Pesquisa

This book provides a complete framework for the fundamental concepts and results of texture spaces and its applications. The principal aim is to present a comprehensive arguments due to connections among the textures, fuzzy sets and rough sets. In this context, direlations, fuzzy direlations and fuzzy relations constitute a bridge for the remarkable observations on rough set theory. In a more general setting, the approximation operators are also inspected for fuzzy rough set models with two domains of discourse.  Since the book is self-contained and reader-friendly, the respected researchers may utilize this source for further investigations of the necessary results for their studies on rough set theory using textures. Therefore, prospective readers are not only mathematicians who interest in purely mathematical theories related to textures, but also engineers of information sciences who need more information for their interdisciplinary studies with respect to rough sets and fuzzy sets.

This book is considered as a monograph but also as a potential textbook for graduate students, focusing on the application of FCMs for modelling and analysing the behaviour of multicomponent systems. In the last two decades, no monograph or textbook has been published on the topic Fuzzy Cognitive Maps (FCM), so this new book is definitely filling a gap in the literature of computational intelligence. The book is built up didactically, the novel results in the field being presented in the way of starting with two real-life case studies, one in the area of waste management, while the other one in modelling bank management systems. In both cases, the book starts with explaining the applied problem and then presenting how the model construction is done and what problems emerge when attempts are made for applying directly earlier results on FCM modelling. In the first case study, the problem of the oversimplification leads to inadequacy of the model, and then it is shown how new, much finer models can be built up based on expert domain knowledge. Then, the new problem of losing transparency and interpretability emerges, and as a solution, a new algorithm family is proposed that reduces FCMs to fewer components, while preserving the essential characteristics of the original model.The second case study raises the problems of stability and sensitivity of FCMs, especially, considering that expert knowledge is often uncertain and subjective. The new results summarised in the book target the questions of how to ascertain whether an FCM is converging to one or several fixed point attractors, whether there is a bifurcation when parameters are changing, etc. Both problems deal with the ultimate question whether the system modelled is stable and sustainable.

This book is used as a reference for engineers, technicians, and researchers who are working in the fields of management science, operation management, computer science, information management, fuzzy mathematics, business intelligence, and other fields.

This book is a collection of papers presented during the 8th World Conference on Soft Computing in February 2022. Some papers are dedicated to fundamental aspects of soft computing, i.e., fuzzy mathematics, type-2 fuzzy sets, evolutionary-based optimization, aggregation, and neural networks.

Among them, hybrid models combining m-polar fuzzy sets with rough, soft and 2-tuple linguistic sets, and m-polar hesitant fuzzy sets and hesitant m-polar fuzzy are presented, together with some significant applications.

This book provides an essential introduction to the field of dynamical models. Starting from classical theories such as set theory and probability, it allows readers to draw near to the fuzzy case. On one hand, the book equips readers with a fundamental understanding of the theoretical underpinnings of fuzzy sets and fuzzy dynamical systems. On the other, it presents some concepts of derivatives, integrals and differential equations applied to the context of fuzzy functions. Each of the major topics is accompanied by examples, worked-out exercises, and exercises to be completed. Moreover, many applications to real problems are presented, mainly in biomathematics where the so-called p-fuzzy systems play an important role. The book has been developed on the basis of the authors' lectures to university students and is accordingly primarily intended as a textbook for both upper-level undergraduates and graduates in applied mathematics, statistics, and engineering. It also offers a valuable resource for practitioners such as mathematical consultants and modelers, and for researchers alike, as it may provide both groups with new ideas and inspirations for projects in the fields of fuzzy logic and biomathematics. This thoroughly updated second edition includes a new chapter on fuzzy optimization, which also presents an application in carbon markets analysis and modeling

As a new interpretable model, three-way decision has also received academic attention in machine learning. With respect to different hesitant fuzzy information, this book deeply discusses the deduction process of decision rules of three-way decision and generates interpretable knowledge with the risk semantics. It further explores the applications of three-way decision to support healthcare management. This book is used as a reference for engineers, technicians, and researchers who are working in the fields of management science, operation management, computer science, information management, fuzzy mathematics, business intelligence, and other fields. It also serves as a textbook for postgraduate and senior undergraduate students of the relevant professional institutions of higher learning.

