TOPSIS-RTCID for range target-based criteria and interval data

A. Jahan, M. Yazdani, K.L. Edwards


The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is receiving considerable attention as an essential decision analysis technique and becoming a leading method. This paper describes a new version of TOPSIS with interval data and capability to deal with all types of criteria. An improved structure of the TOPSIS is presented to deal with high uncertainty in engineering and engineering decision-making. The proposed Range Target-based Criteria and Interval Data model of TOPSIS (TOPSIS-RTCID) achieves the core contribution in decision making theories through a distinct normalization formula for cost and benefits criteria in scale of point and range target-based values. It is important to notice a very interesting property of the proposed normalization formula being opposite to the usual one. This property can explain why the rank reversal problem is limited. The applicability of the proposed TOPSIS-RTCID method is examined with several empirical litreture’s examples with comparisons, sensitivity analysis, and simulation. The authors have developed a new tool with more efficient, reliable and robust outcomes compared to that from other available tools. The complexity of an engineering design decision problem can be resolved through the development of a well-structured decision making method with multiple attributes. Various decision approches developed for engineering design have neglected elements that should have been taken into account. Through this study, engineering design problems can be resolved with greater reliability and confidence.


interval data; uncertainty in data; range target-based criteria; multi-attribute decision making

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Ahn, B.S. (2017). The analytic hierarchy process with interval preference statements. Omega, 67, 177-185.

Alemi-Ardakani, M., Milani, A.S., Yannacopoulos, S., Shokouhi, G. (2016). On the effect of subjective, objective and combinative weighting in multiple criteria decision making: A case study on impact optimization of composites. Expert Systems With Applications, 46, 426-438.

Amiri, M., Nosratian, N.E., Jamshidi, A., Kazemi, A. (2008). Developing a new ELECTRE method with interval data in multiple attribute decision making problems. Journal of Applied Sciences, 8, 4017-4028.

Bahraminasab, M., Jahan, A. (2011). Material selection for femoral component of total knee replacement using comprehensive VIKOR. Materials & Design, 32, 4471-4477.

Baradaran, V., Azarnia, S. (2013). An Approach to Test Consistency and Generate Weights from Grey Pairwise Matrices in Grey Analytical Hierarchy Process. Journal of Grey System, 25.

Behzadian, M., Otaghsara, S.K., Yazdani, M., Ignatius, J. (2012). A state-of the-art survey of TOPSIS applications. Expert Systems with Applications, 39, 13051-13069.

Cables, E., Lamata, M.T., Verdegay, J.L. (2018). FRIM-Fuzzy Reference Ideal Method in Multicriteria Decision Making. In Collan, M. & Kacprzyk, J. (Eds.) Soft Computing Applications for Group Decision-making and Consensus Modeling. Cham, Springer International Publishing.

Çakır, S. (2016). An integrated approach to machine selection problem using fuzzy SMART-fuzzy weighted axiomatic design. Journal of Intelligent Manufacturing, 1-13.

Celen, A. (2014). Comparative analysis of normalization procedures in TOPSIS method: with an application to Turkish deposit banking market. Informatica, 25, 185-208.

Celik, E., Erdogan, M., Gumus, A. (2016). An extended fuzzy TOPSIS-GRA method based on different separation measures for green logistics service provider selection. International Journal of Environmental Science and Technology, 13, 1377-1392.

Dymova, L., Sevastjanov, P., Tikhonenko, A. (2013). A direct interval extension of TOPSIS method. Expert Systems With Applications, 40, 4841-4847.

Garca-Cascales, M.S., Lamata, M.T. (2012). On rank reversal and TOPSIS method. Mathematical and Computer Modelling, 56, 123-132.

Hafezalkotob, A., Hafezalkotob, A. (2015). Comprehensive MULTIMOORA method with target-based attributes and integrated significant coefficients for materials selection in biomedical applications. Materials & Design, 87, 949-959.

Hafezalkotob, A., Hafezalkotob, A. (2016). Interval MULTIMOORA method with target values of attributes based on interval distance and preference degree: biomaterials selection. Journal of Industrial Engineering International, 13, 181-198.

Hafezalkotob, A., Hafezalkotob, A. (2017). Interval target-based VIKOR method supported on interval distance and preference degree for machine selection. Engineering Applications of Artificial Intelligence, 57, 184-196.

Hafezalkotob, A., Hafezalkotob, A., Sayadi, M.K. (2016). Extension of MULTIMOORA method with interval numbers: An application in materials selection. Applied Mathematical Modelling, 40, 1372-1386.

Hajiagha, S.H.R., Hashemi, S.S., Zavadskas, E.K., Akrami, H. (2012). Extensions of LINMAP model for multi criteria decision making with grey numbers. Technological and Economic Development of Economy, 18, 636-650.

Hazelrigg, G.A. (2003). Validation of engineering design alternative selection methods. Engineering Optimization, 35, 103-120.

Hu, J., Du, Y., Mo, H., Wei, D., Deng, Y. (2016). A modified weighted TOPSIS to identify influential nodes in complex networks. Physica A: Statistical Mechanics and its Applications, 444, 73-85.

Huang, Y., Jiang, W. (2018). Extension of TOPSIS Method and its Application in Investment. Arabian Journal for Science and Engineering, 43, 693-705.

Jahan, A. (2018). Developing WASPAS-RTB method for range target-based criteria: toward selection for robust design. Technological and Economic Development of Economy, 24, 1362-1387.

