AT THE JUNCTION OF MATHEMATICS AND PSYCHOLOGY: COGNITIVE ORIENTATION OF THE AHP/ANP AND NEW PERSPECTIVES OF STRUCTURING COMPLEXITY
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Published
Mar 31, 2019
Maria Milkova
Olga Andreichikova
Alexander Andreichikov
Abstract
This paper aims to draw attention to the interdisciplinary research of the AHP/ANP methodology by emphasizing how it can be studied from a cognitive perspective. We provide an overview of the main cognitive approaches in decision-making, and consider different heuristics that lie at the basis of pairwise comparisons. We emphasize that the AHP/ANP must be considered at the junction of mathematics and psychology, and for further development of the methodology, we should examine the AHP/ANP from the cognitive point of view. We review the recent experimental studies of the AHP/ANP that test human behavior in real decision problems. We also discuss the future applicability of the AHP/ANP methodology in the Experience Age - the age of not only digital information and knowledge, but also behavior. This article is just a small step on the way to discovering the cognitive aspects and future extensions of decision making with the AHP/ANP.
How to Cite
Milkova, M., Andreichikova, O., & Andreichikov, A. (2019). AT THE JUNCTION OF MATHEMATICS AND PSYCHOLOGY: COGNITIVE ORIENTATION OF THE AHP/ANP AND NEW PERSPECTIVES OF STRUCTURING COMPLEXITY. International Journal of the Analytic Hierarchy Process, 11(1), 110–126. https://doi.org/10.13033/ijahp.v11i1.611
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Keywords
cognitive decision making, AHP, ANP, heuristics, heuristic decision making, cognitive psychology, Experience Age
References
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Benartzi, S., & Thaler, R. (1995). Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics, 110(1), 73-92. Doi: 10.2307/2118511
Bernasconi, M., Choirat, C., & Seri, R. (2010). The Analytic Hierarchy Process and the theory of measurement. Management Science, 56(4), 699-711. Doi: https://doi.org/10.1287/mnsc.1090.1123
Brugha, C. (2000). Relative measurement and the power function. European Journal of Operational Research, 121, 627–640. Doi: https://doi.org/10.1016/s0377-2217(99)00057-0
Brugha, C. (2004). Phased multicriteria preference finding. European Journal of Operational Research, 158, 308–316. Doi: https://doi.org/10.1016/j.ejor.2003.06.006
Brighton, H. (2006). Robust inference with simple cognitive models. In C. Lebiere, & B. Wray (Eds.), Between a rock and a hard place: Cognitive science principles meet AI-hard problems: Papers from the AAAI Spring Symposium (17-22). Menlo Park, California: AAAI Press.
Camerer C. F., Loewenstein, G., & Prelec, D. (2004). Neuroeconomics: Why economics needs brains. Scandinavian Journal of Economics, 106 (3), 555-579. Doi: 10.1111/j.0347-0520.2004.00377.x
Campos-Vazquez, & R.M., Cuilty, E. (2013). The role of emotions on risk aversion: A Prospect Theory experiment. Journal of Behavioral and Experimental Economics, 50, 1-9. Doi: https://doi.org/10.1016/j.socec.2014.01.001
Czerlinski, J., Gigerenzer, G., & Goldstein, D.G. (1999). How good are simple heuristics? In G. Gigerenzer, P. M. Todd, & the ABC Research Group, Simple heuristics that make us smart (97–118). New York: Oxford University Press. Doi: https://doi.org/10.5751/es-00277-050204
Dean, M., K?br?s, O., & Masatlioglu, Y. (2017). Limited attention and status quo bias. Journal of Economic Theory, 169, 93-127. Doi: https://doi.org/10.1016/j.jet.2017.01.009
Delre, S. A., Jager, W., & Janssen, M.A. (2007). Diffusion dynamics in small-world networks with heterogeneous consumers. Computational and Mathematical Organization Theory, 13(2), 185-202. Doi: https://doi.org/10.1007/s10588-006-9007-2
Dyer, J. (1990). Remarks on the Analytic Hierarchy Process. Management Science, 36(3), 249-258.
