The application of the hybrid interval rough weighted Power-Heronian operator in multi-criteria decision making

  • Dragan Pamučar Department of logistics, Military Academy, University of Defence in Belgrade, Belgrade, Serbia
  • Aleksandar Janković Ministry of Transport and Maritime Affairs, Directorate for Transport, Montenegro
Keywords: Interval rough numbers; Heronian mean; Multi-criteria decision making; Power operator

Abstract

In this paper, a new multi-criteria model which enables the processing of uncertainty and inaccuracy data through the application of interval rough numbers (IRN) is presented. The multi-criteria model represents the integration of the Power Aggregator (PA) and the Weighted Heronian Mean (WHM) operators. The goal of the forming of a hybrid Weighted Power Heronian Mean (WPHM) is to integrate the advantages of both operators into a single multi-criteria model, which has the following advantages: 1) it eliminates the influence of unreasonable arguments; 2) it takes into account the degree of support between input arguments and 3) it takes into account the interconnectedness of input arguments. Based on the mathematical concept of the IRN, the hybrid WPHM operator was extended and the IRNWPHM multi-criteria model was created. The IRNWPHA multi-criteria model enables objective decision-making in the case of imprecise input parameters in the initial decision matrix. Also, the IRNWPHA model allows flexible decision-making and the verification of the robustness of results through a variation of the p and q parameters. The IRNWPHM model was tested on a real-world multi-criteria example. The results showed that the IRNWPHM operator enabled a successful transformation of the uncertainties and inaccuracies that exist in group decision-making.

References

Beliakov, G. (2007). Aggregation Functions: A Guide for Practitioners. Studies in Fuzziness & Soft Computing, 139-141.

Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation Functions: A Guide for Practitioners, Springer-Verlag, Berlin.

Bonferroni, C. (1950). Sulle medie multiple di potenze. Bollettino Matematica Italiana, 5, 267-270.

Dombi, J.A. (1982). general class of fuzzy operators, the demorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets and Systems, 8, 149–163, doi:10.1016/0165-0114(82)90005-7.

Đorđević, D., Stojić, G., Stević, Ž., Pamučar, D., Vulević, A., & Mišić, V. (2019). A New Model for Defining the Criteria of Service Quality in Rail Transport: The Full Consistency Method Based on a Rough Power Heronian Aggregator. Symmetry, 11(8), 992.

Dutta, B., Guha D., & Mesiar, R. (2015). A model based on linguistic 2-tuples for dealing with heterogeneous relationship among attributes in multi-expert decision making, IEEE Transactions on Fuzzy Systems, 23, 1817−1831.

Ecer, F., & Pamucar, D. (2020). Sustainable supplier selection: A novel integrated fuzzy best worst method (F-BWM) and fuzzy CoCoSo with Bonferroni (CoCoSo'B) multi-criteria model. Journal of Cleaner Production, https://doi.org/10.1016/j.jclepro.2020.121981

Hara, T., Uchiyama, M., & Takahasi, S.E. (1998). A refinement of various mean inequalities. Journal of Inequalities and Applications, 2(4), 387-395.

He, Y.D., & He, Z. (2016). Extensions of Atanassov's intuitionistic fuzzy interaction Bonferroni means and their application to multiple attribute decision making. IEEE Transactions on Fuzzy Systems, 24(3), 558–573.

He, Y.D., He, Z., & Wang, G. (2015). Hesitant fuzzy power Bonferroni means and their application to multiple attribute decision making. IEEE Transactions on Fuzzy Systems, 23(3),1655–1668.

Herrera, F., & Martínez, A. (2000). 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems, 8, 746−752.

Liu, H., & Pei, D. (2012). HOWA operator and its application to multi-attribute decision making. Journal of Zhejiang Sci-Tech University, 25, 138-142.

Liu, J. P., Chen, H. Y., Zhou L. G., & Tao, Z. F. (2015). Generalized linguistic ordered weighted hybrid logarithm averaging operators and applications to group decision making, International Journal of Uncertain Fuzzy Knowledge-Based Systems, 23, 421−442.

Liu, P.D., Liu J.L., & Chen, S.M. (2018). Some intuitionistic fuzzy Dombi Bonferroni mean operators and their application to multi-attribute group decision making. Journal of Operational Research Society, 69(1), 1–24.

