HOW TO OBTAIN A GLOBAL REFERENCE THRESHOLD IN AHP/ANP

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Published May 19, 2021
Claudio Garuti

Abstract

This paper has two main objectives. The first objective is to provide a mathematically grounded technique to construct local and global thresholds using the well-known rate of change method. The next objective, which is secondary, is to show the relevance and possibilities of applying the AHP/ANP in absolute measurement (AM) compared to the relative measurement (RM) mode, which is currently widely used in the AHP/ANP community. The ability to construct a global threshold would help increase the use of AHP/ANP in the AM mode (rating mode) in the AHP/ANP community. Therefore, if the first specific objective is achieved, it would facilitate reaching the second, more general objective.

 

For this purpose, a real-life example based on the construction of a multi-criteria index and threshold will be described. The index measures the degree of lag of a neighborhood through the Urban and Social Deterioration Index (USDI) based on an AHP risks model. The global threshold represents the tolerable lag value for the specific neighborhood. The difference or gap between the neighborhood’s current status (actual USDI value) and this threshold represents the level of neighborhood deterioration that must be addressed to close the gap from a social and urban standpoint. The global threshold value is a composition of 45 terminal criteria with their own local threshold that must be evaluated for the specific neighborhood. This example is the most recent in a large list of AHP applications in AM mode in vastly different decision making fields, such as risk disaster assessment, environmental assessment, the problem of medical diagnoses, social responsibility problems, BOCR analysis for the evolution of nuclear energy in Chile in the next 20 years and many others. (See list of projects in Appendix).

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Keywords

threshold, scales, absolute measurement, AHP/ANP, rate of change

References
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Garuti, C. (2016). New advances of the compatibility index G in weighted environments. International Journal of the Analytic Hierarchy Process, 8(3), 514-537. Doi: Garuti C. (2017). Reflections on scale from measurement, not measurement from scales. International Journal of the Analytic Hierarchy Process, 9(3), 349-361.

Garuti, C. (2016). New advances of the compatibility index G in weighted environments. International Journal of the Analytic Hierarchy Process, 8(3), 514-537.

Garuti, C., Solomon V.A. (2011). Compatibility indices between priority vectors. International Journal of the Analytic Hierarchy Process, 4(2), 152-160. Doi: https://doi.org/10.13033/ijahp.v4i2.130

Garuti, C. (2016). Measuring in weighted environments, from metric to order topology (When close really means close). In: De Felice, F., Petrillo, A. & Saaty, T. (Eds.) Applications and theory of Analytic Hierarchy Process - decision making for strategic decisions, Intech Open. Doi: https://doi.org/10.5772/63670

Garuti, C., Solomon V.A. (2011). Compatibility indices between priority vectors. International Journal of the Analytic Hierarchy Process, 4(2), 152-160. Doi: Garuti, C., Solomon V.A. (2011). Compatibility indices between priority vectors. International Journal of the Analytic Hierarchy Process, 4(2), 152-160. Doi: https://doi.org/10.13033/ijahp.v4i2.130

Garuti, C. (2016). Measuring in weighted environments, from metric to order topology (When close really means close). In: De Felice, F., Petrillo, A. & Saaty, T. (Eds.) Applications and theory of Analytic Hierarchy Process - decision making for strategic decisions, Intech Open. Doi: https://doi.org/10.5772/63670

Garuti, C. (2012). Measuring in weighted environments, from metric to order topology (When close really means close). In DeFelice, Petrillo, Saaty (eds) Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions. InTech Open. Doi: 10.5772/63670

Millet, I. & Saaty, T.L. (2000). On the relativity of relative measures – accommodating both rank preservation and rank reversals in the AHP. European Journal of Operational Research, 121, 205–212. Doi: http://dx.doi.org/10.1016/S0377-2217(99)00040-5 S

Orton, A. (1984). Understanding ratio of change “mathematics at school”, 13(5), 23-26.

Saaty, T. L. (1986). Absolute and relative measurement with the AHP. The most livable cities in the United States. Socio-Economic Planning Sciences, 20(6), 327–331. Doi: http://dx.doi.org/10.1016/0038-0121(86)90043-1

Saaty T.L. (1988). Decision making for leaders. Pittsburgh, PA: RWS Publications.

Saaty, T. L., Vargas, L. G., & Whitaker, R. (2009). Addressing with brevity criticism of the analytic hierarchy process. International Journal of the Analytic Hierarchy Process, 1(1), 121-134. Doi: http://dx.doi.org/10.13033/ijahp.v1i2.53.

Saaty, T. L., & Sagir, M. (2009). An essay on rank preservation and reversal. Mathematical and Computer Modelling, 49(5–6), 1230–1243. Doi: http://dx.doi.org/10.1016/j.mcm.2008.08.001.

Saaty, T. & Peniwati, K., (2010). Group decision making: drawing out and reconciling differences. Pittsburgh, PA, USA: RWS Publications.

Salomon V. A. (2016). Absolute measurement and ideal synthesis on AHP. International Journal of the Analytic Hierarchy Process, 8(3), 538-545. Doi:10.13033/ijahp.v8i3.452

Yoon, Hwang and Chin-Lai. (1981). Multiple attribute decision making: methods and application a state of the art survey. Berlin Heidelberg: Springer Verlag. Doi: 10.1007/978-3-642-48318-9

Garuti, C. (2016). Measuring in weighted environments, from metric to order topology (When close really means close). In: De Felice, F., Petrillo, A. & Saaty, T. (Eds.) Applications and theory of Analytic Hierarchy Process - decision making for strategic decisions, Intech Open.

Garuti, C. (2012). Measuring in weighted environments, from metric to order topology (When close really means close). In DeFelice, Petrillo, Saaty (eds) Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions. InTech Open. Doi: 10.5772/63670

Millet, I. & Saaty, T.L. (2000). On the relativity of relative measures – accommodating both rank preservation and rank reversals in the AHP. European Journal of Operational Research, 121, 205–212. Doi: http://dx.doi.org/10.1016/S0377-2217(99)00040-5 S

Orton, A. (1984). Understanding ratio of change “mathematics at school”, 13(5), 23-26.

Saaty, T. L. (1986). Absolute and relative measurement with the AHP. The most livable cities in the United States. Socio-Economic Planning Sciences, 20(6), 327–331. Doi: http://dx.doi.org/10.1016/0038-0121(86)90043-1

Saaty T.L. (1988). Decision making for leaders. Pittsburgh, PA: RWS Publications.

Saaty, T. L., Vargas, L. G., & Whitaker, R. (2009). Addressing with brevity criticism of the analytic hierarchy process. International Journal of the Analytic Hierarchy Process, 1(1), 121-134. Doi: http://dx.doi.org/10.13033/ijahp.v1i2.53.

Saaty, T. L., & Sagir, M. (2009). An essay on rank preservation and reversal. Mathematical and Computer Modelling, 49(5–6), 1230–1243. Doi: http://dx.doi.org/10.1016/j.mcm.2008.08.001.

Saaty, T. & Peniwati, K., (2010). Group decision making: drawing out and reconciling differences. Pittsburgh, PA, USA: RWS Publications.

Salomon V. A. (2016). Absolute measurement and ideal synthesis on AHP. International Journal of the Analytic Hierarchy Process, 8(3), 538-545. Doi:10.13033/ijahp.v8i3.452

Yoon, Hwang and Chin-Lai. (1981). Multiple attribute decision making: methods and application a state of the art survey. Berlin Heidelberg: Springer Verlag. Doi: 10.1007/978-3-642-48318-9
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