intelligence are deeply rooted in the vast apparatus of traditional mathematics. Thus, the investigation of connections and synergy between mathematics and computational intelligence is an eminent goal which is periodically pursued by a group of mathematicians and computational intelligence researchers who regularly attand the annual European Symposia on Computational Intelligence and Mathematics (ESCIM). Some relevant papers from the last ESCIM-2020 are included in this volume.

This two-volume set (CCIS 1601-1602) constitutes the proceedings of the 19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2021, held in Milan, Italy, in July 2022. The 124 papers were carefully reviewed and selected from 188 submissions. The papers are organized in topical sections as follows: aggregation theory beyond the unit interval; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy mathematical analysis and its applications; generalized sets and operators; information fusion techniques based on aggregation functions, pre-aggregation functions, and their generalizations; interval uncertainty; knowledge acquisition, representation and reasoning; logical structures of opposition and logical syllogisms; mathematical fuzzy logics; theoretical and applied aspects of imprecise probabilities; data science and machine learning; decision making modeling and applications; e-health; fuzzy methods in data mining and knowledge discovery; soft computing and artificia intelligence techniques in image processing; soft methods in statistics and data analysis; uncertainty, heterogeneity, reliability and explainability in AI; weak and cautious supervised learning.

This two-volume set (CCIS 1601-1602) constitutes the proceedings of the 19th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2021, held in Milan, Italy, in July 2022. The 124 papers were carefully reviewed and selected from 188 submissions. The papers are organized in topical sections as follows: aggregation theory beyond the unit interval; formal concept analysis and uncertainty; fuzzy implication functions; fuzzy mathematical analysis and its applications; generalized sets and operators; information fusion techniques based on aggregation functions, pre-aggregation functions, and their generalizations; interval uncertainty; knowledge acquisition, representation and reasoning; logical structures of opposition and logical syllogisms; mathematical fuzzy logics; theoretical and applied aspects of imprecise probabilities; data science and machine learning; decision making modeling and applications; e-health; fuzzy methods in data mining and knowledge discovery; soft computing and artificia intelligence techniques in image processing; soft methods in statistics and data analysis; uncertainty, heterogeneity, reliability and explainability in AI; weak and cautious supervised learning.

This book collects the final versions of the highest quality papers presented at the conference 11th European Symposium on Computational Intelligence and Mathematics held on October 2-5, 2019, in Toledo (Spain). The conjugation of computational sciences with different mathematical tools is essential in order to solve different challenges that arise in a wide-ranging knowledge areas. Nowadays, many promising research lines are being developed in this direction from the theoretical and applicational perspectives. In this publication, computational intelligence and mathematics are combined in interesting research works that aim to give answers to complex real problems. Moreover, the technical program of this conference included four excellent keynote speeches, given by Prof. Jose Luis Verdegay (Guidelines to solve Decision Making Problems), Prof. Joao Paulo Carvalho (Recommender Systems: Using Fuzzy Fingerprints for ``Proper'' Recommendations), Dr. Andreja Tepavcevic (Special lattice valued structures and approximate solutions of linear equations), and Prof. Juan Moreno-Garcia (Generating linguistic descriptions using Linguistic Petri Nets).

This book presents appealing contributions on computational intelligence and mathematics, connecting both areas and offering solutions to a number of interesting, real-world problems. Such problems often require novel solutions, as complexity exceeds the tractable size. At the same time, the need for good-quality realistic solutions results in models and algorithms with a good balance of resource intensiveness and model quality (accuracy). Many areas of knowledge call for hybrid solutions that combine traditional mathematical techniques and computational intelligence based on subsymbolic knowledge representation. Important research topics are focused on developing the interaction between computational intelligence and mathematics, in order to address various challenges of the current technological age. Written by influential, leading researchers, this book discusses the latest trends in hybridising mathematics and computational intelligence.

This book combines computational intelligence and mathematics to solve theoretical and real-world problems. The real challenges of engineering and other applied sciences, e.g. economics and management, the social sciences, etc., and even everyday life, are increasingly raising complex problems - both in the usual sense, but also in the mathematical and theoretical computer science sense, which is referred to as intractability. Finding exact solutions to the latest problems in mathematics is impossible, and it has been also shown that no further technical advance will ever make it possible to find general and exact solutions to such complex problems. Rather, the goal is to find solutions that are "good enough" or "acceptably accurate," including models and corresponding algorithms, which is most often achieved by combining traditional mathematical techniques and computational intelligence tools, such as fuzzy systems, evolutionary and memetic algorithms, and artificial neural networks. Consequently, international funding programs, such as the European Commission's current framework program for research and innovation (Horizon 2020), and the preliminary research team building COST Actions, are devoted to developing new instruments for tackling the challenges that we face in the current technological age. And it goes without saying that research topics concerning the interactions between computational intelligence and traditional mathematics play a key role in overcoming the obstacles associated with the intractability of complex problems. In this book, mathematicians, engineers, and other scientists highlight novel methodological results connecting these two main research areas, and focusing on solving real-life problems.

This book presents appealing contributions on computational intelligence and mathematics, connecting both areas and offering solutions to a number of interesting, real-world problems. Such problems often require novel solutions, as complexity exceeds the tractable size. At the same time, the need for good-quality realistic solutions results in models and algorithms with a good balance of resource intensiveness and model quality (accuracy). Many areas of knowledge call for hybrid solutions that combine traditional mathematical techniques and computational intelligence based on subsymbolic knowledge representation. Important research topics are focused on developing the interaction between computational intelligence and mathematics, in order to address various challenges of the current technological age. Written by influential, leading researchers, this book discusses the latest trends in hybridising mathematics and computational intelligence.

Hizo su formacion academica en La Habana y en Filadelfia. Estudio latin y griego. En El Redactor dio a conocer su novela Una lagrima y una gota de rocio. En 1852 comenzo a publicar en El Orden su novela Un joven aleman. Y en 1854 edito los cuadernos No me olvides, redactados casi enteramente por el, donde publico los primeros capitulos de su novela El Doctor In-Fausto y algunas poesias. Colaboro en Diario de La Habana, la Revista de La Habana y La verdad Catolica. La Real Academia Espanola le encomendo la Oracion funebre de Cervantes en 1861.