This book presents an extension of fuzzy set theory allowing for multi-polar information, discussing its impact on the theoretical and practical development of multi-criteria decision making. It reports on set of hybrid models developed by the authors, and show how they can be adapted, case by case, to the lack of certainty under a variety of criteria. Among them, hybrid models combining m-polar fuzzy sets with rough, soft and 2-tuple linguistic sets, and m-polar hesitant fuzzy sets and hesitant m-polar fuzzy are presented, together with some significant applications.  In turn, outranking decision-making techniques such as m-polar fuzzy ELECTRE I, II, III and IV methods, as well as m-polar fuzzy PROMETHEE I and II methods, are developed. The efficiency of these decision-making procedures, as well as other possible extensions studied by the authors, is shown in some real-world applications.  Overall, this book offers a guide on methodologies to deal with the multi-polarity and fuzziness of the real-world problems, simultaneously. By including algorithms and computer programming codes, it provides a practice-oriented reference guide to both researchers and professionals working at the interface between computational intelligence and decision making.

One of the most preeminent ways of applying mathematics in real-world scenario modeling involves graph theory. A graph can be undirected or directed depending on whether the pairwise relationships among objects are symmetric or not. Nevertheless, in many real-world situations, representing a set of complex relational objects as directed or undirected is not su cient. Weighted graphs oer a framework that helps to over come certain conceptual limitations. We show using the concept of an isomorphism that weighted graphs have a natural connection to fuzzy graphs. As we show in the book, this allows results to be carried back and forth between weighted graphs and fuzzy graphs. This idea is in keeping with the important paper by Klement and Mesiar that shows that many families of fuzzy sets are lattice isomorphic to each other. We also outline the important work of Head and Weinberger that show how results from ordinary mathematics can be carried over to fuzzy mathematics. We focus on the concepts connectivity, degree sequences and saturation, and intervals and gates in weighted graphs.

This book is a collection of papers presented during the 8th World Conference on Soft Computing in February 2022. The papers cover multiple areas important for soft computing. Some papers are dedicated to fundamental aspects of soft computing, i.e., fuzzy mathematics, type-2 fuzzy sets, evolutionary-based optimization, aggregation, and neural networks. Others emphasize the application of soft computing methods to data analysis, image processing, decision-making, classification, series prediction, economics, control, and modeling.

This book describes a set of methods for finding more-for-less solutions of various kind of fuzzy transportation problems. Inspired by more-for-less approaches to the basic transportation problem initiated by Abraham Charnes and his collaborators during 1960s and 1970s, this book describes new methods developed by the authors to solve different types of problems, including symmetric balanced fuzzy transportation problems, symmetric intuitionistic fuzzy transportation problems with mixed constraints, and symmetric intuitionistic fuzzy linear fractional transportation problems with mixed constraints. It offers extensive details on their applications to some representative problems, and discusses some future research directions

This book is a collection of papers presented during the 8th World Conference on Soft Computing in February 2022. The papers cover multiple areas important for soft computing. Some papers are dedicated to fundamental aspects of soft computing, i.e., fuzzy mathematics, type-2 fuzzy sets, evolutionary-based optimization, aggregation, and neural networks. Others emphasize the application of soft computing methods to data analysis, image processing, decision-making, classification, series prediction, economics, control, and modeling.

The edited volume includes papers in the fields of fuzzy mathematical analysis and advances in computational mathematics. The book includes selected high-quality papers from the International Conference on Fuzzy Mathematical Analysis and Advances in Computational Mathematics (FMAACM 2020).

The book has 19 chapters addressing various aspects of nasal drug delivery systems such as an overview of anatomy and physiology of the nasal passage from a drug delivery point of view to global market opportunities for nasal drug delivery.

This book examines some issues involving climate change, human trafficking, and other serious world challenges made worse by climate change.

This book briefly reviews the basic concepts of type-2 fuzzy systems and then describes the proposed definitions for interval type-3 fuzzy sets and relations, also interval type-3 inference and systems.

This volume discusses how plant and algae organisms play a pivotal role in the transformation of solar energy to essential metabolites, and explores the numerous beneficial roles these metabolites have at an industrial level.

This book introduces some contemporary approaches on the application of fuzzy and hesitant fuzzy sets in machine learning tasks such as classification, clustering and dimension reduction.

