Fuzziness and Mathematical Logic

Dear Colleagues,

Fuzzy set theory was initiated by Zadeh in 1965, and fuzzy sets and some generalizations have been considered in a variety of fields. Fuzzy sets are somewhat like sets in which elements have degrees of membership. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition—an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0,1]. Fuzzy sets generalize classical sets, since the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1. In fuzzy set theory, classical bivalent sets are usually called crisp sets. The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics. Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Mathematical logic is often divided into the fields of set theory, model theory, recursion theory and proof theory. These areas share basic results on logic, particularly first-order logic and definability.

The aim of this Special Issue is to establish a collection of high-quality original theoretical and applied research papers on “Fuzziness and Mathematical Logic”.

Prof. Young Bae Jun
Prof. Rajab Ali Borzooei
Guest Editors

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