Jahan, A., Bahraminasab, M., Edwards, K.L. (2012). A target-based normalization technique for materials selection. Materials & Design, 35, 647-654.

Jahan, A., Edwards, K.L. (2013). VIKOR method for material selection problems with interval numbers and target-based criteria. Materials & Design, 47, 759-765.

Jahan, A., Edwards, K.L. (2015). A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design. Materials & Design, 65, 335-342.

Jahan, A., Edwards, K.L., Bahraminasab, M. (2016). Multi-criteria decision analysis for supporting the selection of engineering materials in product design, Oxford, Butterworth-Heinemann.

Jahan, A., Mustapha, F., Ismail, M.Y., Sapuan, S.M., Bahraminasab, M. (2011). A comprehensive VIKOR method for material selection. Materials & Design, 32, 1215-1221.

Jahan, A., Zavadskas, E.K. (2018). ELECTRE-IDAT for design decision-making problems with interval data and target-based criteria. Soft Computing, 23, 129-143.

Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Davoodi, A.R. (2009). Extension of TOPSIS for decision-making problems with interval data: Interval efficiency. Mathematical and Computer Modelling, 49, 1137-1142.

Jahanshahloo, G.R., Lotfi, F.H., Izadikhah, M. (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied Mathematics and Computation, 175, 1375-1384.

Kasirian, M., Yusuff, R. (2013). An integration of a hybrid modified TOPSIS with a PGP model for the supplier selection with interdependent criteria. International Journal of Production Research, 51, 1037-1054.

Kuo, T. (2017). A modified TOPSIS with a different ranking index. European Journal of Operational Research, 260, 152-160.

Liang, D., Xu, Z. (2017). The new extension of TOPSIS method for multiple criteria decision making with hesitant Pythagorean fuzzy sets. Applied Soft Computing, 60, 167-179.

Liao, H., Wu, X. (2019). DNMA: A double normalization-based multiple aggregation method for multi-expert multi-criteria decision making. Omega, 94. 102058.

Liu, H.C., You, J.X., Zhen, L., Fan, X.J. (2014). A novel hybrid multiple criteria decision making model for material selection with targetbased criteria. Materials & Design, 60, 380-390.

Maghsoodi, A.I., Maghsoodi, A.I., Poursoltan, P., Antucheviciene, J., Turskis, Z. (2019). Dam construction material selection by implementing the integrated SWARA-CODAS approach with target-based attributes. Archives of Civil and Mechanical Engineering, 19, 1194-1210.

Milani, A.S., Shanian, A., Madoliat, R., Nemes, J.A. (2005). The effect of normalization norms in multiple attribute decision making models: a case study in gear material selection. Structural and Multidisciplinary Optimization, 29, 312-318.

Peldschus, F. (2009). The analysis of the quality of the results obtained with the methods of multi-criteria decisions. Technological and Economic Development of Economy, 15, 580-592.

Peldschus, F. (2018). Recent findings from numerical analysis in multi-criteria decision making. Technological and Economic Development of Economy, 24, 1695-1717.

Perez, E.C., Lamata, M., Verdegay, J. (2016). RIM-Reference Ideal Method in Multicriteria Decision Making. Information Sciences, 337- 338, 1-10.

Sayadi, M.K., Heydari, M., Shahanaghi, K. (2009). Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling, 33, 2257-2262.

Sen, P., Yang, J.B. (1998). MCDM and the Nature of Decision Making in Design, Springer.

Sevastianov, P. (2007). Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster- Shafer theory. Information Sciences, 177, 4645-4661.

Shanian, A., Savadogo, O. (2009). A methodological concept for material selection of highly sensitive components based on multiple criteria decision analysis. Expert Systems With Applications, 36, 1362-1370.

Shen, F., Ma, X., Li, Z., Xu, Z., Cai, D. (2018). An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation. Information Sciences, 428, 105-119.

Shishank, S., Dekkers, R. (2013). Outsourcing: decision-making methods and criteria during design and engineering. Production Planning & Control, 24, 318-336.

Shouzhen, Z., Yao, X. (2018). A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making. Technological and Economic Development of Economy, 24, 969-983.

Stanujkic, D., Magdalinovic, N., Jovanovic, R., Stojanovic, S. (2012). An objective multi-criteria approach to optimization using MOORA method and interval grey numbers. Technological and Economic Development of Economy, 18, 331-363.

Suder, A., Kahraman, C. (2018). Multiattribute evaluation of organic and inorganic agricultural food investments using fuzzy TOPSIS. Technological and Economic Development of Economy, 24, 844-858.

Tilstra, A.H., Backlund, P.B., Seepersad, C.C., Wood, K.L. (2015). Principles for designing products with flexibility for future evolution. International Journal of Mass Customisation, 5, 22-54.

Tsaur, R.C. (2011) Decision risk analysis for an interval TOPSIS method. Applied Mathematics and Computation, 218, 4295-4304.

Turskis, Z., Zavadskas, E.K. (2010) A novel method for multiple criteria analysis: grey additive ratio assessment (ARAS-G) method. Informatica, 21, 597-610.

Wang, Y.M., Luo, Y. (2009) On rank reversal in decision analysis. Mathematical and Computer Modelling, 49, 1221-1229.

Ye, J. (2015) An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. Journal of Intelligent & Fuzzy Systems, 28, 247-255.

Yue, Z. (2013) Group decision making with multi-attribute interval data. Information Fusion, 14, 551-561.

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