MODELLING THE MODIFIED METHOD OF ANALYTIC HIERARCHY PROCESS BY MEANS OF CONSTRUCTIVE AND PRODUCTIVE STRUCTURES
DOI:
https://doi.org/10.15802/stp2016/77926Keywords:
modelling, constructive and productive structure, constructive process, analytic hierarchy process, modificationAbstract
Purpose. In the study it is supposed: 1) to extend the classical method of analytic hierarchy process (AHP) for a great number of alternatives and criteria; 2) to build a model of constructive decision making process using a modified method of analytic hierarchy process with sorting (AHPS). Methodology. To achieve this purpose the mechanism of constructive and productive structures (CPS) was used; the refining transformations of the generalized constructive-productive structure (GCPS) were fulfilled. Findings. The developed model of the constructive process is the interaction between the three structures: the general CPS of AHPS, which allows to set criteria and alternatives and performs the decomposition of task hierarchical structure; CPS of grouping and sorting, which divides alternatives (criteria) into groups and implements the classic single-level AHP for each group, as well as calculates estimates of paired comparisons based on the input data; CPS of single-level classic AHP, which allows to fill the matrix of paired comparisons and calculates the ranks of alternatives. All three structures interact at different levels of transformations: by data conformity at the level of concretization and using of implementations. The proposed model allowed moving to the more abstract level in presentation of decision making problem solving for a great number of criteria and alternatives. Originality. The paper proposes to use CPS mechanism for formalizing modifications of AHP with sorting for decision making problem solving with a great number of criteria and alternatives. Practical value. The formalization of the presentation of the analytic hierarchy process and its modifications allows extending the range of applications of this method, as well as unifying the description of various AHP modifications. Such presentation provides the possibility for developing the programs to implement the method hybrid modifications. Using different interpretations presented in the article of CPS will allow for other approaches in determining the coherence of pairwise comparison matrices, estimate calculation and ranks of alternatives and criteria.
References
Kolesnikova S.I. Modifikatsiya metoda analiza ieyrarkhiy dlya dinamicheskikh naborov alternativ [Modification of hierarchies analysis method for dynamic set of alternatives]. Prikladnaya diskretnaya matematika – Applied Discrete Mathemathics, 2009, no. 4 (6), pp. 102-109.
Mironova N.A. Integratsiya modifikatsiy metoda analiza iyerarkhiy dlya sistem podderzhki prinyatiya gruppovykh resheniy [Integration of modifications of hierarchy analysis method for support systems of group decision making]. Radioelektronika, informatika, upravleniye – Electronics, Computer Science, Management, 2011, no. 2 (25), pp. 47-54.
Saati T.L. Ob izmerenii neosyazayemogo. Podkhod k otnositelnym izmereniyam na osnove glavnogo sobstvennogo vektora matritsy parnykh sravneniy [On the measurement of the intangible. The approach to the relative measurements based on the main eigenvector of pairwise comparisons matrix]. Cloud of Science, 2015, volume 2, issue 1, pp. 5-40. Available at: https://cloudofscience.ru/sites/default/files/pdf/CoS_2_1.pdf (Accessed 17 June 2016).
Saati T.L. Prinyatiye resheniy pri zavisimostyakh i obratnykh svyazyakh: Analiticheskiye seti [Decision making at dependences and feedbacks: Analytic networks]. Moscow, LKI Publ., 2008. 360 p.
Shinkarenko V.I., Zabula H.V. Konstruktivnaya model adaptatsii struktur dannykh v operativnoy pamyati: Chast I. Konstruirovaniye tekstov programm. [Constructive model of data structures adaptation in ram: Part I. Program text constructing]. Nauka ta prohres transportu – Science and Transport Progress, 2016, no. 1 (61), pp. 109-121. doi 10.15802/stp2016/60998.
Shinkarenko V.I, Ilman V.M. Konstruktivno-produktsionnyye struktury i ikh grammaticheskiye interpretatsii. Obobshchennaya formalnaya konstruktivno-produktsionnaya struktura. [Constructive-synthesizing Structures and their Grammatical Interpretations. I. Generalized Formal Constructive-synthesizing Structure]. Kibernetika i sistemnyy analiz – Cybernetics and Systems Analysis, 2014, vol. 49, issue 5, pp. 1-15.
Shinkarenko V.I, Ilman V.M. Konstruktivno-produktsionnyye struktury i ikh grammaticheskiye interpretatsii. Obobshchennaya formalnaya konstruktivno-produktsionnaya struktura. [Constructive-synthesizing Structures and their Grammatical Interpretations. I. Generalized Formal Constructive-synthesizing Structure]. Kibernetika i sistemnyy analiz – Cybernetics and Systems Analysis, 2014, no. 6, pp. 15-28.
Shynkarenko V.I., Vasetska T.M. Modeliuvannia protsesu ranzhuvannia alternatyv metodom analizu iierarkhii zasobamy konstruktsiino-produktsiinykh struktur [Simulation of ranking process of alternatives using the method of analytic hierarchy by means of structurally-productive structures]. Matematychni mashyny i systemy – Mathematical Machines and Systems, 2016, issue 1, pp. 39-47.
Expert Choice for Collaborative Decision Making. Available at: http://expertchoice.com/ (Accessed 17 June 2016).
Saati T.L., Vargas L.G. Models, Methods, Concepts & Applications of the Analytic Hierarchy Process. New York, Springer Science & Business Media Publ., 2012. 345 p.
Saaty T.L. Relative Measurement and Its Generalization in Decision Making Why Pairwise Comparisons are Central in Mathematics for the Measurement of Intangible Factors The Analytic Hierarchy/Network Process. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, 2008, vol. 102, issue 2, pp. 251-318. doi: 10.1007/BF03191825.
Saaty T.L., Vargas L.G. The possibility of group choice: pairwise comparisons and merging functions. Social Choice and Welfare, 2012, vol. 38, issue 3, pp. 481-496. doi: 10.1007/s00355-011-0541-6.
Setiawan H., Istiyanto J.E., Wardoyo R., Santoso P. The Group Decision Support System to Evaluate the ICT Project Performance Using the Hybrid Method of AHP, TOPSIS and Copeland Score. International Journal of Advanced Computer Science and Applications, 2016, no. 7 (4), pp. 334-341. doi: 10.14569/IJACSA.2016.070444.
Shynkarenko V.I., Vasetska T.M., Boiko E.Y. Reducing the number of expert judgments in analytic hierarchy process by sorting and survey management. Systemni tekhnolohii. Rehionalnyi mizhvuzivskyi zbirnyk naukovykh prats [System technologies. Regional Interuniversity collection of scientific papers], 2016, vol. 2 (103), pp. 16-31.
Super Decisions Software. Available at: http://www.superdecisions.com/ (Accessed 17 June 2016).
Downloads
Published
How to Cite
Issue
Section
License
Copyright and Licensing
This journal provides open access to all of its content.
As such, copyright for articles published in this journal is retained by the authors, under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0). The CC BY license permits commercial and non-commercial reuse. Such access is associated with increased readership and increased citation of an author's work. For more information on this approach, see the Public Knowledge Project, the Directory of Open Access Journals, or the Budapest Open Access Initiative.
The CC BY 4.0 license allows users to copy, distribute and adapt the work in any way, provided that they properly point to the author. Therefore, the editorial board of the journal does not prevent from placing published materials in third-party repositories. In order to protect manuscripts from misappropriation by unscrupulous authors, reference should be made to the original version of the work.
