Symmetric implicational restriction method of fuzzy inference

summary:The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy implications. The conditions are obtained for the supremum to become the maximum (or the infimum to be the minimum). Lastly, four concrete examples are provided, and it is shown that the new method is better than the triple I restriction method, because the former is able to let the inference more compact, and lead to more and superior particular inference schemes

Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

Bilattice based Logical Reasoning for Automated Visual Surveillance and other Applications

The primary objective of an automated visual surveillance system is to observe and understand human behavior and report unusual or potentially dangerous activities/events in a timely manner. Automatically understanding human behavior from visual input, however, is a challenging task. The research presented in this thesis focuses on designing a reasoning framework that can combine, in a principled manner, high level contextual information with low level image processing primitives to interpret visual information. The primary motivation for this work has been to design a reasoning framework that draws heavily upon human like reasoning and reasons explicitly about visual as well as non-visual information to solve classification problems. Humans are adept at performing inference under uncertainty by combining evidence from multiple, noisy and often contradictory sources. This thesis describes a logical reasoning approach in which logical rules encode high level knowledge about the world and logical facts serve as input to the system from real world observations. The reasoning framework supports encoding of multiple rules for the same proposition, representing multiple lines of reasoning and also supports encoding of rules that infer explicit negation and thereby potentially contradictory information. Uncertainties are associated with both the logical rules that guide reasoning as well as with the input facts. This framework has been applied to visual surveillance problems such as human activity recognition, identity maintenance, and human detection. Finally, we have also applied it to the problem of collaborative filtering to predict movie ratings by explicitly reasoning about users preferences

Conceptual Factors and Fuzzy Data

With the growing number of large data sets, the necessity of complexity reduction applies today more than ever before. Moreover, some data may also be vague or uncertain. Thus, whenever we have an instrument for data analysis, the questions of how to apply complexity reduction methods and how to treat fuzzy data arise rather naturally. In this thesis, we discuss these issues for the very successful data analysis tool Formal Concept Analysis. In fact, we propose different methods for complexity reduction based on qualitative analyses, and we elaborate on various methods for handling fuzzy data. These two topics split the thesis into two parts. Data reduction is mainly dealt with in the first part of the thesis, whereas we focus on fuzzy data in the second part. Although each chapter may be read almost on its own, each one builds on and uses results from its predecessors. The main crosslink between the chapters is given by the reduction methods and fuzzy data. In particular, we will also discuss complexity reduction methods for fuzzy data, combining the two issues that motivate this thesis.Komplexitätsreduktion ist eines der wichtigsten Verfahren in der Datenanalyse. Mit ständig wachsenden Datensätzen gilt dies heute mehr denn je. In vielen Gebieten stößt man zudem auf vage und ungewisse Daten. Wann immer man ein Instrument zur Datenanalyse hat, stellen sich daher die folgenden zwei Fragen auf eine natürliche Weise: Wie kann man im Rahmen der Analyse die Variablenanzahl verkleinern, und wie kann man Fuzzy-Daten bearbeiten? In dieser Arbeit versuchen wir die eben genannten Fragen für die Formale Begriffsanalyse zu beantworten. Genauer gesagt, erarbeiten wir verschiedene Methoden zur Komplexitätsreduktion qualitativer Daten und entwickeln diverse Verfahren für die Bearbeitung von Fuzzy-Datensätzen. Basierend auf diesen beiden Themen gliedert sich die Arbeit in zwei Teile. Im ersten Teil liegt der Schwerpunkt auf der Komplexitätsreduktion, während sich der zweite Teil der Verarbeitung von Fuzzy-Daten widmet. Die verschiedenen Kapitel sind dabei durch die beiden Themen verbunden. So werden insbesondere auch Methoden für die Komplexitätsreduktion von Fuzzy-Datensätzen entwickelt

Mappings between distance sets or spaces

[no abstract

North American Fuzzy Logic Processing Society (NAFIPS 1992), volume 2

This document contains papers presented at the NAFIPS '92 North American Fuzzy Information Processing Society Conference. More than 75 papers were presented at this Conference, which was sponsored by NAFIPS in cooperation with NASA, the Instituto Tecnologico de Morelia, the Indian Society for Fuzzy Mathematics and Information Processing (ISFUMIP), the Instituto Tecnologico de Estudios Superiores de Monterrey (ITESM), the International Fuzzy Systems Association (IFSA), the Japan Society for Fuzzy Theory and Systems, and the Microelectronics and Computer Technology Corporation (MCC). The fuzzy set theory has led to a large number of diverse applications. Recently, interesting applications have been developed which involve the integration of fuzzy systems with adaptive processes such a neural networks and genetic algorithms. NAFIPS '92 was directed toward the advancement, commercialization, and engineering development of these technologies