Dragan Pamučar, Darko Božanić, Vesko Lukovac, Nenad Komazec

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This paper presents a new approach to the treatment of uncertainty and imprecision in multi-criteria decision-making based on interval rough numbers (IRN). The IRN-based approach provides decision-making using only internal knowledge for the data and operational information of a decision-maker. A new normalized weighted geometric Bonferroni mean operator is developed on the basis of the IRN for the aggregation of the IRN (IRNWGBM). Testing of the IRNWGBM operator is performed through the application in a hybrid IR-DEMATEL-COPRAS multi-criteria model which is tested on real case of selection of optimal direction for the creation of a temporary military route. The first part of hybrid model is the IRN DEMATEL model, which provides objective expert evaluation of criteria under the conditions of uncertainty and imprecision. In the second part of the model, the evaluation is carried out using the new interval rough COPRAS technique.


Interval Rough Numbers, DEMATEL, COPRAS, Bonferroni Mean Operator

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Triantaphyllou, E., Mann, S.H., 1995, Using the analytic hierarchy process for decision making in engineering applications: some challenges, International Journal of Industrial Engineering: Applications and Practice, 2(1), pp. 35-44.

Chen, N., Xu, Z., Xia, M., 2015, The ELECTRE I Multi-Criteria Decision-Making Method Based on Hesitant Fuzzy Sets, International Journal of Information Technology & Decision Making, 14(3), pp. 621–657.

Saaty, T. L., 1980, The Analytic Hierarchy Process, McGraw-Hill, NewYork.

Božanić, D., Pamučar, D., Bojanić, D., 2015, Modification of the Analytic Hierarchy Proces (AHP) Method using fuzzy logic: fuzzy AHP approach as a support to the decision making process concerning engagement of the Group for Additional Hindering, Serbian Journal of Management, 10(2), pp. 151-171.

Yoon, K., 1980, System Selection by Multiple Attribute Decision Making, PhD Thesis, Kansas State University, Manhattan, Kansas.

Opricovic, S., Tzeng, G.-H., 2004, The Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, European Journal of Operational Research, 156(2), pp. 445-455.

Tzeng, G.H., Chiang, C.H., Li, C.W., 2007, Evaluating intertwined effects in e-learning programs: a novel hybrid MCDM model based on factor analysis and DEMATEL, Expert Systems with Applications, 32(4), pp. 1028–1044.

Bernard, R., 1968, Classement et choix en présence de points de vue multiples (la méthode ELECTRE), La Revue d'Informatique et de Recherche Opérationelle (RIRO), 8, pp. 57-75.

Kaklauskas, A., Zavadskas, E.K., Raslanas, S., Ginevicius, R., Komka, A., Malinauskas, P., 2006, Selection of Low-e tribute in retrofit of public buildings by applying multiple criteria method COPRAS: A Lithuanian case, Energy and buildings, 38, pp. 454-462.

Pamučar, D., Ćirović G., 2015, The selection of transport and handling resources in logistics centers using Multi-Attributive Border Approximation area Comparison, Expert Systems with Applications, 42(6), pp. 3016-3028.

Bojanic, D., Kovač, M., Bojanic, M., Ristic, V., 2018, Multi-criteria decision-making in A defensive operation of THE Guided anti-tank missile battery: an example of the hybrid model fuzzy AHP – MABAC, Decision Making: Applications in Management and Engineering, 1(1), pp. 51-66.

Ghorabaee, M.K, Zavadskas, E.K., Olfat, L., Turskis, Z., 2015, Multi-Criteria Inventory Classification Using a New Method of Evaluation Based on Distance from Average Solution (EDAS), Informatica, 26(3), pp. 435-51.

Stević, Ž., Pamučar, D, Vasiljević, M., Stojić, G., Korica, S., 2017, Novel integrated multi-criteria model for supplier selection: Case study construction company, Symmetry, 9(11), 279, pp. 1-34.

Keshavarz G. M., Zavadskas, E. K., Turskis, Z., Antucheviciene, J., 2016, A new combinative distance-based assessment (CODAS) method for multi-criteria decision-making, Economic Computation & Economic Cybernetics Studies & Research, 50(3), pp. 25–44.

Badi, I.A., Abdulshahed, A.M., Shetwan, A.G., 2018, A case study of supplier selection for a steelmaking company in Libya by using the Combinative Distance-based ASsessment (CODAS) model, Decision Making: Applications in Management and Engineering, 1(1), pp. 1-12.

Pamučar, D., Vasin, Lj., Lukovac, L., 2014, Selection of railway level crossings for investing in security equipment using hybrid DEMATEL-MARICА model, XVI International Scientific-expert Conference on Railway, Railcon 2014, pp. 89-92, Niš.

