This chapter presents an introduction to fuzzy logic and to fuzzy databases. With regard to the first topic, we have introduced the main concepts in this field to facilitate the understanding of the rest of the chapters to novel readers in fuzzy subjects. With respect to the fuzzy databases, this chapter gives a list of six research topics in this fuzzy area. All these topics are briefly commen...

We look at the problem of revising fuzzy be­ lief bases, i.e., belief base revision in which both formulas in the base as well as revision­ input formulas can come attached with vary­ ing truth-degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy log­ ics, we show how the idea of rational...

A fuzzy inference framework based on fuzzy relations is explored and applied to a real set of simulated forecasts and experimental data referring to temperature and humidity in specific coffee crop sites in Brazil. In short, the used model consists of fuzzy relations over possibility distributions, resulting in a fuzzy model analog to a Bayesian inference process. The application of the fuzzy m...

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that...

In this paper we model the concept of ”coarseness”, typically used in texture image descriptions, by means of fuzzy sets. Specifically, we relate representative measures of this kind of texture with its presence degree. To obtain these ”presence degrees”, we collect assessments from polls filled by human subjects, performing an aggregation of these assessments by means of OWA operators. Using t...

The eigen fuzzy set of a given fuzzy relation often corresponds to an occurrence of invariability in natural sciences. By determining the fuzzy relations as connections between pairs of symptoms we utilize the greatest and the least eigen fuzzy sets in order to find the estimates of the medicine effectiveness levels.

In a binary choice voting scenario, voters may have fuzzy preferences but are required to make crisp choices. In order to compare a crisp voting procedure with more general mechanisms of fuzzy preference aggregation, we first focus on the latter. We present a formulation of strategy-proofness in this setting and study its consequences. On one hand, we achieve an axiomatic recommendation of the ...

From Fine and Kamp in the 70’s—through Osherson and Smith in the 80’s, Williamson, Kamp and Partee in the 90’s and Keefe in the 00’s—up to Sauerland in the present decade, the objection continues to be run that fuzzy logic based theories of vagueness are incompatible with ordinary usage of compound propositions in the presence of borderline cases. These arguments against fuzzy theories have bee...

In this work, we present a fuzzy systems approach for assessing the relative potential risk associated with computer network assets exposed to attack by vulnerabilities. We use this approach to rank vulnerabilities so that analysts can prioritize their work based on the potential risk exposure of assets and networks. We associate vulnerabilities with individual assets, and therefore networks, a...

In this work, we address the transposition of a fragment of the modeling of the Sociology of Organized Action to the fuzzy setting. We present two different ways of developing fuzzy models in this context, that depend on the kind of available data furnished by the user: one based on the extension principle and another using fuzzy rule-based inference with similarity relations. We illustrate our...