This monograph is special in its orientation and contribution to current state of our understanding of decision-choice process and knowledge production. Its special orientation is to bring to the scientific community the discussions on the epistemic structure of the relationships among uncertainty, expectations, risk, possibility, probability and how the rules of fuzzy paradigm and the methods of fuzzy rationality bring new and different understanding to the relationships. At the level of theory of knowledge, it presents the structure and epistemic analysis of uncertainty, expectations and risk in decision-choice actions through the characteristics of substitution-transformation and input-output processes in categorial dynamics of actual-potential duality. The interactive effects of rationality and expectation are examined around belief, prospect, time and conditions of belief justification where the relationship between possibility and probability as a sequential link between potential and actual is analyzed to provide some understanding of the role of relative costs and benefits in defining risk in both nature and society. The concepts of possibilistic and probabilistic beliefs are explicated in relation to rationality and the decision-choice process where the analytical relationship between uncertainty and expectation formation is presented leading to the introduction of two types of uncertainty composed of fuzzy uncertainty and stochastic uncertainty.

This volume provides an up-to-date picture of the current status of theoretical and empirical developments in the application of fuzzy sets in psychology. Fuzzy set theory could benefit researchers in at least two ways: first, as a metaphor or model for ordinary thought, and secondly, as an aid to data analysis and theory construction. One can find examples for both kinds in the volume, which will be of interest both to the advanced student in the field as well as to anyone possessing a basic scientific background.

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.

This book presents a comprehensive report on the evolution of Fuzzy Logic since its formulation in Lotfi Zadeh’s seminal paper on “fuzzy sets,” published in 1965. In addition, it features a stimulating sampling from the broad field of research and development inspired by Zadeh’s paper. The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Conceived by the editors as an academic celebration of the fifty years’ anniversary of the 1965 paper, this work is a must-have for students and researchers willing to get an inspiring picture of the potentialities, limitations, achievements and accomplishments of Fuzzy Logic-based systems.

This monograph is a treatment on optimal fuzzy rationality as an enveloping of decision-choice rationalities where limited information, vagueness, ambiguities and inexactness are essential characteristics of our knowledge structure and reasoning processes. The volume is devoted to a unified system of epistemic models and theories of decision-choice behavior under total uncertainties composed of fuzzy and stochastic types. The unified epistemic analysis of decision-choice models and theories begins with the question of how best to integrate vagueness, ambiguities, limited information, subjectivity and approximation into the decision-choice process. The answer to the question leads to the shifting of the classical paradigm of reasoning to fuzzy paradigm. This is followed by discussions and establishment of the epistemic foundations of fuzzy mathematics where the nature and role of information and knowledge are explicated and represented. The epistemic foundation allows total uncertainties that constrain decision-choice activities, knowledge enterprise, logic and mathematical structures as our cognitive instruments to be discussed in reference to the phenomena of fuzzification, defuzzification and fuzzy logic. The discussions on these phenomena lead us to analyze and present models and theories on decision-choice rationality and the needed mathematics for problem formulation, reasoning and computations. The epistemic structures of two number systems made up of classical numbers and fuzzy numbers are discussed in relation to their differences, similarities and relative relevance to decision-choice rationality. The properties of the two number systems lead to the epistemic analysis of two mathematical systems that allow the partition of the mathematical space in support of decision-choice space of knowledge and non-knowledge production into four cognitively separate but interdependent cohorts whose properties are analyzed by the methods and techniques of category theory. The four cohorts are identified as non-fuzzy and non-stochastic, non-fuzzy and stochastic both of which belong to the classical paradigm and classical mathematical space; and fuzzy and non-stochastic, and fuzzy and stochastic cohorts both of which belong to the fuzzy paradigm and fuzzy mathematical space. The differences in the epistemic foundations of the two mathematical systems are discussed. The discussion leads to the establishment of the need for fuzzy mathematics and computing as a new system of reasoning in both exact and inexact sciences. The mathematical structures of the cohorts are imposed on the decision-choice process to allow a grouping of decision-choice models and theories. The corresponding classes of decision-choice theories have the same characteristics as the logico-mathematical cohorts relative to the assumed information-knowledge structures. The four groupings of models and theories on decision-choice activities are then classified as: 1) non-fuzzy and non-stochastic class with exact and full information-knowledge structure (no uncertainty), 2) non-fuzzy and stochastic class with exact and limited information-knowledge structure (stochastic uncertainty), 3) fuzzy and non-stochastic class with full and fuzzy information-knowledge structure (fuzzy uncertainty) and 4) Fuzzy and stochastic class with fuzzy and limited information-knowledge structure (fuzzy and stochastic uncertainties). All these different classes of decision choice problems have their corresponding rationalities which are fully discussed to present a unified logical system of theories on decision-choice process. The volume is concluded with epistemic discussions on the nature of contradictions and paradoxes viewed as logical decision-choice problems in the classical paradigm, and how these contradictions and paradoxes may be resolved through fuzzy paradigm and the methods and techniques of optimal fuzzy decision-choice rationality. The logical problem of sorites paradox with its resolution is given as an example. Interested audience includes those working in the areas of economies, decision-choice theories, philosophy of sciences, epistemology, mathematics, computer science, engineering, cognitive psychology, fuzzy mathematics and mathematics of fuzzy-stochastic processes.

