Basil K. Papadopoulos

Distance and similarity measures for fuzzy operators

We introduce and study a new family of normalized distance measures between binary fuzzy operators, along with its dual family of similarity measures. Both are based on matrix norms and arise from the study of the aggregate plausibility of set-operations. We also suggest a new family of normalized distance measures between fuzzy sets, based on binary operators and matrix norms, and discuss its qualitative and quantitative features. All measures proposed are intended for applications and may be customized according to the needs and intuition of the user.

Real time DDoS detection using fuzzy estimators

We propose a method for DDoS detection by constructing a fuzzy estimator on the mean packet inter arrival times. We divided the problem into two challenges, the first being the actual detection of the DDoS event taking place and the second being the identification of the offending IP addresses. We have imposed strict real time constraints for the first challenge and more relaxed constraints for the identification of addresses. Through empirical evaluation we confirmed that the detection can be completed within improved real time limits and that by using fuzzy estimators instead of crisp statistical descriptors we can avoid the shortcomings posed by assumptions on the model distribution of the traffic. In addition we managed to obtain results under a 3 sec detection window.

L-fuzzy Sets and Intuitionistic Fuzzy Sets

In this article we firstly summarize some notions on L−fuzzy sets, where L denotes a complete lattice. We then study a special case of L−fuzzy sets, namely the “intuitionistic fuzzy sets”. The importance of these sets comes from the fact that the negation is being defined independently from the fuzzy membership function. The latter implies both flexibility and effectiveness in fuzzy inference applications. We additionally show several practical applications on intuitionistic fuzzy sets, in the context of computational intelligence.

On the fuzzy difference equation x n +1 = A + x n /x n-m

In this paper we study the existence the boundedness and the asymptotic behavior of the positive solutions of the fuzzy equation xn÷1 = A+xn/xn-m, n=0,1... where xn is a sequence of fuzzy numbers, A is a fuzzy number and m ∈ {1,2,...}.

Similarities in fuzzy regression models

The solutions of a fuzzy regression model are obtained by converting the problem into a linear programming problem. For each level h, h∈[0, 1), there exists a solution. In this paper, we study the set of all the solutions to the fuzzy regression model that comes from a set of data as a metric space with an appropriate metric on it. We define a similarity ratio that allows us to compare the spaces of solutions of a fuzzy regression model that come from different sets of data. We also give an application using data sets concerning the GNP–money relationship.

On the fuzzy difference equation xn+1 = A+B/xn.

Abstract In this paper we study the existence the oscillatory behavior the boundedness and the asymptotic behavior of the positive solutions of the fuzzy equation xn+1=A+B/xn,n=0,1,… where xn is a sequence of fuzzy numbers, A, B are fuzzy numbers.

Computational method to evaluate fuzzy arithmetic operations

Abstract In this paper we propose a computational method to evaluate the arithmetic operations on fuzzy numbers with nonlinear membership functions. The simplicity and the overall effectiveness in the implementation are the attractions of the method and this is shown by some numerical examples.

Topologies on function spaces

In the present paper we introduce notions of A-splitting and A-jointly continuous topology on the set C(Y,Z) of all continuous maps of a topological space Y into a topological space Z, where A is any family of spaces. These notions satisfy the basic properties of splitting and jointly continuous topologies on C(Y,Z). In particular, for every A, the greatest A-splitting topology on C(Y,Z) (denoted by τ(A) always exists. We indicate some families A of spaces for which the topology τ(A) coincides with the greatest splitting topology on C(X,Y). We give a notion of equivalent families of spaces and try to find a “simple” family which is equivalent to a given family. In particular, we prove that every family is equivalent to a family consisting of one space, and the family of all spaces is equivalent to a family of all T1-spaces containing at most one nonisolated point. We compare the topologies τ({X}) for distinct compact metrizable spaces X and give some examples. Bibliography: 13 titles.

Fuzzy Performance Evaluation of Workflow Stochastic Petri Nets by Means of Block Reduction

Workflow management becomes increasingly important in todays information-oriented society. An important research area of workflow management is performance analysis that is driven by the need for improved efficiency of business processes. The study of the performance of a workflow process, as the focus of this paper, requires the estimation of the duration of tasks, which is often unpredictable and nondeterministic. Current research in this field has focused on workflow stochastic Petri nets (PNs)-which are a class of workflow nets with exponential distributed execution times assigned to transitions. In this paper, in order to deal with this uncertainty, we use fuzzy estimators constructed from statistical data to describe time, and we present an analytical method to proceed with the performance evaluation of workflow stochastic PNs based on block reduction. A comparison example is provided to show the benefits of the proposed method.

Convergences in fuzzy topological spaces

In this paper we introduce the notions of fuzzy upper limit, fuzzy lower limit and the fuzzy continuous convergence on the set of fuzzy continuous functions. In examining these aforementioned notions in the present paper we find on the one hand many properties of them whilst on the other, the following applications take place: (α) the characterization of fuzzy compact spaces through the contribution of fuzzy upper limit and (β) the characterization of the fuzzy continuous convergence through the assistance of fuzzy upper limit.