Advertisement

On Consistency and Incoherence in Analytical Hierarchy Process and Intertemporal Choices Models

  • Fabrizio Maturo
  • Viviana Ventre
  • Angelarosa Longo
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)

Abstract

A rational choice is based on conditions of coherence, that are universally accepted rules to which a decision-maker must comply in expressing his/her preferences. In this paper, we focus on two different approaches in decision-making processes, i.e. the Analytical Hierarchy Process and Intertemporal Choices models, highlighting the consistency conditions usually adopted. After a general discussion on consistence and incoherence in the framework of these two different approaches, we show that sometimes it is preferable to weaken or reinforce coherence conditions according to the specific context.

Keywords

AHP models Intertemporal choice models Coherence Allowing inconsistency 

References

  1. Amirabadi S. (2011): A mathematical method for preventing inconsistency in decision maker’s comparisons. In: XI Symposium of Analytic Hierarchy/Network Process. Sorrento, Naples (Italy)Google Scholar
  2. Antampoufis, N., Hoskova-Mayerova, S.: A brief survey on the two different approaches of fundamental equivalence relations on hyperstructures. Ratio Math. 33, 47–60 (2017). doi:http://dx.doi.org/10.23755/rm.v33i0.388
  3. Al Tahan, M., Hoskova-Mayerova, S., Davvaz, B.: An overview of topological hypergroupoids. J. Intell. Fuzzy Syst. 34(3), 1907–1916 (2018)CrossRefGoogle Scholar
  4. Arabameri, A.: Application of the analytic hierarchy process (AHP) for locating fire stations: case study Maku City. Merit Res. J. Art Soc. Sci. Humanities 2(1) (2014)Google Scholar
  5. Bakhshi, M., Borzooei, R.: Ordered Polygroups. Ratio Math. 24(1), 31–40 (2013)Google Scholar
  6. Bechara, A.: The role of emotion in decision-making: evidence from neurological patients with orbitofrontal damage. Brain Cogn. 55, 30–40 (2004)CrossRefGoogle Scholar
  7. Bechara, A., Damasio, H., Tranel, D., Damasio, A.R.: Deciding advantageously before knowing the advantageous strategy. Science 275, 1293–1295 (1997)CrossRefGoogle Scholar
  8. Bozóki, S., Rapcsák, T.: On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. J. Global Optim. 42(2), 157–175 (2008)MathSciNetCrossRefGoogle Scholar
  9. Calderon Güémez, G., Elbittar, A.A., Lever Guzmán, C.: Inconsistencias en la teoría de la elección intertemporal: un enfoque económico. In Santoyo Velasco, C., Vázquez Pineda (Coord.). Teoría Conductual de la Elección: Decisiones Que Se Revierten, pp. 207–229 (2004)Google Scholar
  10. Chvalina, J., Hoskova-Mayerova, S.: General ω-hyperstructures and certain applications of those. Ratio Math. 23(1), 3–20 (2012)Google Scholar
  11. Cruz Rambaud, S., Maturo, F., Sánchez Pérez, A.M.: Expected present and final value of an annuity when some non-central moments of the capitalization factor are unknown: theory and an application using R. Stud. Syst. Decis. Control 104, 233–248 (2017).  https://doi.org/10.1007/978-3-319-54819-7_16CrossRefGoogle Scholar
  12. Cruz Rambaud, S., Maturo, F., Sánchez, A.: Approach of the value of an annuity when non-central moments of the capitalization factor are known: An R application with interest rates following normal and beta distributions. Ratio Math. 28(1), 15–30 (2015).  https://doi.org/10.23755/rm.v28i1.25CrossRefGoogle Scholar
  13. Dadkhah, K.M., Zahedi, F.: A mathematical treatment of inconsistency in the analytic hierarchy process. Math. Comput. Model. 17(4), 111–122 (1993)MathSciNetCrossRefGoogle Scholar
  14. Damasio, A.R.: Descartes’ Error: Emotion, Reason, and the Human Brain. Grosset/Putnam, New York (1994)Google Scholar
  15. Delli Rocili, L., Maturo., A.: Teaching mathematics to children: social aspects, psychological problems and decision-making models. Interdisciplinary Approaches in Social Sciences. Editura Universitatii A.I. Cuza, Iasi, Romania (2013)Google Scholar
  16. Delli, Rocili L., Maturo, A.: Social problems and decision making for teaching approaches and relationship management in an elementary school. Stud. Syst. Decis. Control 104, 81–94 (2017).  https://doi.org/10.1007/978-3-319-54819-7_7CrossRefGoogle Scholar
