1. Arbab-Zadeh A, Miller JM, Rochitte CE, et al. Diagnostic accuracy of computed tomography coronary angiography according to pre-test probability of coronary artery disease and severity of coronary arterial calcification. The CORE-64 (Coronary Artery Evaluation Using 64Row Multidetector Computed Tomography Angiography) International Multicenter Study. J Am Coll Cardiol 2012;59:379–87. 2. Arbab...

Zadeh proposed and developed the theory of approximate reasoning in a long series of papers in the 1970’s (see e.g. [28, 29, 30, 31, 32, 34, 35]), at the same time when he introduced possibility theory [33] as a new approach to uncertainty modeling. His original approach is based on a fuzzy set-based representation of the contents of factual statements (expressing elastic restrictions on the po...

After Zadeh has introduced his theory, many-valued logic began to have a new interest. Especially, Łukasiewicz logic was enclosed quite closely in fuzzy sets. There is a strong opinion that Łukasiewicz infinite-valued logic has the role as the logic of fuzzy sets, similarly as classical logic has the role as the logic of crisp sets. But actually, it seems that Kleene’s 3-valued logic was the cl...

The goal of this paper is to consider properties of the composition of interval-valued fuzzy relations which were introduced by L.A. Zadeh in 1975. Fuzzy set theory turned out to be a useful tool to describe situations in which the data are imprecise or vague. Interval-valued fuzzy set theory is a generalization of fuzzy set theory which was introduced also by Zadeh in 1965. This paper generali...

The operations in the set of fuzzy numbers are usually obtained bythe Zadeh extension principle. But these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. In fact the Zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

Ontologies have succeeded as a knowledge representation formalism in many domains of application. Nevertheless, they are not suitable to represent vague or imprecise information. To overcome this limitation, several extensions to classical ontologies based on fuzzy logic have been proposed. Even though different fuzzy logics lead to fuzzy ontologies with very different logical properties, the c...

This issue is dedicated to Professor Lotfi A. Zadeh, the founder of fuzzy set theory, on the occasion of celebrating 50 years of his first publication on fuzzy sets in 1965 [1]. The idea of fuzzy sets has influenced a very large number of researchers all over the world. Since 1965 many thousands of research papers on fuzzy set theory and its applications have been published as well as many thou...

Contrasting to Description Logics (DLs), there are some inherent shortcomings in classical fuzzy Description Logics (FDLs). For example, they no longer satisfy the complementary laws. In this paper, to analyze these shortcomings derived from Zadeh semantics, an improved fuzzy set definition using Boolean lattices is approached, whereas, the analogous definition of Zadeh Fuzzy Set can only use a...