Forman, E.H., & Gass, S. I. (2001). The Analytic Hierarchy Process: An exposition. Operations Research, 49(4), 469-486. Doi: https://doi.org/10.1287/opre.49.4.469.11231
Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103 (4), 650-669. Doi: https://doi.org/10.1037//0033-295x.103.4.650
Gigerenzer, G., & Gaissmaier, W. (2011). Heuristic decision making. Annual Review of Psychology, 62, 451-482. Doi: https://doi.org/10.1146/annurev-psych-120709-145346
Goldstone, R.L., & Lupyan, G. (2016). Discovering psychological principles by mining naturally occurring data sets. Topics in Cognitive Science, 8, 548–568. Doi: 10.1111/tops.12212
Helbing, D. (2019). Towards digital enlightenment: Essays on the dark and light sides of the digital revolution. Springer. Doi: https://doi.org/10.1007/978-3-319-90869-4
Huizingh E., & Vrolijk H (1997). Extending the applicability of the analytic hierarchy process. Socio-Economic Planning Sciences, 31(1), 29–39. Doi: https://doi.org/10.1016/s0038-0121(96)00025-0
Ishizaka, A., Balkenborg, D., & Kaplan, T. (2011). Does AHP help us make a choice? An experimental evaluation. Journal of the Operational Research Society, 62, 1801–1812. Doi: https://doi.org/10.1057/jors.2010.158
Ishizaka, A. (2012). Clusters and pivots for evaluating a large number of alternatives in AHP. Pesquisa Operacional, 32(1), 87-101. Doi: https://doi.org/10.1590/s0101-74382012005000002
Jandri?, P., Knox, J., Besley, T., Ryberg, T., Suoranta, J., & Hayes, S. (2018). Postdigital science and education. Educational Philosophy and Theory, 50(10), 893-899. Doi: 10.1080/00131857.2018.1454000
Kahneman, D. & Tversky, A. (1979). Prospect Theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. Doi: https://doi.org/10.2307/1914185
Kahneman, D. & Tversky, A. (1996). On the reality of cognitive illusions. Psychological Review, 103(3), 582–591. Doi: https://doi.org/10.1037//0033-295x.103.3.582
Kahneman, D. (2003). A perspective on judgment and choice: Mapping bounded rationality. American Psychologist, 58(9), 697-720. Doi: https://doi.org/10.1037/0003-066x.58.9.697
Katsikopoulos, K. V., Schooler, L.J., & Hertwig, R. (2010). The robust beauty of ordinary information. Psychological Review, 117 (4), 1259–1266. Doi: https://doi.org/10.1037/a0020418
Korhonen, P. & Topdagi, H. (2003). Performance of the AHP in comparison of gains and losses. Mathematical and Computer Modelling, 37, 757–766. Doi: https://doi.org/10.1016/s0895-7177(03)00083-9
Loewenstein, G., & Lerner, J. S. (2003). The role of affect in decision making. In R. J. Davidson, K. R. Scherer, & H. H. Goldsmith (Eds.), Series in affective science. Handbook of affective sciences (619-642). New York, NY: Oxford University Press.
Martignon, L., & Hoffrage, U. (2002). Fast, frugal, and fit: simple heuristics for paired comparisons. Theory and Decision, 52 (1), 29–71. Doi: https://doi.org/10.1093/acprof:oso/9780199744282.003.0012
Miller, G.A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63(2), 81-97. Doi: https://doi.org/10.1037/h0043158
Moreno-Jiménez, J.M., & Vargas, L.G. (2018). Cognitive AHP-Multifactor decision making. International Symposium on the Analytic Hierarchy Process, Hong Kong, HK.
