A Bipolar Fuzzy Extension of the MULTIMOORA Method

Stanujkic, Dragisa; Karabasevic, Darjan; Zavadskas, Edmundas Kazimieras; Smarandache, Florentin; Brauers, Willem K.M.

doi:10.15388/Informatica.2019.201

Informatica

A Bipolar Fuzzy Extension of the MULTIMOORA Method

Volume 30, Issue 1 (2019), pp. 135–152

Dragisa Stanujkic Darjan Karabasevic Edmundas Kazimieras Zavadskas Florentin Smarandache Willem K.M. Brauers

https://doi.org/10.15388/Informatica.2019.201

Pub. online: 1 January 2019 Type: Research Article

Open Access

Received
1 October 2018

Accepted
1 February 2019

Published
1 January 2019

Abstract

The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to the bipolar-valued fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to some implicit counter-property corresponding to the bipolar-valued fuzzy set. By using single-valued bipolar fuzzy numbers, the MULTIMOORA method can be more efficient for solving some specific problems whose solving requires assessment and prediction. The suitability of the proposed approach is presented through an example.

References

Adali, E.A., Işik, A.T. (2017). The multi-objective decision making methods based on MULTIMOORA and MOOSRA for the laptop selection problem. Journal of Industrial Engineering International, 13(2), 229–237.

Akram, M., Arshad, M. (2018). A novel trapezoidal bipolar fuzzy TOPSIS method for group decision-making. Group Decision and Negotiation, 1–20.

Alghamdi, M.A., Alshehri, N.O., Akram, M. (2018). Multi-criteria decision-making methods in bipolar fuzzy environment. International Journal of Fuzzy Systems, 20(6), 2057–2064.

Aouni, B., Doumpos, M., Pérez-Gladish, B., Steuer, R.E. (2018). On the increasing importance of multiple criteria decision aid methods for portfolio selection. Journal of the Operational Research Society, 69(10), 1525–1542.

Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.

Baležentis, T., Zeng, S. (2013). Group multi-criteria decision making based upon interval-valued fuzzy numbers: an extension of the MULTIMOORA method. Expert Systems with Applications, 40(2), 543–550.

Baležentis, A., Baležentis, T., Brauers, W.K. (2012). MULTIMOORA-FG: a multi-objective decision making method for linguistic reasoning with an application to personnel selection. Informatica, 23(2), 173–190.

Baležentis, T., Zeng, S., Balezentis, A. (2014). MULTIMOORA-IFN: a MCDM method based on intuitionistic fuzzy number for performance management. Economic Computation and Economic Cybernetics Studies and Research, 48(4), 85–102.

Bana e Costa, C.A., Vansnick, J.C. (1994). MACBETH – an interactive path towards the construction of cardinal value functions. International Transactions in Operational Research, 1(4), 489–500.

Bellman, R.E., Zadeh, L.A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), 141–164.

Brans, J.P. (1982). Língénierie de la décision. Elaboration dínstruments dáide à la décision. Méthode PROMETHEE. In: Nadeau, R., Landry, M. (Eds.), L´aide a la Décision: Nature, Instruments et Perspectives d´avenir. Presses de l´Université, Laval, Québec, Canada, pp. 183–214.

Brauers, W.K.M., Ginevičius, R. (2010). The economy of the Belgian regions tested with MULTIMOORA. Journal of Business Economics and Management, 11(2), 173–209.

Brauers, W.K., Zavadskas, E.K. (2006). The MOORA method and its application to privatization in a transition economy. Control and Cybernetics, 35(2), 445–469.

Brauers, W.K.M., Zavadskas, E.K. (2010a). Project management by MULTIMOORA as an instrument for transition economies. Technological and Economic Development of Economy, 16(1), 5–24.

Brauers, W.K.M., Zavadskas, E.K. (2010b). Robustness in the MULTIMOORA model: the example of Tanzania. Transformations in Business and Economics, 9(3), 67–83.

Brauers, W.K.M., Zavadskas, E.K. (2011a). From a centrally planned economy to multiobjective optimization in an enlarged project management: the case of China. Economic Computation and Economic Cybernetics Studies and Research, 45(1), 167–188.

Brauers, W.K.M., Zavadskas, E.K. (2011b). Multimoora optimization used to decide on a bank loan to buy property. Technological and Economic Development of Economy, 17(1), 174–188.

Brauers, W.K., Balezentis, A., Balezentis, T. (2011). MULTIMOORA for the EU Member States updated with fuzzy number theory. Technological and Economic Development of Economy, 17(2), 259–290.

Charnes, A., Cooper, W.W., Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444.

Charnes, A., Cooper, W.W., Wei, Q.L., Huang, Z.M. (1989). Cone ratio data envelopment analysis and multi-objective programming. International Journal of Systems Science, 20(7), 1099–1118.

Das, M.C., Sarkar, B., Ray, S. (2012). Decision making under conflicting environment: a new MCDM method. International Journal of Applied Decision Sciences, 5(2), 142–162.

