Andrzej Z. Grzybowski

Note on a new optimization based approach for estimating priority weights and related consistency index

The generation of priority vectors from pairwise comparison matrices is an essential part of the Analytic Hierarchy Process. Perhaps the most popular approach for deriving the priority weights is the right eigenvalue method (REV) which was proposed by Saaty. Despite its popularity some shortcomings of the REV have been reported in literature. Among the alternative approaches one can find the statistical estimation techniques, methods founded on constrained optimization models and models based on fuzzy description of decision maker preferences. In this paper new optimization techniques for deriving priority weights are introduced. In the proposed approach, the constrained optimization models are based on the same idea which underlies the REV. The properties of the resulting prioritization techniques are studied via computer simulations. This study demonstrates that the new methods perform very well in comparison with other popular techniques known from literature. What is especially important, the new approach provides the decision maker with a meaningful index that can be used to measure consistency of his/her judgments. The new index is closely related to the well-known Saatys consistency index CI, but in difference to the latter, it can be applied to both reciprocal as well as nonreciprocal comparison matrices. Hence the new index can be considered as a natural extension of the CI to all types of matrices. Some additional advantages resulting from the new approach are discussed and illustrated by numerical examples.

Computer Simulations in Constructing a Coefficient of Uncertainty in Regression Estimation - Methodology and Results

The paper is devoted to the problem of incorporating prior information in the regression estimation. On the base of computer simulation we construct a coefficient which allows incorporating the prior information along with its uncertainty. Performance of estimators based upon the coefficient of uncertainty is examined through computer simulations.

On Some Advancements within Certain Multicriteria Decision Making Support Methodology

Deriving true priority vectors from intuitive pairwise comparison matrices (PCMs) and consistency measurement of decision makers judgments about their genuine weights are crucial issues within the multicriteria decision making support methodology called Analytic Hierarchy Process (AHP). The most popular procedure in the ranking process, constitutes the Right Eigenvector Method (REV). The inventor of the AHP convinces that as long as inconsistent PCMs are allowed in the AHP none of the other existing procedures qualify and the REV provides the only right solution in this process. The objective of this scientific paper is to examine if the former opinion can be considered as experimentally confirmed. For this purpose it was decided to apply Monte Carlo methodology. However, rather than simulate and analyze simulations results for a single PCM, as it has been done so far by many other authors, we decided to design and analyze computer simulations results for a singular model of the AHP framework. Our findings lead to inevitable conclusion that the REV cannot longer be perceived as a dominant procedure within the AHP methodology, especially when nonreciprocal PCMs are considered. It was verified empirically in our research that in the situation when nonreciprocal PCMs are considered the REV impoverishes the entire AHP methodology by its lack of PCMs inconsistency measure in such cases. Moreover, it provides less accurate rankings for a particular decision in comparison to other presented methods. It was also unequivocally verified that the enforced reciprocity of PCM leads directly to worse estimates of priorities weights. Altogether, it seems very important from the perspective of methodology supporting multicriteria decision making, the crucial process embedded in most of management activity. In the consequence, because the REV recedes other prioritization procedures available for the AHP methodology, it is advised to consider them instead, especially under some circumstances of an important and very tight managerial decisions. Normal 0 false false false EN-US X-NONE AR-SA

Classical Young Measures Generated by Oscillating Sequences with Uniform Representation

The paper is devoted to the theory of classical Young measures. It focuses on the situation where a sequence of rapidly oscillating functions has uniform representation in a sense that is defined in this article. There is stated a proposision characterizing the Young measures generated by such a class of sequences. This characterization enables one to find an explicit formulae for the density functions of these generated measures as well as the computations of the values of the related Young functionals. Examples of possible applications of the new results are presented as well.

Analysis of sequential algorithms as tools for modeling the chain-like-body evolution

This presentation is devoted to the algorithmization of the chain-like bodys movements. An ample set of experimental data and recent theoretical achievements show that chain-like polymers traversing a membrane opening undergo multiple changes of their shape. These changes are mostly due to a mechanical tension induced by an environment with its chemical interactions that affect polymers mobility. Known analytical approaches yield qualitative description of chain-shape deformations whereas a quantitative insight mostly relies on numerical experiments. These experiments are conducted with the help of a Monte-Carlo-like class of algorithms to mimic evolutions of chain trajectory in the space. Obviously, an efficient generation of trajectories with high acceptance ratio is crucial. In this paper we focus on our algorithm employing sequentialization of the chain move into one-chain-segments steps. An image of sequentially decomposed chains move used by us in the process of the trajectory reconstruction involves the tension propagation mechanism as well. The sequences of virtual chain-segment steps followed by the progressed tension are in the core of our sequential algorithm. In this paper we analyze this algorithm as a tool for mimicking the real polymer evolution. For this propose we compare our movement assumptions with these that are adopted in other algorithms employed in the polymer studies. In this context we also address some important physical features that should be manifested by any well simulated movement trajectory.

Optimal Stopping Rules For Some Blackjack Type Problems

The paper deals with a class of optimal stopping problems having some features of blackjack type games. A decision maker observes sequentially the values of a finite sequence of non‐negative random variables. After each observation he decides whether to stop or to continue. If he decides to stop, he obtains a payoff dependent on the sum of already observed values. The greater the sum, the more the decision maker gains, unless the sum exceeds a positive number T−a limit given in the problem. If so, the decision maker loses all or part of his payoff. A sufficient condition for existence of a simple optimal stopping rule for such problems is formulated. Then some special cases are considered in detail. Some numerical examples and practical questions are discussed as well.

Trybula's papers related to optimal control

W pewnym okresie Trybula zwrocil uwage na zagadnienia adaptacyjnego sterowania (patrz [20, 21]). Wydaje sie, ze zainspirowala Go monografia Aoki [1]. Do tematu wrocil po dośc dlugim czasie. Zauwazyl, ze w literaturze zaklada sie, iz zaklocenia w systemach stochastycznych mają charakter gaussowski, podczas gdy w praktyce sygnaly, a wiec i zaklocenia, są dyskretne. Przypominamy tutaj typowy model analizowany w tej serii prac jako, ze wspolczesne zastosowania modeli liniowych w ekonomii i technice wymuszają sygnaly zarowno typu ciąglego, jak i dyskretne. Ograniczymy sie do szczegolowego przedstawienia konstrukcji sterowan bayesowskich przy kwadratowej funkcji kosztu i zakloceniach z wykladniczej klasy, spelniających dodatkowe warunki nalozone na momenty. W konkluzji podajemy odsylacze do prac, w ktorych wyznaczono sterowania minimaksowe. Slowa kluczowe: system liniowy, zaklocenia addytywne, wykladnicza klasa rozkladow, sterowanie bayesowskie, sterowanie minimaksowe.