IDEAS home Printed from https://ideas.repec.org/p/arx/papers/0709.4358.html
   My bibliography  Save this paper

Projective Market Model Approach to AHP Decision-Making

Author

Listed:
  • Anna Szczypinska
  • Edward W. Piotrowski

Abstract

In this paper we describe market in projective geometry language and give definition of a matrix of market rate, which is related to the matrix rate of return and the matrix of judgements in the Analytic Hierarchy Process (AHP). We use these observations to extend the AHP model to projective geometry formalism and generalise it to intransitive case. We give financial interpretations of such generalised model and propose its simplification. The unification of the AHP model and projective aspect of portfolio theory suggests a wide spectrum of new applications such extended model.

Suggested Citation

  • Anna Szczypinska & Edward W. Piotrowski, 2007. "Projective Market Model Approach to AHP Decision-Making," Papers 0709.4358, arXiv.org, revised Nov 2007.
    • Handle: RePEc:arx:papers:0709.4358
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/0709.4358
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Piotrowski, E.W & Sładkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
    2. Zambrzycka, Anna & Piotrowski, Edward W., 2007. "The matrix rate of return," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 347-353.
    3. Piotrowski, Edward W. & Sładkowski, Jan, 2007. "Geometry of financial markets—Towards information theory model of markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 228-234.
    4. Sładkowski, Jan, 2003. "Giffen paradoxes in quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 234-240.
    5. Edward W. Piotrowski & Marcin Makowski, "undated". "Cat's Dilemma," Departmental Working Papers 20, University of Bialtystok, Department of Theoretical Physics.
    6. Kwiesielewicz, M., 1996. "The logarithmic least squares and the generalized pseudoinverse in estimating ratios," European Journal of Operational Research, Elsevier, vol. 93(3), pages 611-619, September.
    7. Vargas, Luis G., 1990. "An overview of the analytic hierarchy process and its applications," European Journal of Operational Research, Elsevier, vol. 48(1), pages 2-8, September.
    8. Ernest H. Forman & Saul I. Gass, 2001. "The Analytic Hierarchy Process---An Exposition," Operations Research, INFORMS, vol. 49(4), pages 469-486, August.
    9. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    10. Marcin Makowski & Edward W. Piotrowski, "undated". "Quantum Cat's Dilemma: an Example of Intransitivity in a Quantum Game," Departmental Working Papers 28, University of Bialtystok, Department of Theoretical Physics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Szczypińska, Anna & Piotrowski, Edward W., 2009. "Inconsistency of the judgment matrix in the AHP method and the decision maker’s knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 907-915.
    2. Wang, Jiang-Jiang & Jing, You-Yin & Zhang, Chun-Fa & Shi, Guo-Hua & Zhang, Xu-Tao, 2008. "A fuzzy multi-criteria decision-making model for trigeneration system," Energy Policy, Elsevier, vol. 36(10), pages 3823-3832, October.
    3. Jing, You-Yin & Bai, He & Wang, Jiang-Jiang, 2012. "A fuzzy multi-criteria decision-making model for CCHP systems driven by different energy sources," Energy Policy, Elsevier, vol. 42(C), pages 286-296.
    4. Edward W. Piotrowski & Jerzy Luczka, "undated". "The relativistic velocity addition law optimizes a forecast gambler's profit," Departmental Working Papers 31, University of Bialtystok, Department of Theoretical Physics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. P Ji & R Jiang, 2003. "Scale transitivity in the AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 896-905, August.
    2. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Influence of aggregation and measurement scale on ranking a compromise alternative in AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 700-710, April.
    3. A Ishizaka & D Balkenborg & T Kaplan, 2011. "Does AHP help us make a choice? An experimental evaluation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1801-1812, October.
    4. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    5. Szczypińska, Anna & Piotrowski, Edward W., 2009. "Inconsistency of the judgment matrix in the AHP method and the decision maker’s knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 907-915.
    6. Ouesleti, Bilel & Costa-Font, Montserrat & Kallas, Zein & Chema Gil, Jose Maria, 2015. "Determinant Factors Affecting The Point of Purchase Selection: valuation and Perceptions," 2015 Conference, August 9-14, 2015, Milan, Italy 212603, International Association of Agricultural Economists.
    7. Wenshuai Wu & Gang Kou, 2016. "A group consensus model for evaluating real estate investment alternatives," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-10, December.
    8. Korpela, Jukka & Tuominen, Markku, 1996. "A decision aid in warehouse site selection," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 169-180, August.
    9. Ormerod, Richard J. & Ulrich, Werner, 2013. "Operational research and ethics: A literature review," European Journal of Operational Research, Elsevier, vol. 228(2), pages 291-307.
    10. Melachrinoudis, Emanuel & Min, Hokey, 2007. "Redesigning a warehouse network," European Journal of Operational Research, Elsevier, vol. 176(1), pages 210-229, January.
    11. Lucas, Rochelle Irene & Promentilla, Michael Angelo & Ubando, Aristotle & Tan, Raymond Girard & Aviso, Kathleen & Yu, Krista Danielle, 2017. "An AHP-based evaluation method for teacher training workshop on information and communication technology," Evaluation and Program Planning, Elsevier, vol. 63(C), pages 93-100.
    12. Sato, Yuji, 2012. "Optimal budget planning for investment in safety measures of a chemical company," International Journal of Production Economics, Elsevier, vol. 140(2), pages 579-585.
    13. S. Lipovetsky, 2009. "Global Priority Estimation in Multiperson Decision Making," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 77-91, January.
    14. Vivek Sharma & Sandeep Grover & S. K. Sharma, 2020. "An integrated AHP-GTA approach for measuring effectiveness of quality tools and techniques," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(1), pages 54-63, February.
    15. Zsuzsanna Katalin Szabo & Zsombor Szádoczki & Sándor Bozóki & Gabriela C. Stănciulescu & Dalma Szabo, 2021. "An Analytic Hierarchy Process Approach for Prioritisation of Strategic Objectives of Sustainable Development," Sustainability, MDPI, vol. 13(4), pages 1-26, February.
    16. Xu, Zeshui & Chen, Jian, 2008. "Some models for deriving the priority weights from interval fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 184(1), pages 266-280, January.
    17. Dong, Yucheng & Xu, Yinfeng & Li, Hongyi & Dai, Min, 2008. "A comparative study of the numerical scales and the prioritization methods in AHP," European Journal of Operational Research, Elsevier, vol. 186(1), pages 229-242, April.
    18. Tohid Atashbar, 2013. "Iranian Disease: Why a Developing Country's Government Did Not Listen to Economists' Advices," American Journal of Economics and Sociology, Wiley Blackwell, vol. 72(3), pages 732-760, July.
    19. Zhu, Bin & Xu, Zeshui, 2014. "Analytic hierarchy process-hesitant group decision making," European Journal of Operational Research, Elsevier, vol. 239(3), pages 794-801.
    20. Devesh Kumar & Gunjan Soni & Rohit Joshi & Vipul Jain & Amrik Sohal, 2022. "Modelling supply chain viability during COVID-19 disruption: A case of an Indian automobile manufacturing supply chain," Operations Management Research, Springer, vol. 15(3), pages 1224-1240, December.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:0709.4358. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.