Liu, X., Tao, T., Chen, H., & Zhou, L. (2016). A MAGDM Method Based on 2-Tuple Linguistic Heronian Mean and New Operational Laws. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 24(4), 593-627.

Maclaurin C. A. (1729). second letter to Martin Folkes, Esq.; concerning the roots of equations, with demonstration of other rules of algebra, Philos Trans Roy Soc London Ser A, 36, 59–96.

Muirhead, R.F. (1902). Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters. Proceedings of the Edinburgh Mathematical Society, 21(3), 144-162.

Pamucar, D., Božanić, D., Lukovac, V., & Komazec, N. (2018). Normalized weighted geometric Bonferroni mean operator of interval rough numbers – application in interval rough DEMATEL-COPRAS. Facta Universitatis, series: Mechanical Engineering. 16(2), 171-191

Pamučar, D., Chatterjee, K., & Zavadskas, E.K. (2019). Assessment of third-party logistics provider using multi-criteria decision-making approach based on interval rough numbers. Computers and industrial engineering, 127, 383-407.

Pamucar, D., Deveci, M., Canitezd, F., & Bozanic, D. (2020). A Fuzzy Full Consistency Method-Dombi-Bonferroni Model for Priorititizing Transportation Demand Management Measures. Applied Soft Computing, 87, https://doi.org/10.1016/j.asoc.2019.105952.

Pamučar, D., Deveci, M., Canitezd, F., & Bozanic, D. (2020). A Fuzzy Full Consistency Method-Dombi-Bonferroni Model for Priorititizing Transportation Demand Management Measures. Applied Soft Computing, 87, https://doi.org/10.1016/j.asoc.2019.105952

Pamučar, D., Mihajlović, M., Obradović, R., & Atanasković, 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, 58-80.

Pamucar, D., Sremac, S., Stevic, Z., Cirovic, G., & Tomic, D. (2019). New multi-criteria LNN WASPAS model for evaluating the work of advisors in the transport of hazardous goods. Neural Computing and Applications, 31(9), 5045-5068.

Pawlak, Z. (1982). Rough sets. International Journal of Computer & Information Sciences, 11(5), 341–356.

Sinani, F., Erceg, Živko, & Vasiljević, M. (2020). An evaluation of a third-party logistics provider: The application of the rough Dombi-Hamy mean operator. Decision Making: Applications in Management and Engineering, 3(1), 92-107.

Sremac, S., Stević, Ž., Pamučar D, Arsić, M., & Matić, B. (2018). Evaluation of a Third-Party Logistics (3PL) Provider Using a Rough SWARA–WASPAS Model Based on a New Rough Dombi Agregator. Symmetry, 10(8), 305.

Xu Z.-S., & Yager, R.R. (2011). Intuitionistic fuzzy Bonferroni means, IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, 41, 568-578.

Xu, Y. J., Merigó, J. M., & Wang, H.M. (2012). Linguistic power aggregation operators and their application to multiple attribute group decision making, Applied Mathematical Modeling, 36, 5427−5444.

Yager, R.R. (2001). The power average operator. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 31, 724-731.

Yazdani, M., Tavana, M., Pamucar, D., & Chatterjee, P. (2020). A Rough Based Multi-Criteria Evaluation Method for Healthcare Waste Disposal Location Decisions. Computeras and Industrial Engineering, 143, 106394. https://doi.org/10.1016/j.cie.2020.106394

Yu, D. (2013). Intuitionistic fuzzy geometric Heronian mean aggregation operators. Applied Soft Computing, 13, 1235-1246.

Zadeh, L.A. (1965). Fuzzy sets, Information and Control, 8, 338-353.

Zhao, S., Wang, D., Liang, C., Leng, Y., & Xu, J. (2019). Some Single-Valued Neutrosophic Power Heronian Aggregation Operators and Their Application to Multiple-Attribute Group Decision-Making. Symmetry, 11, 653.

Published
2020-07-03
How to Cite
Pamučar, D., & Janković, A. (2020). The application of the hybrid interval rough weighted Power-Heronian operator in multi-criteria decision making. Operational Research in Engineering Sciences: Theory and Applications, 54-73. Retrieved from https://oresta.rabek.org/index.php/oresta/article/view/54
Section
Articles