This book presents a selection of current research results in the field of intelligent systems and draws attention to their practical applications and issues connected with the areas of decision-making, economics, business and finance.

This book covers the introduction, theory, development and applications of type-2 fuzzy logic systems, which represent the current state-of-the-art in various domains such as control applications, power plants, health care, image processing, mathematical applications etc. The book is also rich in discussing different applications in order to give the researchers a flavor of how type-2 fuzzy logic is designed for different types of problems. Type-2 fuzzy logic systems are now used extensively in engineering applications for many purposes. In simple language, this book covers the practical use of type-2 fuzzy logic and its optimization through different training methods. Furthermore, this book maintains the relationship between mathematics and practical implementations in the real world. This book chapter also contains the proper comparisons with available literature work. It shows that the presented enhanced techniques have better results. This book would serve as a handy reference guide for a variety of readers, primarily targeting research scholars, undergraduate and postgraduate researchers and practicing engineers working in Type-2 fuzzy logic systems and their applications. 

This book examines some issues involving climate change, human trafficking, and other serious world challenges made worse by climate change. Climate change increases the risk of natural disasters and thus creates poverty and can cause situations of conflict and instability. Displacement can occur giving traffickers an opportunity to exploit affected people. In the fuzzy graph theory part of the book, the relatively new concepts of fuzzy soft semigraphs and graph structures are used to study human trafficking, as well as its time intuitionistic fuzzy sets that have been introduced to model forest fires. The notion of legal and illegal incidence strength is used to analyze immigration to the USA. The examination of return refugees to their origin countries is undertaken. The neighborhood connectivity index is determined for trafficking in various regions in the world. The cycle connectivity measure for the directed graph of the flow from South America to the USA is calculated. It is determined that there is a need for improvement in government response by countries. Outside the area of fuzzy graph theory, a new approach to examine climate change is introduced. Social network theory is used to study feedback processes that effect climate forcing. Tipping points in climate change are considered. The relationship between terrorism and climate change is examined. Ethical issues concerning the obligation of business organizations to reduce carbon emissions are also considered. Nonstandard analysis is a possible new area that could be used by scholars of mathematics of uncertainty. A foundation is laid to aid the researcher in the understanding of nonstandard analysis. In order to accomplish this, a discussion of some basic concepts from first-order logic is presented as some concepts of mathematics of uncertainty. An application to the theory of relativity is presented.

This edited book discusses creative and recent developments of fuzzy systems and its real-life applications of multiple criteria decision making. Keeping on the existing fuzzy sets and recent developed fuzzy sets, viz., intuitionistic fuzzy, Pythagorean fuzzy, Fermatean fuzzy, Hesitant fuzzy and multiple criteria decision approaches, this book is committed to probing the soft computing techniques and fuzzy multiple criteria decision making in favour of fuzzy intelligent system and business analytics. It also addresses novel development of fuzzy set theory as well as real-life applications of fuzzy systems. It presents challenging and useful real-world applications based on problems of decision making in various fields. The modelling and solution procedures of such real-world problems will be provided concisely although all topics start with a more developed resolution. The contributory chapters will be based on the vast research experiences of the authors in real-world decision-making problems. This book provides readers with a valuable conspectus of several decision-making problems as a reference for researchers and industrial practitioners in this field. This book will broadly cover recent development of fuzzy systems and its applications of multiple criteria decision making in the areas of management and production, manufacturing management, selections problems, group decision making, transportation and logistics, inventory control systems and interval technique/fuzzy technique (uncertainty) of the above mentioned areas.

This book explains the basic concepts, theory and applications of fuzzy systems in control in a simple unified approach with clear ex-amples and simulations in the MATLAB programming language. Fuzzy systems, especially, type-2 neuro-fuzzy systems, are now used extensively in various engineering fields for different purposes. In plain language, this book aims to practically explain fuzzy sys-tems and different methods of training and optimizing these systems. For this purpose, type-2 neuro-fuzzy systems are first analyzed along with various methods of training and optimizing these systems through implementation in MATLAB. These systems are then em-ployed to design adaptive fuzzy controllers. The authors aim at pre-senting all the well-known optimization methods clearly and code them in the MATLAB language.

The first part points out the fuzzy differential equations and the second one is related to the fuzzy integral equations. The book contains nine chapters that six chapters are about fuzzy differential equations and three of them are about fuzzy integral equations.