Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

The Usefulness of Complete Lattices in Reliability Theory

The main aim of this paper is to show how lattice theory in the very next future will be a useful tool in analysing complex real reliability problems, not properly modelled within classical reliability theory. The introduction of a complete lattice as a state space appears not only of theoretical importance that allows to understand several phenomena with respect to reliability theory better, but as a need claimed from practical engineering. Two important topics are discussed in this general framework: incomparability of component and system states and the duality principle. The strong relationship between the ideas of fuzzy set theory and the ideas that led to the introduction of the theory of multistate structure functions will become clear

Group Decision Making with Incomplete Interval-valued Fuzzy Preference Relations Based on the Minimum Operator

This paper presents a new method to estimate the unknown values in incomplete interval-valued fuzzy preference relations (IVFPRs). The method is based on the min-consistency and is used to develop the algorithm for group decision making (GDM) dealing with incomplete IVFPRs

A New Fuzzy Additive Noise Reduction Method

Die Kurzsichtigkeit der Kölner Stadtpolitiker, die jetzt einen Planungsstopp für das Kölner Stadtarchiv wollen und die Integration der gemeinsamen Museumsbibliothek in Frage stellen, ist schändlich. Es geht nicht um ein Luxusarchiv, sondern darum, dass das durch die größte Archivkatastrophe in Deutschland nach 1945 gebeutelte Stadtarchiv zuverlässige bauliche Grundlagen bekommt. Unsinnig ist es, an eine Zerschlagung der gemeinsamen Museumsbibliothek zu denken, die als weiterer Nutzer des gepl..

Inclusion–based approximate reasoning

Abstract. We present a kind of fuzzy reasoning, dependent on a measure of fulfilment of the antecedent clause, that captures all the expressiveness of the traditional approximate reasoning methodology based on the Compositional Rule of Inference (CRI) and at the same time rules out a good deal of its inherent complexity. We also argue why this approach offers a more genuine solution to the implementation of analogical reasoning than the classically proposed similarity measures.