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Using Inconsistency Reduction Algorithms in Comparison Matrices to Improve the Performance of Generating Random Comparison Matrices with a Given Inconsistency Coefficient Range

Kuraś Paweł, Gerka Alicja

Advances in Science and Technology. Research Journal

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2023

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Vol. 17, no 1

222-229

EN

The aim of this paper is to present a new method for generating random pairwise comparison matrices with a given inconsistency ratio (CR) interval using inconsistency reduction algorithms. Pairwise comparison (PC) is a popular technique for multi-criteria decision-making, its purpose is to assign weights to the compared entities, thus ranking them from best to worst. The presented method combines the traditional random generation of comparison matrices supported by inconsistency reduction algorithms: the “Xu and Wei” algorithm and the “Szybowski” algorithm. This paper presents research that shows an increase in performance when generating such matrices relative to the standard random comparison matrix generation procedure using the “Szybowski” algorithm. The other algorithms also improve the process, but to a lesser extent, making the “Szybowski” supporting algorithm the preferred solution for the new process. As a result of the research, a free online tool “PC MATRICES GENERATOR” has also been made available to efficiently generate a large number of comparison matrices with a given CR factor range, any matrix size, and any number of matrices, enabling much more efficient and less time-consuming research in many fields that use comparison matrices, as the analytic hierarchy/network process (AHP/ANP), ELECTREE, PAPRIKA, PROMETHE, VIKOR or the Best-Worst method (BWM).

2

Identification of key factors for the successful development of agricultural biogas plants in Poland

Ginda Grzegorz, Szyba Marta

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2022

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Vol. 16

19--31

EN

In Poland, the potential for biogas production is high. important source of renewable energy and contributes to reducing the emissions of methane, a greenhouse gas. In this article, based on materials from the National Agricultural Advisory Centre (KOWR), literature, and statistical data, the implementation of the agrigas plant construction programme was evaluated in individual voivodeships. Based on the collected data, it was concluded that the most meaningful factors for the successful development of Polish agricultural biogas plants are biogas production technology, substrate availability, energy price from renewable energy sources, waste disposal costs, population density in the commune, and allocation of places in local spatial development plans (MPZP). DEMATEL technique was used to identify key development factors. The results of the study provide useful information for both government and local authorities in the search for effective ways to drive the sector's development.

3

Remarks about geometric scale in the analytic hierarchy process

Starczewski T.

Journal of Applied Mathematics and Computational Mechanics

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2018

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Vol. 17, nr 3

71--82

EN

The Analytic Hierarchy Process (AHP) is perhaps the most popular approach to decision-making problems of prioritization. The basis of the AHP is pairwise comparison, which is used to compare alternatives. This comparisons are provided by decision makers usually as linguistic expressions which are next converted to numbers from a fixed set called a scale. The influence of the scale on the quality of prioritization was investigated in a number of papers. One of the most important types of judgment scale is the Geometric Scale. Its elements depend on specific parameters. In this paper, the impact of the choice of this scale’s parameters on errors in priority vectors and on values of the inconsistency indices is studied via Monte Carlo simulations.

4

Remarks on the impact of the adopted scale on the priority estimation quality

Starczewski T.

Journal of Applied Mathematics and Computational Mechanics

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2017

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Vol. 16, nr 3

105--116

EN

The Analytic Hierarchy Process (AHP) is the method that supports people’s decisions in the multi-criteria decision making problems. In this method the decision process is based on pairwise comparing of every two possible alternatives. The decision maker (DM) compares alternatives by choosing an appropriate “linguistic phrase” or a number from a proper set. This set of “linguistic phrases” and/or the numbers connected with them are referred to as the priority scale. There are several different scales that are described in literature and used in AHP practice. In dependence of the scale chosen by the DM, the final decisions might differ. In the AHP it is assumed that DMs make mistakes over comparing pairs of alternatives, but it was also observed that the assumed scale increases these errors as well. In our paper, we investigate the impact of the adopted scale to the number and magnitude of errors in the final decision. Our results show that the choice of the scale has a big impact on the final decision, so it is crucial part of AHP. It turns out that scales with bigger resource of options result in better evaluations of priority vectors.

5

Usprawnianie podejmowania decyzji w budownictwie dzięki zróżnicowaniu sposobów wykorzystywania porównywania parami

Dytczak M., Ginda G., Jastrząbek B.

Materiały Budowlane

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2016

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nr 6

94--96

PL

Złożoność uwarunkowań otoczenia powoduje, że rozwiązywane zagadnienia decyzyjne w budownictwie wymagają uwzględniania informacji o niedoskonałym charakterze. W tym celu wykorzystywane są różne narzędzia. Jednym z nich są porównania parami (PP), które stały się podstawą wielu metod wspomagania decyzji. Są one również używane wspólnie z innymi narzędziami oraz ułatwiają ich implementację. Takie sposoby stosowania wzbogacają inne narzędzia, a także poszerzają potencjał aplikacyjny porównań parami (PP). W artykule omówiono zaawansowane sposoby stosowania PP, które okazują się użyteczne w przypadku podejmowania decyzji w budownictwie i dziedzinach pokrewnych.

EN

The complexity of surrounding environment results in a need for utilizing imperfect information while solving decision making problems in civil engineering. Diverse pair-wise comparison-based tools are often applied to make use of imperfect information. They are applied both in a standalone mode as well as together with other tools. Their common application with other tools provides necessary means for mutual enhancement in application potential of them and the other tools they are used together with. The utilization modes which prove to be useful in solving decision making problemin civil engineering and related fields are therefore presented in the paper.