In this work - both psychologists working on concepts and mathematicians working on fuzzy logic - reassess the usefulness of fuzzy logic for the psychology of concepts.

Readings in Fuzzy Sets for Intelligent Systems is a collection of readings that explore the main facets of fuzzy sets and possibility theory and their use in intelligent systems. Basic notions in fuzzy set theory are discussed, along with fuzzy control and approximate reasoning. Uncertainty and informativeness, information processing, and membership, cognition, neural networks, and learning are also considered. Comprised of eight chapters, this book begins with a historical background on fuzzy sets and possibility theory, citing some forerunners who discussed ideas or formal definitions very close to the basic notions introduced by Lotfi Zadeh (1978). The reader is then introduced to fundamental concepts in fuzzy set theory, including symmetric summation and the setting of fuzzy logic; uncertainty and informativeness; and fuzzy control. Subsequent chapters deal with approximate reasoning; information processing; decision and management sciences; and membership, cognition, neural networks, and learning. Numerical methods for fuzzy clustering are described, and adaptive inference in fuzzy knowledge networks is analyzed. This monograph will be of interest to both students and practitioners in the fields of computer science, information science, applied mathematics, and artificial intelligence.

The notion of Fuzziness stands as one of the really new concepts that have recently enriched the world of Science. Science grows not only through technical and formal advances on one side and useful applications on the other side, but also as consequence of the introduction and assimilation of new concepts in its corpus. These, in turn, produce new developments and applications. And this is what Fuzziness, one of the few new concepts arisen in the XX Century, has been doing so far. This book aims at paying homage to Professor Lotfi A. Zadeh, the “father of fuzzy logic” and also at giving credit to his exceptional work and personality. In a way, this is reflected in the variety of contributions collected in the book. In some of them the authors chose to speak of personal meetings with Lotfi; in others, they discussed how certain papers of Zadeh were able to open for them a new research horizon. Some contributions documented results obtained from the author/s after taking inspiration from a particular idea of Zadeh, thus implicitly acknowledging him. Finally, there are contributions of several “third generation fuzzysists or softies” who were firstly led into the world of Fuzziness by a disciple of Lotfi Zadeh, who, following his example, took care of opening for them a new road in science. Rudolf Seising is Adjoint Researcher at the European Centre for Soft Computing in Mieres, Asturias (Spain). Enric Trillas and Claudio Moraga are Emeritus Researchers at the European Centre for Soft Computing, Mieres, Asturias (Spain). Settimo Termini is Professor of Theoretical Computer Science at the University of Palermo, Italy and Affiliated Researcher at the European Centre for Soft Computing, Mieres, Asturias (Spain)

The main objective of this special issue is to divulge the applicability of the Neutrosophic Theory and to explore the possibilities and advantages of neutrosophic tools, through both the presentation of thorough research and case studies in solving social problems in Latin America. The best presentations discussed at the III International Congress of Educational Research and University Innovation, turned into papers, show us the capacity for socialization of neutrosophic knowledge and its link with this science of validation and consolidation of scientific knowledge. This publication with authors from 11 countries that we place in the hands of the international scientific community, constitutes an example of how in Latin America the Neutrosophy is contributing to complex solutions based on the results of scientific research carried out by teachers and students committed to the social responsibility of continuing to progress for the benefit of humanity.