Morewedge, C.K., & Giblin, C.E. (2015). Explanations of the endowment effect: an integrative review. Trends in Cognitive Science, 19(6), 339-348. Doi: https://doi.org/10.1016/j.tics.2015.04.004
Mousavi, S., & Gigerenzer, G. (2014). Risk, uncertainty, and heuristics. Journal of Business Research, 67, 1671-1678. Doi: https://doi.org/10.1016/j.jbusres.2014.02.013
Novemsky, N., & Kahneman, D. (2005). The boundaries of loss aversion. Journal of Marketing Research, 42, 119–128. Doi: https://doi.org/10.1509/jmkr.42.2.119.62292
Pachur, T., & Biele, G. (2007). Forecasting from ignorance: The use and usefulness of recognition in lay predictions of sports events. Acta Psychologica, 125(1), 99-116. Doi: https://doi.org/10.1016/j.actpsy.2006.07.002
Paxton, A., & Griffiths, T.L. (2017). Finding the traces of behavioral and cognitive processes in big data and naturally occurring datasets. Behavior Research Methods, 49(5), 1630-1638. Doi: 10.3758/s13428-017-0874-x
Pohl, R. F. (2006). Empirical tests of the recognition heuristic. Journal of Behavioral Decision Making, 19(3), 251-271. Doi: https://doi.org/10.1002/bdm.522
Rottenstreich, Y., Burson, K., & Faro, D. (2013). Multiple unit holdings yield attenuated endowment effect. Management Science, 59, 545-555. Doi: https://doi.org/10.1287/mnsc.1120.1562
Saaty, T. L. (1990). How to make a decision: the Analytic Hierarchy Process. European Journal of Operational Research, 48, 9-26. Doi: https://doi.org/10.1016/0377-2217(90)90057-i
Saaty, T. L. (2008). Relative measurement and its generalization in decision making: Why pairwise comparisons are central in mathematics for the measurement of intangible factors. RACSAM, 102(2), 251-318. Doi: https://doi.org/10.1007/bf03191825
Saaty, T. L., & Ozdemir, M. S. (2003). Why the magic number seven plus or minus two. Mathematical and Computer Modelling, 38, 233-244. Doi: https://doi.org/10.1016/s0895-7177(03)90083-5
Saaty, T. L., & Vargas Luis G. (2006). Decision making with the Analytic Network Process: Economic, political, social and technological applications with benefits, opportunities, costs and risks. New York: Springer.
Saaty, T.L., & Vargas, L.G. (2012). The possibility of group choice: Pairwise comparisons and merging functions, Social Choice and Welfare, 38(3), 481-496. Doi: https://doi.org/10.1007/s00355-011-0541-6
Saaty, T. L. (2013). On the measurement of intangibles. A principal eigenvector approach to relative measurement derived from paired comparisons. Notes of the AMS, 60(2).Doi: https://doi.org/10.1090/noti944
Saaty, T.L. (2015). The Neural Network Process (NNP): Generalization of the AHP and ANP to the continuous case of neural firing. Pittsburgh, PA: RWS Publications.
Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review, 63(2), 129–138.
Simon, H. A. (1957). Models of man. New York: Wiley & Sons.