Dorfeshan, Y., Mousavi, S.M., Mohagheghi, V., Vahdani, B. (2018). Selecting project-critical path by a new interval type-2 fuzzy decision methodology based on MULTIMOORA, MOOSRA and TPOP methods. Computers and Industrial Engineering, 120, 160–178.

Dyer, J.S., Fishburn, P.C., Steuer, R.E., Wallenius, J., Zionts, S. (1992). Multiple criteria decision making, multiattribute utility theory: the next ten years. Management Science, 38(5), 645–654.

Ecker, J.G., Kouada, I.A. (1978). Finding all efficient extreme points for multiple objective linear programs. Mathematical Programming, 14(1), 249–261.

Edwards, W. (1977). 12 use of multiattribute utility measurement for social decision making. Conflicting, 247.

Eghbali-Zarch, M., Tavakkoli-Moghaddam, R., Esfahanian, F., Sepehri, M.M., Azaron, A. (2018). Pharmacological therapy selection of type 2 diabetes based on the SWARA and modified MULTIMOORA methods under a fuzzy environment. Artificial Intelligence in Medicine, 87, 20–33.

Fishburn, P.C. (1967). Letter to the editor – additive utilities with incomplete product sets: application to priorities and assignments. Operations Research, 15(3), 537–542.

Gabus, A., Fontela, E. (1972). World Problems, an Invitation to Further Thought within the Framework of DEMATEL. Battelle Geneva Research Center, Geneva, Switzerland, pp. 1–8.

Greco, S., Slowiński, R., Figueira, J.R., Mousseau, V. (2010). Robust ordinal regression. In: Trends in Multiple Criteria Decision Analysis. Springer, Boston, MA, pp. 241–283.

Hafezalkotob, A., Hafezalkotob, A., Sayadi, M.K. (2016). Extension of MULTIMOORA method with interval numbers: an application in materials selection. Applied Mathematical Modelling, 40(2), 1372–1386.

Han, Y., Lu, Z., Du, Z., Luo, Q., Chen, S. (2018). A YinYang bipolar fuzzy cognitive TOPSIS method to bipolar disorder diagnosis. Computer Methods and Programs in Biomedicine, 158, 1–10.

Hwang, C.L., Yoon, K. (1981). Methods for multiple attribute decision making. In: Multiple Attribute Decision Making. Springer, Berlin, Heidelberg, pp. 58–191.

Karabasevic, D., Stanujkic, D., Urosevic, S., Maksimovic, M. (2015). Selection of candidates in the mining industry based on the application of the SWARA and the MULTIMOORA methods. Acta Montanistica Slovaca, 20(2), 116–124.

Karande, P., Zavadskas, E., Chakraborty, S. (2016). A study on the ranking performance of some MCDM methods for industrial robot selection problems. International Journal of Industrial Engineering Computations, 7(3), 399–422.

Lazauskas, M., Kutut, V., Zavadskas, E.K. (2015). Multicriteria assessment of unfinished construction projects. Gradevinar, 67(4), 319–328.

Lee, K.M. (2000). Bipolar-valued fuzzy sets and their basic operations. In: Proceeding International Conference, Bangkok, Thailand, pp. 307–317.

Liang, W., Zhao, G., Hong, C. (2018). Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach. Neural Computing and Applications, 1–16.

Luenberger, D.G., Ye, Y. (1984). Linear and Nonlinear Programming (Vol. 2). Addison-Wesley, Reading, MA.

MacCrimon, K.R. (1968). Decision Marking Among Multiple-Attribute Alternatives: a Survey and Consolidated Approach. RAND Memorandum, RM-4823-ARPA. The Rand Corporation, Santa Monica, CA.

Maghsoodi, A.I., Abouhamzeh, G., Khalilzadeh, M., Zavadskas, E.K. (2018). Ranking and selecting the best performance appraisal method using the MULTIMOORA approach integrated Shannon’s entropy. Frontiers of Business Research in China, 12(1), 2.

Masri, H., Pérez-Gladish, B., Zopounidis, C. (2018). Financial Decision Aid Using Multiple Criteria: Recent Models and Applications. Springer.

Opricovic, S. (1998). Multicriteria optimization of civil engineering systems. Faculty of Civil Engineering, Belgrade, 2(1), 5–21.

Pramanik, S., Dalapati, S., Roy, T.K. (2018). Neutrosophic multi-attribute group decision making strategy for logistics center location selection. Neutrosophic Operational Research, 3, 13–32.

Roy, B. (1968). Classement et choix en présence de points de vue multiples. Revue franiaise d’informatique et de recherche opérationnelle, 2(8), 57–75.

Saaty, T.L. (1978). Modeling unstructured decision problems – the theory of analytical hierarchies. Mathematics and Computers in Simulation, 20(3), 147–158.

Saaty, T.L. (1996). The ANP for Decision Making with Dependence and Feedback. RWS Publications, USA.