  17. Forcini, S., Maturo A., Ventre, A.G.S.: The role of folk dance in the processes of individual and social wellbeing: a comparison with other popular recreational activities through models of decision theory and game theory. Proc.: Soc. Behav. Sci. 84, 1750–1756 (2013)CrossRefGoogle Scholar
  18. Green, L., Myerson, J.: Exponential versus hyperbolic discounting of delayed outcomes: risk and waiting time. Am. Zool. 36(4), 496–505 (1996)CrossRefGoogle Scholar
  19. Hedayati, H., Ameri, R.: Construction of k-Hyperideals by P-Hyperoperations. Ratio Math. 15, 75–89 (2005)Google Scholar
  20. Hedayati, H.: On properties of fuzzy subspaces of vectorspaces. Ratio Math. 19(1), 1–10 (2009)Google Scholar
  21. Hoskova-Mayerova, S.: An overview of topological and fuzzy topological hypergroupoids. Ratio Math. 33, 21–38 (2017).  https://doi.org/10.23755/rm.v33i0.389CrossRefGoogle Scholar
  22. Hošková-Mayerová, Š.: Quasi-order hypergroups and T-hypergroups. Ratio Math. 32, 37–44 (2017).  https://doi.org/10.23755/rm.v32i0.333CrossRefGoogle Scholar
  23. Hošková-Mayerová, Š., Maturo, A.: Decision-making process using hyperstructures and fuzzy structures in social sciences. Stud. Fuzziness Soft Comput. 357, 103–111 (2018).  https://doi.org/10.1007/978-3-319-60207-3_7CrossRefzbMATHGoogle Scholar
  24. Hošková-Mayerová, Š., Talhofer, V., Hofmann, A.: Decision-making process with respect to the reliability of geo-database. Stud. Fuzziness Soft Comput. 357, 179–194 (2013).  https://doi.org/10.1007/978-3-642-35635-3_15CrossRefGoogle Scholar
  25. Karapetrovic, S., Rosenbloom, E.S.: A quality control approach to consistency paradoxes in AHP. Eur. J. Oper. Res. 119(3), 704–718 (1999)CrossRefGoogle Scholar
  26. Linares, P.: Are inconsistent decisions better? An experiment with pairwise comparisons. Eur. J. Oper. Res. 193(2), 492–498 (2009)CrossRefGoogle Scholar
  27. Loewenstein, G., Thaler, R.H.: Anomalies: intertemporal choice. J. Econ. Persp. 3(4), 181–193 (1989)CrossRefGoogle Scholar
  28. Loewenstein, G., Prelec, D.: Anomalies in intertemporal choice: evidence and an interpretation. Q. J. Econ. 107(2), 573–597 (1992)CrossRefGoogle Scholar
  29. Longo, A., Ventre, V.: Influence of information on behavioral effects in decision processes. Ratio Math. 28, 31–43 (2015).  https://doi.org/10.23755/rm.v28i1.26CrossRefGoogle Scholar
  30. Longo, A., Ventre, V.: The level of information held by a problem solver influences decision processes. J. Math. Econ. Finan. 2(2) (2016)Google Scholar
  31. Longo, A., Squillante, M., Ventre, A.G.S., Ventre, V.: The intertemporal choice behavior: the role of emotions in a multi-agent decision problem. Atti Accad. Pelorit. Pericol. Cl. Sci. Fis. Mat. Nat. 93(2) (2015)Google Scholar
  32. Lygeros, N., Vougiouklis, T.: The LV-hyperstructures. Ratio Math. 25, 59–66 (2013)Google Scholar
  33. Marcarelli, G., Simonetti, B., Ventre, V.: Analyzing AHP Matrix by Robust Regression. Studies in Computational Intelligence, pp. 223–231 (2013).  https://doi.org/10.1007/978-3-642-32903-6_16CrossRefGoogle Scholar
  34. Massouros, C.G., Massouros, G.G.: The transposition axiom in hypercompositional structures. Ratio Math. 21, 75–90 (2011)Google Scholar
  35. Massouros, G.G.: Hypercompositional structures from the computer theory. Ratio Math. 13, 37–42 (1999)MathSciNetzbMATHGoogle Scholar
  36. Maturo, A., Zappacosta, M.G.: Mathematical models for the comparison of teaching strategies in primary school. Sci. Philos. 5(2), 25–38 (2017).  https://doi.org/10.23756/sp.v5i2.392CrossRefGoogle Scholar
  37. Maturo, A., D’Orazio, A., De Crescenzo, A.: A decision model for the sustainable protection of human rights in Italian Prison system. Sci. Philos. 2(2), 91–100 (2014)Google Scholar
  38. Maturo, A., Squillante, M., Ventre, A.G.S.: Consistency for assessments of uncertainty evaluations in non-additive setting. In: Metodi, Modelli e Tecnologie dell’Informazione a Supporto delle Decisioni, Franco Angeli, Milano, pp. 75–88 (2006b)Google Scholar
  39. Maturo, A., Squillante, M., Ventre, A.G.S.: Consistency for Non Additive Measures: Analytical and Algebraic Methods in Computational Intelligence, Theory and Applications, pp. 29–40. Springer, Berlin (2006)Google Scholar