6

The limit of inconsistency reduction in pairwise comparisons

Koczkodaj W. W., Szybowski J.

International Journal of Applied Mathematics and Computer Science

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2016

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Vol. 26, no. 3

721--729

EN

This study provides a proof that the limit of a distance-based inconsistency reduction process is a matrix induced by the vector of geometric means of rows when a distance-based inconsistent pairwise comparisons matrix is transformed into a consistent PC matrix by stepwise inconsistency reduction in triads. The distance-based inconsistency indicator was defined by Koczkodaj (1993) for pairwise comparisons. Its convergence was analyzed in 1996 (regretfully, with an incomplete proof) and finally completed in 2010. However, there was no interpretation provided for the limit of convergence despite its considerable importance. This study also demonstrates that the vector of geometric means and the right principal eigenvector are linearly independent for the pairwise comparisons matrix size greater than three, although both vectors are identical (when normalized) for a consistent PC matrix of any size.

7

Two Squares of Oppositions and Their Applications in Pairwise Comparisons Analysis

Schumann A., Woleński J.

Fundamenta Informaticae

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2016

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Vol. 144, nr 3/4

241--254

EN

This paper examines two main possibilities of pairwise comparisons analysis: first, pairwise comparisons within a lattice, in this case these comparisons can be measurable by numbers; second, comparisons beyond any lattice, in this case these comparisons cannot be measurable in principle. We show that the first approach to pairwise comparisons analysis is based on the conventional square of opposition and its generalization, but the second approach is based on unconventional squares of opposition. Furthermore, the first approach corresponds to lateral inhibition in transmission signals and the second approach corresponds to lateral activation in transmission signals.

8

Representation of The Pairwise Comparisons in AHP Using Hesitant Cloud Linguistic Term Sets

Huang H.-C., Yang X.

Fundamenta Informaticae

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2016

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Vol. 144, nr 3/4

349--362

EN

The analytic hierarchy process (AHP) is the most popular extension to the pairwise comparisons method which is based on the observation that it is much easier to rank several objects when restricted to two objects at one time. As the pairwise comparisons are subjective, the use of linguistic expressions rather than numerical values is straightforward and friendlier due to the uncertainties that are inherent in human judgments. In this paper, to handle the uncertainty and hesitancy in practical decisionmaking situations, we represent pairwise comparisons in AHP using hesitant cloud linguistic term sets (HCLTSs) which are proposed based on hesitant fuzzy linguistic term sets (HFLTSs) and normal cloud models. Then, the synthetic cloud model aggregation algorithm is proposed to transform the HCLTS pairwise comparison matrix into the positive reciprocal synthetic cloud matrix. A prioritization method using the geometric mean technique is adopted, and the ranking method based on comparing of the parameters of normal cloud models is proposed. Thus, we extend the traditional AHP method in hesitant and uncertain environment, and we call it HCLTS-AHP method. The comparative linguistic expressions of preferences become more flexible and richer and are more similar to human beings’ cognitive models. Furthermore, the synthetic cloud model is consistent with objectivity and the calculations are easy to implement. An illustrated example is applied to the ranking of four alternatives to show the usefulness of the proposed HCLTS-AHP method.

9

Wielokryterialne wspomaganie decyzji. Przegląd metod i zastosowań

Trzaskalik T.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2014

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z. 74

239--263

EN

The universality of the decision situations and the importance of many of them contributed to the development of multicriteria decision support methods. These are mainly the two-stage methods – the analytical and synthesis stage are distinguished. Among the presented methods there are AHP, ANP, ELECTRE, PROMETHEE, verbal methods, TOPSIS, BIPOLAR, and interactive methods in terms of risk. The aim of the paper is to present the most frequently used multicriteria discrete methods and the examples of their applications.

PL

Powszechność sytuacji, w których podejmujemy decyzje, oraz wielka waga wielu z nich przyczyniły się do rozwoju wielokryterialnych metod wspomagania decyzji. Są to głównie metody dwuetapowe – wyróżniamy etap analityczny i etap syntezy. Wśród przedstawionych metod znajdują się m.in. metody AHP, ANP, ELECTRE, PROMETHEE, metody werbalne, TOPSIS, BIPOLAR oraz metody interaktywne w warunkach ryzyka. Celem artykułu jest prezentacja najczęściej wykorzystywanych wielokryterialnych metod dyskretnych oraz możliwości ich zastosowań.

10

How to support government procurement by a pairwise comparisons model

Koczkodaj W. W., Mackasey W. O., Smolewski I., Tadeusiewicz R.

Studia Informatica : systems and information technology

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2013

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Vol. 1-2(17)

19--28

EN

This study demonstrates how a government procurement process could be improved by the pairwise comparisons method. A case study, related to assessment of project proposals is used for demonstration purpose. The project proposals were requested by a Canadian government agency to assess the environmental and public safety hazards of abandoned mines. However, the presented model is applicable (with easy-to-implement modifications) to any other case of government procurement.

11

Classifying Visual Objects with the Consistency-Driven Pairwise Comparisons Method

Koczkodaj W. W., Robidoux N., Tadeusiewicz R.

Machine Graphics and Vision

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2009

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Vol. 18, No. 2

143-154

EN

The classification of the various image features or visual objects can be carried out by the consistency-driven pairwise comparisons method based on their relative importance. A key issue in the proposed approach is a weight-based synthesis for combining various image features. When compared with the traditional experience-based linear assignment method, the proposed approach is more effective and easy to communicate.