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

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Models and Theories in Social Systems

Part of the book series: Studies in Systems, Decision and Control ((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.

The views expressed in the studies are those of the author Angelarosa Longo and do not involve the responsibility of the institution to which she belong.

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References

  • 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 

  • 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

  • Al Tahan, M., Hoskova-Mayerova, S., Davvaz, B.: An overview of topological hypergroupoids. J. Intell. Fuzzy Syst. 34(3), 1907–1916 (2018)

    Article  Google Scholar 

  • 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 

  • Bakhshi, M., Borzooei, R.: Ordered Polygroups. Ratio Math. 24(1), 31–40 (2013)

    Google Scholar 

  • Bechara, A.: The role of emotion in decision-making: evidence from neurological patients with orbitofrontal damage. Brain Cogn. 55, 30–40 (2004)

    Article  Google Scholar 

  • Bechara, A., Damasio, H., Tranel, D., Damasio, A.R.: Deciding advantageously before knowing the advantageous strategy. Science 275, 1293–1295 (1997)

    Article  Google Scholar 

  • Bozóki, S., Rapcsák, T.: On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices. J. Global Optim. 42(2), 157–175 (2008)

    Article  MathSciNet  Google Scholar 

  • 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 

  • Chvalina, J., Hoskova-Mayerova, S.: General ω-hyperstructures and certain applications of those. Ratio Math. 23(1), 3–20 (2012)

    Google Scholar 

  • 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_16

    Article  Google Scholar 

  • 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.v28i1.25

    Article  Google Scholar 

  • Dadkhah, K.M., Zahedi, F.: A mathematical treatment of inconsistency in the analytic hierarchy process. Math. Comput. Model. 17(4), 111–122 (1993)

    Article  MathSciNet  Google Scholar 

  • Damasio, A.R.: Descartes’ Error: Emotion, Reason, and the Human Brain. Grosset/Putnam, New York (1994)

    Google Scholar 

  • 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 

  • 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_7

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Green, L., Myerson, J.: Exponential versus hyperbolic discounting of delayed outcomes: risk and waiting time. Am. Zool. 36(4), 496–505 (1996)

    Article  Google Scholar 

  • Hedayati, H., Ameri, R.: Construction of k-Hyperideals by P-Hyperoperations. Ratio Math. 15, 75–89 (2005)

    Google Scholar 

  • Hedayati, H.: On properties of fuzzy subspaces of vectorspaces. Ratio Math. 19(1), 1–10 (2009)

    Google Scholar 

  • Hoskova-Mayerova, S.: An overview of topological and fuzzy topological hypergroupoids. Ratio Math. 33, 21–38 (2017). https://doi.org/10.23755/rm.v33i0.389

    Article  Google Scholar 

  • Hošková-Mayerová, Š.: Quasi-order hypergroups and T-hypergroups. Ratio Math. 32, 37–44 (2017). https://doi.org/10.23755/rm.v32i0.333

    Article  Google Scholar 

  • 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_7

    Article  MATH  Google Scholar 

  • 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_15

    Article  Google Scholar 

  • Karapetrovic, S., Rosenbloom, E.S.: A quality control approach to consistency paradoxes in AHP. Eur. J. Oper. Res. 119(3), 704–718 (1999)

    Article  Google Scholar 

  • Linares, P.: Are inconsistent decisions better? An experiment with pairwise comparisons. Eur. J. Oper. Res. 193(2), 492–498 (2009)

    Article  Google Scholar 

  • Loewenstein, G., Thaler, R.H.: Anomalies: intertemporal choice. J. Econ. Persp. 3(4), 181–193 (1989)

    Article  Google Scholar 

  • Loewenstein, G., Prelec, D.: Anomalies in intertemporal choice: evidence and an interpretation. Q. J. Econ. 107(2), 573–597 (1992)

    Article  Google Scholar 

  • 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.v28i1.26

    Article  Google Scholar 

  • 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 

  • 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 

  • Lygeros, N., Vougiouklis, T.: The LV-hyperstructures. Ratio Math. 25, 59–66 (2013)

    Google Scholar 

  • 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_16

    Chapter  Google Scholar 

  • Massouros, C.G., Massouros, G.G.: The transposition axiom in hypercompositional structures. Ratio Math. 21, 75–90 (2011)

    Google Scholar 

  • Massouros, G.G.: Hypercompositional structures from the computer theory. Ratio Math. 13, 37–42 (1999)

    MathSciNet  MATH  Google Scholar 

  • 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.v5i2.392

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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_17

    Chapter  Google Scholar 

  • 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.2017.08.016

    Article  Google Scholar 

  • 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.v33i0.372

    Article  Google Scholar 

  • 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

  • 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_26

    Google Scholar 

  • 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_21

    Google Scholar 

  • Muñoz Torrecillas, M.J.: Anomalías en la elección intertemporal: obtención de la tasa social de descuento. Universidad de Almería (PhD Thesis) (2004)

    Google Scholar 

  • Nikolaidou, P., Vougiouklis, T.: The Lie-Santilli admissible hyperalgebras of type An. Ratio Math. 26(1), 113–128 (2014)

    Google Scholar 

  • Novak, M.: EL-hyperstructures: an overview. Ratio Math. 23(1), 65–80 (2012)

    Google Scholar 

  • Nussbaum, M.C.: Upheavals of Thought. The Intelligence of Emotions. Cambridge University Press, Cambridge (2001)

    Google Scholar 

  • 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.v31i0.316

    Article  Google Scholar 

  • 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.v29i1.23

    Article  Google Scholar 

  • Saaty, T.L.: What is the analytic hierarchy process? Mathematical Models for Decision Support, pp. 109–121. Springer, Berlin Heidelberg (1988)

    Chapter  Google Scholar 

  • Saaty, T.L.: Decision making with the analytic hierarchy process. Int. J. Serv. Sci. 1(1), 83–98 (2008)

    MathSciNet  Google Scholar 

  • 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 

  • 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)

    Article  Google Scholar 

  • Urban, R., Hošková-Mayerová, Š.: Threat life cycle and its dynamics. Deturope 9(2), 93–109 (2017)

    Google Scholar 

  • 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 

  • 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.v27i1.36

    Article  Google Scholar 

  • Vougiouklis, T.: Bar and theta hyperoperations. Ratio Math. 21(1), 27–42 (2011)

    Google Scholar 

  • Vougiouklis, T., Vougiouklis, S.: Helix-hopes on finite hyperfields. Ratio Math. 31(1), 65–78 (2016). https://doi.org/10.23755/rm.v31i0.321

    Article  Google Scholar 

  • Vougiouklis, T., Spartalis, S., Kessoglides, M.: Weak hyperstructures on small sets. Ratio Math. 12(1), 90–96 (1997)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Fabrizio Maturo .

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Maturo, F., Ventre, V., Longo, A. (2019). On Consistency and Incoherence in Analytical Hierarchy Process and Intertemporal Choices Models. In: Flaut, C., Hošková-Mayerová, Š., Flaut, D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-00084-4_18

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