  40. Maturo, A., Squillante, M., Ventre, A.G.S.: Coherence for Fuzzy Measures and Applications to Decision Making. Studies in Fuzziness and Soft Computing, vol. 257, pp. 291–304. Springer, Berlin (2010).  https://doi.org/10.1007/978-3-642-15976-3_17CrossRefGoogle Scholar
  41. Maturo, F., Di Battista, T.: A functional approach to Hill’s numbers for assessing changes in species variety of ecological communities over time. Ecol. Ind. 84, 70–81 (2018).  https://doi.org/10.1016/j.ecolind.2017.08.016CrossRefGoogle Scholar
  42. Maturo, A., Maturo, F.: On Some Applications of the Vougiouklis Hyperstructures to Probability Theory. Ratio Math. 33, 5–20 (2017).  https://doi.org/10.23755/rm.v33i0.372CrossRefGoogle Scholar
  43. Maturo, A., Maturo, F.: Finite geometric spaces, steiner systems and cooperative games. Analele Universitatii “Ovidius” Constanta - Seria Matematica, 22(1), (2014)  https://doi.org/10.2478/auom-2014-0015
  44. Maturo, F., Ventre, V.: Consensus in Multiperson Decision Making Using Fuzzy Coalitions. Studies in Fuzziness and Soft Computing, vol. 357, pp. 451–464 (2018).  https://doi.org/10.1007/978-3-319-60207-3_26Google Scholar
  45. Maturo, F., Hošková-Mayerová, Š.:: Fuzzy Regression Models and Alternative Operations for Economic and Social Sciences. Studies in Systems, Decision and Control, vol. 66, pp. 235–247 (2017).  https://doi.org/10.1007/978-3-319-40585-8_21Google Scholar
  46. Muñoz Torrecillas, M.J.: Anomalías en la elección intertemporal: obtención de la tasa social de descuento. Universidad de Almería (PhD Thesis) (2004)Google Scholar
  47. Nikolaidou, P., Vougiouklis, T.: The Lie-Santilli admissible hyperalgebras of type An. Ratio Math. 26(1), 113–128 (2014)Google Scholar
  48. Novak, M.: EL-hyperstructures: an overview. Ratio Math. 23(1), 65–80 (2012)Google Scholar
  49. Nussbaum, M.C.: Upheavals of Thought. The Intelligence of Emotions. Cambridge University Press, Cambridge (2001)Google Scholar
  50. Olivieri, M., Squillante, M., Ventre, V.: Information and intertemporal choices in multi-agent decision problems. Ratio Math. 31(1), 3–24 (2016).  https://doi.org/10.23755/rm.v31i0.316CrossRefGoogle Scholar
  51. Rezaei, A., Saeid, A.Borumand, Smarandache, F.: Neutrosophic filters in BE-algebras. Ratio Math. 29(1), 65–79 (2015).  https://doi.org/10.23755/rm.v29i1.23CrossRefGoogle Scholar
  52. Saaty, T.L.: What is the analytic hierarchy process? Mathematical Models for Decision Support, pp. 109–121. Springer, Berlin Heidelberg (1988)CrossRefGoogle Scholar
  53. Saaty, T.L.: Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1(1), 83–98 (2008)MathSciNetGoogle Scholar
  54. Shiv, B., Loewenstein, G., Bechara, A., Damasio, H., Damasio, A.R.: Investment behavior and the negative side of emotion. Psychol. Sci. 16, 435–439 (2005)Google Scholar
  55. Szczypińska, A., Piotrowski, E.W.: Inconsistency of the judgment matrix in the AHP method and the decision maker’s knowledge. Physica A 388(6), 907–915 (2009)CrossRefGoogle Scholar
  56. Urban, R., Hošková-Mayerová, Š.: Threat life cycle and its dynamics. Deturope 9(2), 93–109 (2017)Google Scholar
  57. Ventre, A.G.S., Ventre, V.: The intertemporal choice behavior: classical and alternative delay discounting models and control techniques. Atti Accad. Pelorit. Pericol. Cl. Sci. Fis. Mat. Nat. 90, Suppl. No. 1, C3 (2012)Google Scholar
  58. Ventre, V.: The intertemporal choice behavior: the role of emotions in a multiagent decision problem. Ratio Math. 27(1), 91–110 (2014).  https://doi.org/10.23755/rm.v27i1.36CrossRefGoogle Scholar
  59. Vougiouklis, T.: Bar and theta hyperoperations. Ratio Math. 21(1), 27–42 (2011)Google Scholar
  60. Vougiouklis, T., Vougiouklis, S.: Helix-hopes on finite hyperfields. Ratio Math. 31(1), 65–78 (2016).  https://doi.org/10.23755/rm.v31i0.321CrossRefGoogle Scholar
  61. Vougiouklis, T., Spartalis, S., Kessoglides, M.: Weak hyperstructures on small sets. Ratio Math. 12(1), 90–96 (1997)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Fabrizio Maturo
    • 1
  • Viviana Ventre
    • 2
  • Angelarosa Longo
    • 3
  1. 1.Department of Management and Business Administration“G. D’Annunzio” University of Chieti-PescaraPescaraItaly
  2. 2.Department of Mathematics and Physics“Luigi Vanvitelli” University of CampaniaCasertaItaly
  3. 3.Servizio Gestione Circolazione Monetaria, Banca d’ItaliaRomeItaly

Personalised recommendations