Type-2 fuzzy sets were introduced by Zadeh in 1975 in a series of papers. The basic idea is to generalize the notion of ordinary fuzzy sets (type-1), a¤ording wider applicability. This paper gives a general overview of some of the mathematical aspects of type-2 fuzzy set theory, emphasizing precisely how type-2 generalizes type-1 and interval-valued fuzzy set theory. We will summarize the theor...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez  Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. ...

This paper uses a formal approach to incorporating uncertainty of input information into the fusion process and decision making. Fuzzy set theory (fuzzy numbers, and fuzzy operators) is used to characterize and then manipulate (reason about) uncertainty. A library of speci cations of fuzzy set theory is developed using category theory and Specware, a tool that supports category theory based alg...

This document or any other document produced within the SUSTELNET project does not represent the opinion of the European Commission. Neither the European Commission, nor any person acting on behalf of the Commission, is responsible for the use that might be made of the information arising from the SUSTELNET project. Abstract This report identifies the main factors at play with regard to the int...

Confluence in abstract parallel category systems is established for net class-rewriting in iterative closed multilevel quotient graph structures with uncountable node arities by multi-dimensional transducer operations in topological metrics defined by alphabetically abstracting net block homomorphism. We obtain minimum prerequisites for the comprehensive connector pairs in a multitude dimension...

Motivated by applications in software verification, we explore automated reasoning about the non-disjoint combination of theories of infinitely many finite structures, where the theories share set variables and set operations. We prove a combination theorem and apply it to show the decidability of the satisfiability problem for a class of formulas obtained by applying propositional connectives ...

Monads have become a fundamental tool for structuring denotational semantics and programs by abstracting a wide variety of computational features such as side-effects, input/output, exceptions, continuations and non-determinism. In this setting, the notion of a monad is equipped with operations that allow programmers to manipulate these computational effects. For example, a monad for side-effec...

This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-width and clique-width. It will review applications to the construction of algorithms, to Graph Theory and to the extension to graphs of Formal Language Theory concepts. We first explain the role of Logic. A graph, eith...