Fuzzy languages and fuzzy automata are considered using techniques from algebraic theory of automata. Syntactic monoids of fuzzy languages play a crucial role in the study. Varieties of fuzzy languages are introduced and an Eilenberg-type correspondence between varieties of fuzzy languages, varieties of ordinary languages and varieties of monoids is established.

We study the structure of partially ordered monoids generated by certain operators on families of fuzzy languages. These operators are induced by simple, well-known operations on fuzzy languages, like fuzzy homomorphism, fuzzy finite substitution and intersection with regular fuzzy languages. The structure of these monoids provides better insight in the (in)dependency of closure properties of s...

fuzzy decision tree (fdt) classifiers combine decision trees with approximate reasoning offered by fuzzy representation to deal with language and measurement uncertainties. when a fdt induction algorithm utilizes stopping criteria for early stopping of the tree's growth, threshold values of stopping criteria will control the number of nodes. finding a proper threshold value for a stopping crite...

One of the most serious shortcomings of multidimensional languages is their inability to collaborate with conventional programming languages and systems. Multidimensional languages are used in order to define (potentially infinite) streams, grids, cubes, and so on, concepts which resemble in nature to the familiar imperative arrays. The main difference is that the former entities are lazy while...

We study operations on fuzzy languages such as union, concatenation, Kleene ⋆, intersection with regular fuzzy languages, and several kinds of (iterated) fuzzy substitution. Then we consider families of fuzzy languages, closed under a fixed collection of these operations, which results in the concept of full Abstract Family of Fuzzy Languages or full AFFL. This algebraic structure is the fuzzy ...

We discuss the issue of searching the best K objects in more attributes for more users. Every user prefers objects in different ways. User preferences are modelled locally with a fuzzy function and globally with an aggregation function. Also, we discuss the issue of searching the best K objects without accessing all objects. We deal with the use of local preferences when computing Fagin’s algor...

Fuzzy rule based systems have been very popular in many engineering applications. However, when generating fuzzy rules from the available information, it may result in a sparse fuzzy rule base. Fuzzy rule interpolation techniques have been established to solve the problems encountered by sparse rule bases. In most engineering applications, the use of more than one input variable is common. This...

Multidimensional databases and OLAP (On Line Analytical Processing) tools provide an eÆcient framework for data mining and have led to the so-called OLAP Mining architecture ([10]). Besides, data from real world are often imperfect, either because they are uncertain, or because they are imprecise. Moreover, the use of fuzzy set theory in data mining systems enhances the understandability of the...