Taffel, S. (2015). Perspectives on the postdigital: Beyond rhetorics of progress and novelty. Convergence, 22(3), 324-338. Doi: https://doi.org/10.1177/1354856514567827
The Guardian (2017). https://www.theguardian.com/commentisfree/2017/feb/02/digital-revolution-age-of-experience-books-vinyl (23.10.2018)
Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review, 79, 281-299. Doi: https://psycnet.apa.org/doi/10.1037/h0032955
Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice, Science, 211(4481), 453-458. Doi: 10.1126/science.7455683
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, New Series, 185, 4157. Doi: https://doi.org/10.1037/h0032955
Vargas, L.G. (2017). How to write a contract with the AHP. International Journal of the Analytic Hierarchy Process, 9(2), 274-284. Doi: https://doi.org/10.13033/ijahp.v9i2.490
Weiss, E. N., 1987. Using the Analytic Hierarchy Process in a dynamic environment, Mathematical Modelling, 9/3-5, 211 -218. Doi: http://dx.doi.org/10.1016/0270-0255(87)90478-7
Whitaker, R. (2007). Criticisms of the Analytic Hierarchy Process: Why they often make no sense. Mathematical and Computer Modelling, 46, 948–961. Doi: https://doi.org/10.1016/j.mcm.2007.03.016
Wübben, M., & Wangenheim, F. (2008). Instant customer base analysis: Managerial heuristics often “get It right”, Journal of Marketing, 72, 82–93. Doi: https://doi.org/10.1093/acprof:oso/9780199744282.003.0036
Zhang, H., Chen, X., Dong, Y. et al. (2018) . Analyzing Saaty’s consistency test in pairwise comparison method: a perspective based on linguistic and numerical scale. Soft Computing, 22(6), 1933–1943. Doi: https://doi.org/10.1007/s00500-016-2454-x
Benartzi, S., & Thaler, R. (1995). Myopic loss aversion and the equity premium puzzle. The Quarterly Journal of Economics, 110(1), 73-92. Doi: 10.2307/2118511
Bernasconi, M., Choirat, C., & Seri, R. (2010). The Analytic Hierarchy Process and the theory of measurement. Management Science, 56(4), 699-711. Doi: https://doi.org/10.1287/mnsc.1090.1123
Brugha, C. (2000). Relative measurement and the power function. European Journal of Operational Research, 121, 627–640. Doi: https://doi.org/10.1016/s0377-2217(99)00057-0
Brugha, C. (2004). Phased multicriteria preference finding. European Journal of Operational Research, 158, 308–316. Doi: https://doi.org/10.1016/j.ejor.2003.06.006
Brighton, H. (2006). Robust inference with simple cognitive models. In C. Lebiere, & B. Wray (Eds.), Between a rock and a hard place: Cognitive science principles meet AI-hard problems: Papers from the AAAI Spring Symposium (17-22). Menlo Park, California: AAAI Press.
Camerer C. F., Loewenstein, G., & Prelec, D. (2004). Neuroeconomics: Why economics needs brains. Scandinavian Journal of Economics, 106 (3), 555-579. Doi: 10.1111/j.0347-0520.2004.00377.x
Campos-Vazquez, & R.M., Cuilty, E. (2013). The role of emotions on risk aversion: A Prospect Theory experiment. Journal of Behavioral and Experimental Economics, 50, 1-9. Doi: https://doi.org/10.1016/j.socec.2014.01.001
Czerlinski, J., Gigerenzer, G., & Goldstein, D.G. (1999). How good are simple heuristics? In G. Gigerenzer, P. M. Todd, & the ABC Research Group, Simple heuristics that make us smart (97–118). New York: Oxford University Press. Doi: https://doi.org/10.5751/es-00277-050204
Dean, M., K?br?s, O., & Masatlioglu, Y. (2017). Limited attention and status quo bias. Journal of Economic Theory, 169, 93-127. Doi: https://doi.org/10.1016/j.jet.2017.01.009
Delre, S. A., Jager, W., & Janssen, M.A. (2007). Diffusion dynamics in small-world networks with heterogeneous consumers. Computational and Mathematical Organization Theory, 13(2), 185-202. Doi: https://doi.org/10.1007/s10588-006-9007-2
Dyer, J. (1990). Remarks on the Analytic Hierarchy Process. Management Science, 36(3), 249-258.
