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 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.

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.

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 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.