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Modeling unstructured decision problems — the theory of analytical hierarchies

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  • Saaty, Thomas L.

Abstract

Quantitative modeling of unstructured decision problems with social implications is new and challenging and has pressing needs. A new approach to scaling using largest eigenvalues and reciprocal matrices and the effect of inconsistent judgment are introduced and relevant theory discussed. In this approach inconsistency is accepted as a fact but measured to determine how bad it is. Since most decision problems are hierarchical in form as they fulfill higher and still higher objectives, the appropriate structure for representation is a hierarchy. A new formal definition of a hierarchy is given and the notion of measurement with eigenvalues is extended to hierarchies. Both the eigenvalue approach to measurement and the hierarchical approach are illustrated with examples. Finally, unstructured problems are illustrated through applications of forward-backward planning, a two-point boundary value problem.

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  • Saaty, Thomas L., 1978. "Modeling unstructured decision problems — the theory of analytical hierarchies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 20(3), pages 147-158.
    • Handle: RePEc:eee:matcom:v:20:y:1978:i:3:p:147-158
    DOI: 10.1016/0378-4754(78)90064-2
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    References listed on IDEAS

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    1. Thomas L. Saaty & Mohamad W. Khouja, 1976. "A Measure of World Influence," Conflict Management and Peace Science, Peace Science Society (International), vol. 2(1), pages 31-48, February.
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    2. Kang Xu & Jiuping Xu, 2020. "A direct consistency test and improvement method for the analytic hierarchy process," Fuzzy Optimization and Decision Making, Springer, vol. 19(3), pages 359-388, September.
    3. Gong, Zaiwu & Guo, Weiwei & Herrera-Viedma, Enrique & Gong, Zejun & Wei, Guo, 2020. "Consistency and consensus modeling of linear uncertain preference relations," European Journal of Operational Research, Elsevier, vol. 283(1), pages 290-307.
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    5. Emete Toros & Yavuz Gazibey, 2018. "Priorities of the citizens in city brand development: comparison of two cities (Nicosia and Kyrenia) by using analytic hierarchy process (AHP) approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(1), pages 413-437, December.
    6. Guh, Yuh-Yuan, 1997. "Introduction to a new weighting method -- Hierarchy consistency analysis," European Journal of Operational Research, Elsevier, vol. 102(1), pages 215-226, October.
    7. Zhe Liu & Jianhong Chen & Yakun Zhao & Shan Yang, 2023. "A Novel Method for Predicting Rockburst Intensity Based on an Improved Unascertained Measurement and an Improved Game Theory," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    8. Paul, Manashi & Negahban-Azar, Masoud & Shirmohammadi, Adel & Montas, Hubert, 2020. "Assessment of agricultural land suitability for irrigation with reclaimed water using geospatial multi-criteria decision analysis," Agricultural Water Management, Elsevier, vol. 231(C).
    9. Ying Xu & Meiyan Wang & Yicheng Xu & Xin Li & Yun Wu & Fang’ai Chi, 2023. "Evaluation System Creation and Application of “Zero-Pollution Village” Based on Combined FAHP-TOPSIS Method: A Case Study of Zhejiang Province," Sustainability, MDPI, vol. 15(16), pages 1-26, August.
    10. Leanda C. Garvie & David J. Lee & Biljana Kulišić, 2024. "Towards a Bioeconomy: Supplying Forest Residues for the Australian Market," Energies, MDPI, vol. 17(2), pages 1-19, January.
    11. Rediske, Graciele & Siluk, Julio Cezar M. & Michels, Leandro & Rigo, Paula D. & Rosa, Carmen B. & Cugler, Gilberto, 2020. "Multi-criteria decision-making model for assessment of large photovoltaic farms in Brazil," Energy, Elsevier, vol. 197(C).
    12. Saaty, T.L., 1983. "Introduction to a modeling of social decision processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 25(2), pages 105-107.
    13. Ergu, Daji & Kou, Gang & Peng, Yi & Shi, Yong, 2011. "A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP," European Journal of Operational Research, Elsevier, vol. 213(1), pages 246-259, August.
    14. Roman Vavrek, 2019. "Evaluation of the Impact of Selected Weighting Methods on the Results of the TOPSIS Technique," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1821-1843, November.
    15. Muna A. Al-Ansari & Hamad Nabeel & Galal M. Abdella & Tarek El Mekkawy & Adeeb A. Kutty, 2024. "A Non-Parametric Approach-Based Trade-Off between Food System Efficiency and Robustness," Sustainability, MDPI, vol. 16(15), pages 1-21, July.
    16. Qing Wang & Yufeng Liu & Xudong Zhang & Huicheng Fu & Sen Lin & Shengyuan Song & Cencen Niu, 2020. "Study on an AHP-Entropy-ANFIS Model for the Prediction of the Unfrozen Water Content of Sodium-Bicarbonate-Type Salinization Frozen Soil," Mathematics, MDPI, vol. 8(8), pages 1-20, July.
    17. Zehong Li & Xinran Miao & Mengyuan Wang & Shuguang Jiang & Yuxian Wang, 2022. "The Classification and Regulation of Mountain Villages in the Context of Rural Revitalization—The Example of Zhaotong, Yunnan Province," Sustainability, MDPI, vol. 14(18), pages 1-19, September.
    18. Saaty, Thomas L., 1979. "Mathematical modeling of dynamic decisions; priorities and hierarchies with time dependence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(4), pages 352-358.
    19. Saaty, Thomas L., 1979. "Applications of analytical hierarchies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(1), pages 1-20.
    20. Pranith K. Roy & Krishnendu Shaw, 2023. "A credit scoring model for SMEs using AHP and TOPSIS," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 372-391, January.
    21. Wang, Xiaojun & Chan, Hing Kai & Li, Dong, 2015. "A case study of an integrated fuzzy methodology for green product development," European Journal of Operational Research, Elsevier, vol. 241(1), pages 212-223.
    22. Benjamin Radcliff, 1986. "Computer-Assisted Approaches To Multiattribute Decision Making," Evaluation Review, , vol. 10(5), pages 578-593, October.

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