Chatterjee, K., Pamučar, D., Zavadskas, E.K., 2018, Evaluating the performance of suppliers based on using the R’AMATEL-MAIRCA method for green supply chain implementation in electronics industry, Journal of Cleaner Production, 184, pp. 101-129.

Roy, J., Pamučar, D., Adhikary, K., Kar, S., 2018, A rough strength relational DEMATEL model for analysing the key success factors of hospital service quality, Decision Making: Applications in Management and Engineering, 1(1), pp. 121-142.

Dombi, J., 1982, A general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators, Fuzzy Sets Syst, 8, pp. 149–163.

Bonferroni, C., 1950, Sulle medie multiple di potenze, Bollettino dell'Unione Matematica Italiana, 5, pp. 267–270.(Only in Italian).

Wang, W. Z., Liu, X.W., 2011, Intuitionistic fuzzy geometric aggregation operators based on Einstein operations, International Journal of Intelligent Systems, 26(11), pp. 1049-1075.

Xu, Z., Yager, R.R., 2006, Some geometric aggregation operators based on intuitionistic fuzzy sets, International Journal of General Systems, 35(4), pp. 417-433.

Herrera, F., Herrera-Viedma, E., Verdegay, L., 1996, A model of consensus in group decision making under linguistic assessments, Fuzzy Sets and Systems, 78(1), pp. 73–87.

Liu, P.D., Teng, F., 2016, An extended TODIM method for multiple attribute group decision-making based on 2-dimension uncertain linguistic variable, Complexity, 21, pp. 20–30.

Yang, W., Pang, Y., Shi, J., Yue, H., 2017, Linguistic hesitant intuitionistic fuzzy linear assignment method based on choquet integral, Journal of Intelligent & Fuzzy Systems, 32(1), pp. 767–780.

Zhao, H., Xu, Z., Ni, M., Liu, S., 2010, Generalized aggregation operators for intuitionistic fuzzy sets, International Journal of Intelligent Systems, 25 (1), pp. 1-30.

Li, Y.H., Liu, P.D., Chen, Y.B., 2016, Some single valued neutrosophic number Heronian mean operators and their application in multiple attribute group decision making, Informatica, 27(1), pp. 85–110.

Ye, J., 2014, Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment, Journal of Intelligent & Fuzzy Systems, 27(6), pp. 2927–2935.

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 (1), pp. 247–255.

Fang, Z., Ye, J., 2017, Multiple Attribute Group Decision-Making Method Based on Linguistic Neutrosophic Numbers, Symmetry, 9(7), 111, pp. 1-12.

Liang, W., Zhao, G., Wu, H., 2017, Evaluating Investment Risks of Metallic Mines Using an Extended TOPSIS Method with Linguistic Neutrosophic Numbers, Symmetry, 9(8), 149, 1-18.

Ranjan, R., Chatterjee, P., Chakraborty, S., 2016, Performance evaluation of Indian railway zones using DEMATEL and VIKOR methods, Benchmarking: An International Journal, 23(1), pp.78 – 95.

Ranjan, R., Chatterjee, P., Chakraborty, S., 2015, Evaluating performance of engineering departments in an Indian University using DEMATEL and compromise ranking methods, OPSEARCH, 52(2), pp. 307-328.

Pamucar, D., Mihajlovic, M., Obradovic, R., Atanaskovic, P., 2017, Novel approach to group multi-criteria decision making based on interval rough numbers: Hybrid DEMATEL-ANP-MAIRCA model, Expert Systems with Applications, 88, pp. 58-80.

Stević, Ž., Pamučar D, Zavadskas, E.K., Ćirović, G., Prentkovskis, O., 2017, The selection of wagons for the internal transport of a logistics company: A novel approach based on rough BWM and rough SAW methods, Symmetry, 9(11), 264, pp. 1-25.

Vasiljevic, M., Fazlollahtabar, H., Stevic, Z., Veskovic, S., 2018, A rough multicriteria approach for evaluation of the supplier criteria in automotive industry, Decision Making: Applications in Management and Engineering, 1(1), pp. 82-96.

Gigović, Lj., Pamučar, D., Bajić, Z., Milićević, M., 2016, The combination of expert judgment and GIS-MAIRCA analysis for the selection of sites for ammunition depot, Sustainability, 8(4), 372, pp. 1-30.

Wang, J., Tang, P., 2011, A rough random multiple criteria decision making method based on Interval rough operator, Control and decision making, 26(7), pp. 1056-1059.

Španović, I., 1983, Vojni putevi, VIZ, Belgrade. (Only in Serbian).



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