Sahu, A.K., Sahu, N.K., Sahu, A.K. (2016). Application of modified MULTI-MOORA for CNC machine tool evaluation in IVGTFNS environment: an empirical study. International Journal of Computer Aided Engineering and Technology, 8(3), 234–259.

Smarandache, F. (1999). A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic. American Research Press, Rehoboth.

Stanujkic, D., Zavadskas, E.K., Brauers, W.K., Karabasevic, D. (2015). An extension of the MULTIMOORA method for solving complex decision-making problems based on the use of interval-valued triangular fuzzy numbers. Transformations in Business and Economics, 14(2B), 355–377.

Stanujkic, D., Zavadskas, E.K., Karabasevic, D., Smarandache, F., Turskis, Z. (2017a). The use of the pivot pairwise relative criteria importance assessment method for determining the weights of criteria. Romanian Journal of Economic Forecasting, 20(4), 116–133.

Stanujkic, D., Zavadskas, E.K., Smarandache, F., Brauers, W.K., Karabasevic, D. (2017b). A neutrosophic extension of the MULTIMOORA method. Informatica, 28(1), 181–192.

Tian, Z.P., Zhang, H.Y., Wang, J., Wang, J.Q., Chen, X.H. (2016). Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets. International Journal of Systems Science, 47(15), 3598–3608.

Uluçay, V., Deli, I., Şahin, M. (2018). Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making. Neural Computing and Applications, 29(3), 739–748.

Wallenius, J., Dyer, J.S., Fishburn, P.C., Steuer, R.E., Zionts, S., Deb, K. (2008). Multiple criteria decision making, multiattribute utility theory: Recent accomplishments and what lies ahead. Management Science, 54(7), 1336–1349.

Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

Zavadskas, E.K., Turskis, Z. (2010). A new additive ratio assessment (ARAS) method in multicriteria decision-making. Technological and Economic Development of Economy, 16(2), 159–172.

Zavadskas, E.K., Kaklauskas, A., Sarka, V. (1994). The new method of multicriteria complex proportional assessment of projects. Technological and Economic Development of Economy, 1(3), 131–139.

Zavadskas, E.K., Turskis, Z., Kildienė, S. (2014). State of art surveys of overviews on MCDM/MADM methods. Technological and Economic Development of Economy, 20(1), 165–179.

Zavadskas, E.K., Antucheviciene, J., Razavi Hajiagha, S.H., Hashemi, S.S. (2015). The interval-valued intuitionistic fuzzy MULTIMOORA method for group decision making in engineering. Mathematical Problems in Engineering. Art. No. 560690.

Zeleny, M. (1973). Compromise programming. In: Cochrane, J.L., Zeleny, M. (Eds.), Multiple Criteria Decision Making. University of South Carolina Press, Columbia, SC, pp. 262–301.

Zhang, W.R. (1994). Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. In: Proceedings of Industrial Fuzzy Control and Intelligent Systems Conference, San Antonio, USA, December 18–21, 1994, pp. 305–309.

Biographies

Stanujkic Dragisa

dstanujkic@tfbor.bg.ac.rs

D. Stanujkic is an associate professor of information technology at the Technical Faculty in Bor, University of Belgrade. He has received his MSc degree in information science and PhD in organizational sciences from the Faculty of Organizational Sciences, University of Belgrade. His current research is focused on decision-making theory, expert systems and intelligent decision support systems.

Karabasevic Darjan

darjan.karabasevic@mef.edu.rs

D. Karabasevic is an assistant professor at the Faculty of Applied Management, Economics and Finance, University Business Academy in Novi Sad. He obtained his degrees at all the levels of studies (BSc appl. in economics, BSc in economics, academic specialization in the management of business information systems and PhD in management and business) at the Faculty of Management in Zajecar, John Naisbitt University, Belgrade. His current research is focused on the human resource management, management and decision-making theory.

Zavadskas Edmundas Kazimieras

edmundas.zavadskas@vgtu.lt

E.K. Zavadskas is a professor of the Department of Construction Management and Real Estate, director of Institute of Sustainable Construction, and Chief Research Fellow of Laboratory of Operational Research at Vilnius Gediminas Technical University, Vilnius, Lithuania. He has a PhD in building structures (1973) and DrSc (1987) in building technology and management. He is a member of the Lithuanian and several foreign Academies of Sciences. He is doctor honoris causa at Poznan, Saint Petersburg, and Kiev universities. He is the editor in chief and a member of editorial boards of a number of research journals. He is an author and coauthor of more than 400 papers and a number of monographs. Research interests are: building technology and management, decision-making theory, automation in design and decision support systems.

Smarandache Florentin

fsmarandache@gmail.com

Brauers Willem K.M.

willem.brauers@uantwerpen.be

Full article Related articles Cited by

Open access article under the CC BY license.

Keywords

bipolar fuzzy set single-valued bipolar fuzzy number MULTIMOORA MCDM

Metrics

since January 2020

1973

Article info
views

893

Full article
views

733

PDF
downloads

304

XML
downloads

RSS

Authors

Abstract

References

Biographies

Export citation

Copy and paste formatted citation

Download citation in file