Forman, E.H., & Gass, S. I. (2001). The Analytic Hierarchy Process: An exposition. Operations Research, 49(4), 469-486. Doi: https://doi.org/10.1287/opre.49.4.469.11231
Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103 (4), 650-669. Doi: https://doi.org/10.1037//0033-295x.103.4.650
Gigerenzer, G., & Gaissmaier, W. (2011). Heuristic decision making. Annual Review of Psychology, 62, 451-482. Doi: https://doi.org/10.1146/annurev-psych-120709-145346
Goldstone, R.L., & Lupyan, G. (2016). Discovering psychological principles by mining naturally occurring data sets. Topics in Cognitive Science, 8, 548–568. Doi: 10.1111/tops.12212
Helbing, D. (2019). Towards digital enlightenment: Essays on the dark and light sides of the digital revolution. Springer. Doi: https://doi.org/10.1007/978-3-319-90869-4
Huizingh E., & Vrolijk H (1997). Extending the applicability of the analytic hierarchy process. Socio-Economic Planning Sciences, 31(1), 29–39. Doi: https://doi.org/10.1016/s0038-0121(96)00025-0
Ishizaka, A., Balkenborg, D., & Kaplan, T. (2011). Does AHP help us make a choice? An experimental evaluation. Journal of the Operational Research Society, 62, 1801–1812. Doi: https://doi.org/10.1057/jors.2010.158
Ishizaka, A. (2012). Clusters and pivots for evaluating a large number of alternatives in AHP. Pesquisa Operacional, 32(1), 87-101. Doi: https://doi.org/10.1590/s0101-74382012005000002
Jandri?, P., Knox, J., Besley, T., Ryberg, T., Suoranta, J., & Hayes, S. (2018). Postdigital science and education. Educational Philosophy and Theory, 50(10), 893-899. Doi: 10.1080/00131857.2018.1454000
Kahneman, D. & Tversky, A. (1979). Prospect Theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. Doi: https://doi.org/10.2307/1914185
Kahneman, D. & Tversky, A. (1996). On the reality of cognitive illusions. Psychological Review, 103(3), 582–591. Doi: https://doi.org/10.1037//0033-295x.103.3.582
Kahneman, D. (2003). A perspective on judgment and choice: Mapping bounded rationality. American Psychologist, 58(9), 697-720. Doi: https://doi.org/10.1037/0003-066x.58.9.697
Katsikopoulos, K. V., Schooler, L.J., & Hertwig, R. (2010). The robust beauty of ordinary information. Psychological Review, 117 (4), 1259–1266. Doi: https://doi.org/10.1037/a0020418
Korhonen, P. & Topdagi, H. (2003). Performance of the AHP in comparison of gains and losses. Mathematical and Computer Modelling, 37, 757–766. Doi: https://doi.org/10.1016/s0895-7177(03)00083-9
Loewenstein, G., & Lerner, J. S. (2003). The role of affect in decision making. In R. J. Davidson, K. R. Scherer, & H. H. Goldsmith (Eds.), Series in affective science. Handbook of affective sciences (619-642). New York, NY: Oxford University Press.
Martignon, L., & Hoffrage, U. (2002). Fast, frugal, and fit: simple heuristics for paired comparisons. Theory and Decision, 52 (1), 29–71. Doi: https://doi.org/10.1093/acprof:oso/9780199744282.003.0012
Miller, G.A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63(2), 81-97. Doi: https://doi.org/10.1037/h0043158
Moreno-Jiménez, J.M., & Vargas, L.G. (2018). Cognitive AHP-Multifactor decision making. International Symposium on the Analytic Hierarchy Process, Hong Kong, HK.
