Determination of the regularity radius r∗ of interval matrices is known to be a NP-hard problem. In this paper, a method for determining r∗ is suggested whose numerical complexity is not a priori exponential. The method is based on an equivalent transformation of the original problem to the problem of determining the real maximum magnitude eigenvalue μ∗ of an associated interval generalized eig...

This paper presents a stability analysis of the iterative learning control (ILC) problem when the plant Markov parameters are subject to interval uncertainty. Using the super-vector approach to ILC, vertex Markov matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ILC process. It is shown that Kharitonov segments between vertex m...

In this paper we propose a general framework for the interval comparison which finds different classes of preference structures having an interval representation. First of all we propose an axiomatisation for an interval representation and then we present some results which generalise the characterisation of some classical properties such as transitivity, Ferrers relation, etc. We make use of t...

We study matrices of morphisms preserving the family of words coding 3-interval exchange transformations. It is well known that matrices of morphisms preserving sturmian words (i.e. words coding 2-interval exchange transformations with the maximal possible factor complexity) form the monoid {M ∈ N | det M = ±1} = {M ∈ N | MEM = ±E}, where E = ( 0 1 −1 0 ). We prove that in case of exchange of t...

In this paper, we present several verifiable conditions for eigenvalue intervals of real symmetric interval matrices overlapping or not overlapping. To above cases, two new methods with algorithms for computing eigenvalue bounds of real symmetric matrices are developed. We can estimate eigenvalue bounds moving away the assumption that two intervals containing two eigenvalues of real symmetric i...

A comparison is made between the most commonly used decision-making method (AHP), and two methods developed by the authors (APM and CSM). It is shown that the newly developed methods do not change the correlations and types of inequalities between the global priorities of the alternatives when the number of alternatives changes. This differentiates them from the AHP, which does change them. Als...

Pairwise comparison matrices are often used in Multi-attribute Decision Making for weighting the attributes or for the evaluation of the alternatives with respect to a criteria. Matrices provided by the decision makers are rarely consistent and it is important to index the degree of inconsistency. In the paper, the minimal number of matrix elements by the modification of which the pairwise comp...

In comparison to dense matrices multiplication, sparse matrices multiplication real performance for CPU is roughly 5–100 times lower when expressed in GFLOPs. For sparse matrices, microprocessors spend most of the time on comparing matrices indices rather than performing floating-point multiply and add operations. For 16-bit integer operations, like indices comparisons, computational power of t...

In 1965, Zadeh introduced the concept of fuzzy subsets. Latter many authors defined different directions of fuzzy subsets. Turksen (1986) generalized the concept of fuzzy set in terms of interval-valued fuzzy set (IVFS). Several researchers present a number of results using IVFSs. Using these concept of (IVFS) Pal and Shyamal (2006) introduced interval-valued fuzzy matrices and shown several pr...

The author previously proposed an extension of differential evolution. The proposed method extends the processes of DE to handle interval numbers as genotype values so that DE can be applied to interval-valued optimization problems. The interval DE can employ either of two interval models, the lower and upper model or the center and width model, for specifying genotype values. Ability of the in...