Open Journal Systems


Kristophorus Hadiono


One of the well-established methods that help the decision makers deal with multiple criteria is the Analytical Hierarchy Process (AHP) which utilizes a weighting approach. The process of decision making with multiple criteria is faster if all the weights of the factors related to a particular problem are clearly stated. However, if the weights of said factors are not well defined, or only their lower and upper weight limits are known, then the decision makers face considerable uncertainty because the standard AHP numerical procedure operates with deterministic values. As a result, the corresponding assessment preferences cannot be expressed in the form of a sequence of numerical values and implemented in the AHP evaluation. A practical approach is presented in this work to deal with the data uncertainty by implementing interval arithmetic in the AHP calculations so that the assessment preferences are presented in the form of interval numbers.


AHP; interval arithmetic; interval numbers; decision making

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Dawood, H. (2011). Theories of interval arithmetic: Mathematical foundation and Applications. Saarbrücken, LAP LAMBERT Academic Publishing GmbH & Co. KG Dudweiler Landstr.

Hickey, T., Ju, Q., & Emden, M. Van. (2001). Interval arithmetic: from principles to implementation. Journal of the ACM, 48(5), 1038-1068. doi:10.1145/502102.502106

Jamali, S. K., Samadi, B., & Marthandan, G. (2014). Prioritizing electronic commerce technologies in Iranian family SMEs. Interdisciplinary Journal of Contemporary Research in Business, 6(2), 147-180.

Javanbarg, M. B., Scawthorn, C., Kiyono, J., & Shahbodaghkhan, B. (2012). Fuzzy AHP-based multicriteria decision making systems using particle swarm optimization. Expert Systems with Applications, 39(1), 960–966. doi:10.1016/j.eswa.2011.07.095

Koul, S., & Verma, R. (2012). Dynamic vendor selection: A fuzzy AHP approach. International Journal of the Analytic Hierarchy Process, 4(2), 118–136. doi:

Lahby, M., Cherkaoui, L., & Adib, A. (2013). A novel ranking algorithm based network selection. Journal Of Networks, 8(2), 263–272. doi:10.4304/jnw.8.2.263-272

Lane, E. F., & Verdini, W. A. (1989). A consistency test for AHP decision makers. Decision Sciences, 20(3), 575–590. doi:10.1111/j.1540-5915.1989.tb01568.x.

Saaty, T. L. (1994). How to make a decision: the Analytic Hierarchy Process. Interfaces, 24(6), 19-43. doi:

Saaty, T. L. (1990). An exposition on the AHP in reply to the paper “Remarks on the Analytic Hierarchy Process”. Management Science, 36(3), 259–268. doi:

Saaty, T., & Vargas, L. (1987). Uncertainty and rank order in the Analytic Hierarchy Process. European Journal of Operational Research, 32, 107–117. doi:10.1016/0377-2217(87)90275-X

Yu, J. R., Hsiao, Y., & Sheu, H. (2011). A multiplicative approach to derive weights in the interval Analytic Hierarchy Process. International Journal of Fuzzy Systems, 13(3), 225–231.

Wang, Y. M., & Chin, K. S. (2011). Fuzzy Analytic Hierarchy Process: algorithmic fuzzy preference programming methodology. International Journal of Approximate Reasoning, 52(4), 541-553. doi:10.1016/j.ijar.2010.12.004

Zahedi, F. (1986). The Analytic Hierarchy Process: a survey of the method and its applications. Interfaces, 16(4), 96–108. doi: