In this paper we shall introduce an approach that forms a basis for temporal data mining. A relation algebra is applied for the purpose of representing simultaneously dependencies among instants, dependencies between instants and intervals, and dependencies between intervals. This enables one to specify and recognise complex interrelationships among point events in data streams. An example is s...

This paper deals with two problems: the first concerns the design of the HW architecture of a high speed Fuzzy Processor that works at 50 Mega Fuzzy Inference per Second (MFIPS). It has eight 7 bit inputs and one 7 bit output. It is foreseen to apply it as a part of the trigger device in HEP (High Energy Physics) experiments, the second one concerns the 1.0 μm CMOS VLSI design of the fuzzificat...

Fuzzy logic has proven to be a promising method for developing simple, robust controllers for uncertain or nonlinear systems. One problem with fuzzy controllers, however, is that they are difficult to apply to higher-order systems. The reason for this is that the number of rules required for the rule base increases geometrically with the number of states. For example, if a system was fourth-ord...

Let X be a compact metric space, let φ be a continuous self-map on X , and let F(X) denote the space of fuzzy sets on X equipped with the levelwise topology. In this paper we study relations between various dynamical properties of a given (crisp) dynamical system (X,φ) and its Zadeh’s extension Φ on F(X). Among other things we study various (weak, strong, mild etc.) mixing properties and also s...

The present article proposes a fuzzy set-based classifier with a better learning and generalization capability. The proposed classifier exploits the feature-wise degree of belonging of a pattern to all classes, generalization in the fuzzification process and the combined class-wise contribution of features effectively. The classifier uses a -type membership function and product aggregation reas...

We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK-ideals of BCK-algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK-ideal. We state a relation between a fuzzy hyper BCK-ideal and a fuzzymultiply positive implicative hyper BCK-ideal. Moreov...

We consider the intuitionistic fuzzification of the concept of prime ideals in commutative BCK-algebras, and investigate some of their properties. We show that if P is a prime ideal of commutative BCK-algebra X iff ∼ P = 〈XP , − XP 〉 is an intuitionistic fuzzy prime ideal of X. We also prove that An IFS A = 〈μA, λA〉 of commutative BCK-algebra X is an intuitionistic fuzzy prime ideal of X if and...

In [1, 2] we studied various concepts of bipolar queries (cf. Dubois and Prade [3]). We advocated there the use of a fuzzified version of the original crisp definition introduced by Lacroix and Lavency [4]. However, the fuzzification proposed, as general as it was, leaves open the choice of a representation of logical entities, notably the logical connectives and quantifiers. In the present pap...

Compared to companies engaged in traditional commerce, sports e-commerce companies are involved with more kinds of business data, encounter higher demands on data processing, and experience more complex data processing methods. In this dissertation, dynamic fuzzification method is adopted to improve the original evaluation method for weight quota distribution, optimize representation method of ...

The paper presents methods of preparing students’ rankings based on the results of final secondary school examination test in mathematics in Poland. The currently used method is based on the percentage of earned points and does not take into account levels of acquirement of learning outcomes by students. The data used in this article contains results of students who earned the same number of po...