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Transitive approximation to pairwise comparison matrices by using interval goal programming

  • Theoretical Paper
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Journal of the Operational Research Society

Abstract

Paired comparison is a very popular method for establishing the relative importance of n objects, when they cannot be directly rated. The challenge faced by the pairwise comparison method stems from some missing properties in its associated matrix. In this paper, we focus on the following general problem: given a non-reciprocal and inconsistent matrix computing intransitivities, what is its associated ranking (defined by importance values)? We propose to use inconsistencies as a source of information for obtaining importance values. For this purpose, a methodology with a decomposition and aggregation phase is proposed. Interval Goal Programming will be a useful tool for implementing the aggregation process defined in the second phase.

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References

  • Saaty TL (1980). The Analityc Hierarchy Process. McGraw-Hill: New York.

    Google Scholar 

  • Saaty TL (1977). A scaling method for priorities in hierarchical structure. J Math Psychol 15: 317–332.

    Article  Google Scholar 

  • Holsztynski W and Koczkodaj W (1996). Convergence of inconsistency algorithms for the pairwise comparisons. Inform Process Lett 59: 197–202.

    Article  Google Scholar 

  • González-Pachón J and Ríos-Insua S (1999). Mixture of maximal quasi orders: a new approach to preference modeling. Theory Decision 47: 73–88.

    Article  Google Scholar 

  • González-Pachón J and Romero C (1999). Distance-based consensus methods: a goal programming approach. OMEGA, Int J Mngt Sci 27: 341–347.

    Article  Google Scholar 

  • González-Pachón J and Romero C (2001). Aggregation of partial ordinal rankings: an interval goal programming approach. Comput Opns Res 28: 827–834.

    Article  Google Scholar 

  • Roberts F (1979). Measurement Theory. Addison-Wesley: Reading, MA.

    Google Scholar 

  • May KO (1954). Intransitivity, utility and the aggregation of preference patterns. Econometrica 22: 1–13.

    Article  Google Scholar 

  • González-Pachón J and Ríos-Insua S (1997). A method for searching rationality in pairwise choices. In: Fandel G and Gal T (eds). Multiple Criteria Decision Making, Lecture Notes in Economics and Mathematical Systems, vol. 448, Springer: Berlin, pp 374–382.

    Chapter  Google Scholar 

  • Maas A, Bezembinder T, Wakker P (1995). On solving intransitivities in repeated pairwise choices. Math Soc Sci 29: 83–101.

    Article  Google Scholar 

  • Cook WD, Kress M and Seiford LM (1996). A general framework for distance-based consensus in ordinal ranking model. Eur J Opl Res 92: 392–397.

    Google Scholar 

  • LINGO (1998). LINGO the Modeling Language and Optimizer. LINDO Systems Inc.: Chicago.

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Acknowledgements

The work of Carlos Romero was supported by ‘Comisión Interministerial de Ciencia y Tecnología’ and ‘Consejería de Educación y Cultura de la Comunidad de Madrid’. Comments and suggestions raised by one reviewer have greatly improved the presentation and accuracy of the paper. Thanks are due to Mrs. Rachel Elliot for reviewing the English.

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Authors and Affiliations

  1. Technical University of Madrid, Madrid, Spain

    J González-Pachón, M I Rodríguez-Galiano & C Romero

Authors
  1. J González-Pachón
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  2. M I Rodríguez-Galiano
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  3. C Romero
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Correspondence to J González-Pachón.

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González-Pachón, J., Rodríguez-Galiano, M. & Romero, C. Transitive approximation to pairwise comparison matrices by using interval goal programming. J Oper Res Soc 54, 532–538 (2003). https://doi.org/10.1057/palgrave.jors.2601542

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  • DOI: https://doi.org/10.1057/palgrave.jors.2601542

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