Morewedge, C.K., & Giblin, C.E. (2015). Explanations of the endowment effect: an integrative review. Trends in Cognitive Science, 19(6), 339-348. Doi: https://doi.org/10.1016/j.tics.2015.04.004
Mousavi, S., & Gigerenzer, G. (2014). Risk, uncertainty, and heuristics. Journal of Business Research, 67, 1671-1678. Doi: https://doi.org/10.1016/j.jbusres.2014.02.013
Novemsky, N., & Kahneman, D. (2005). The boundaries of loss aversion. Journal of Marketing Research, 42, 119–128. Doi: https://doi.org/10.1509/jmkr.42.2.119.62292
Pachur, T., & Biele, G. (2007). Forecasting from ignorance: The use and usefulness of recognition in lay predictions of sports events. Acta Psychologica, 125(1), 99-116. Doi: https://doi.org/10.1016/j.actpsy.2006.07.002
Paxton, A., & Griffiths, T.L. (2017). Finding the traces of behavioral and cognitive processes in big data and naturally occurring datasets. Behavior Research Methods, 49(5), 1630-1638. Doi: 10.3758/s13428-017-0874-x
Pohl, R. F. (2006). Empirical tests of the recognition heuristic. Journal of Behavioral Decision Making, 19(3), 251-271. Doi: https://doi.org/10.1002/bdm.522
Rottenstreich, Y., Burson, K., & Faro, D. (2013). Multiple unit holdings yield attenuated endowment effect. Management Science, 59, 545-555. Doi: https://doi.org/10.1287/mnsc.1120.1562
Saaty, T. L. (1990). How to make a decision: the Analytic Hierarchy Process. European Journal of Operational Research, 48, 9-26. Doi: https://doi.org/10.1016/0377-2217(90)90057-i
Saaty, T. L. (2008). Relative measurement and its generalization in decision making: Why pairwise comparisons are central in mathematics for the measurement of intangible factors. RACSAM, 102(2), 251-318. Doi: https://doi.org/10.1007/bf03191825
Saaty, T. L., & Ozdemir, M. S. (2003). Why the magic number seven plus or minus two. Mathematical and Computer Modelling, 38, 233-244. Doi: https://doi.org/10.1016/s0895-7177(03)90083-5
Saaty, T. L., & Vargas Luis G. (2006). Decision making with the Analytic Network Process: Economic, political, social and technological applications with benefits, opportunities, costs and risks. New York: Springer.
Saaty, T.L., & Vargas, L.G. (2012). The possibility of group choice: Pairwise comparisons and merging functions, Social Choice and Welfare, 38(3), 481-496. Doi: https://doi.org/10.1007/s00355-011-0541-6
Saaty, T. L. (2013). On the measurement of intangibles. A principal eigenvector approach to relative measurement derived from paired comparisons. Notes of the AMS, 60(2).Doi: https://doi.org/10.1090/noti944
Saaty, T.L. (2015). The Neural Network Process (NNP): Generalization of the AHP and ANP to the continuous case of neural firing. Pittsburgh, PA: RWS Publications.
Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review, 63(2), 129–138.
Simon, H. A. (1957). Models of man. New York: Wiley & Sons.
Taffel, S. (2015). Perspectives on the postdigital: Beyond rhetorics of progress and novelty. Convergence, 22(3), 324-338. Doi: https://doi.org/10.1177/1354856514567827
The Guardian (2017). https://www.theguardian.com/commentisfree/2017/feb/02/digital-revolution-age-of-experience-books-vinyl (23.10.2018)
Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review, 79, 281-299. Doi: https://psycnet.apa.org/doi/10.1037/h0032955
Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice, Science, 211(4481), 453-458. Doi: 10.1126/science.7455683
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, New Series, 185, 4157. Doi: https://doi.org/10.1037/h0032955
Vargas, L.G. (2017). How to write a contract with the AHP. International Journal of the Analytic Hierarchy Process, 9(2), 274-284. Doi: https://doi.org/10.13033/ijahp.v9i2.490
Weiss, E. N., 1987. Using the Analytic Hierarchy Process in a dynamic environment, Mathematical Modelling, 9/3-5, 211 -218. Doi: http://dx.doi.org/10.1016/0270-0255(87)90478-7
Whitaker, R. (2007). Criticisms of the Analytic Hierarchy Process: Why they often make no sense. Mathematical and Computer Modelling, 46, 948–961. Doi: https://doi.org/10.1016/j.mcm.2007.03.016
Wübben, M., & Wangenheim, F. (2008). Instant customer base analysis: Managerial heuristics often “get It right”, Journal of Marketing, 72, 82–93. Doi: https://doi.org/10.1093/acprof:oso/9780199744282.003.0036
Zhang, H., Chen, X., Dong, Y. et al. (2018) . Analyzing Saaty’s consistency test in pairwise comparison method: a perspective based on linguistic and numerical scale. Soft Computing, 22(6), 1933–1943. Doi: https://doi.org/10.1007/s00500-016-2454-x
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