An extended intuitionistic fuzzy modified group complex proportional assessment approach

Document Type: Research Paper


Department of Industrial Engineering and Management Systems, Amirkabir University of Technology, Tehran, Iran


Complex proportional assessment (COPRAS) methodology is one of the well-known multiple criteria group decision-making (MCGDM) frameworks that can focus on proportional and direct dependences of the significance and utility degree of candidates under the presence of mutually conflicting criteria in real-worldcases. This studyelaboratesa newintuitionistic fuzzy modified group complex proportional assessment (IF-MGCOPRAS) method.This group decision-making methodologymakes the suitable decision by considering both concepts of the intuitionistic fuzzy positive ideal and negative ideal solutions.The performance of the candidates with respect to various criteria and corresponding criteria weights are linguistic termsthat expressed as intuitionistic fuzzy numbers. Then,intuitionistic fuzzy weighted averaging (IFWA) relation is employed to aggregate individual opinions of experts.Furthermore, a new intuitionistic modified relativeindex is manipulatedto specify the most appropriate candidate for a particular engineering application in a manufacturing industry.In this respect, an illustrative example for group decision making in an equipment selection problem is considered to demonstrate theprocedure ofproposed complex assessment method. The obtainedresults of IF-MGCOPRAS method represented that a reasonable and satisfactory assessmentfor equipment decision makingproblem is occurred. Finally, a comparative analysis and discussion with the intuitionistic fuzzy group TOPSIS method is provided.


Main Subjects

Atanassov K., Georgiev C. (1993) Intuitionistic fuzzy prolog. Fuzzy Sets Syst 53: 121–128.

Atanassov K., Pasi G.,  Yager R.R. (2005) Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. Int J Syst Sci 36: 859–868.

Atanassov K.T. (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20: 87–96.

Atanassov K.T. (1994) New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets Syst 61: 137-142.

Atanassov K.T., Nikolov N.G., Aladjov H.T. (2001) Remark on two operations over intuitionistic fuzzy sets. Int J Uncertain Fuzziness Knowl Based Syst 9(1): 71-75.

Boran F.E., Genc S., Kurt M., Akay D. (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36: 11363–11368.

Burillo P., Bustince H. (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78: 305-316.

Büyüközkan, G., &Güleryüz, S. (2016). A new integrated intuitionistic fuzzy groUp decision making approach for product development partner selection. Computers & Industrial Engineering.

Büyüközkan, G., &Göçer, F. (2016). Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem. Applied Soft Computing.

Chatterjee P., Athawale V.M., Chakraborty S. (2011) Materials selection using complex proportional assessment and evaluation of mixed data methods. Mater Des 32: 851–860.

Chen T. (2007) Remarks on the subtraction and division operations over intuitionistic fuzzy sets and interval-valued fuzzy sets. Int J Fuzzy Syst 9(3): 169-172.

Chen, S. M., Cheng, S. H., & Lan, T. C. (2016). A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Information Sciences, 343, 15-40.

Dagdeviren M. (2008). Decision making in equipment selection: an integrated approach with AHP and PROMETHEE. J IntellManuf 19: 397–406.

Datta S., Beriha G.S., Patnaik B., Mahapatra S.S. (2009) Use of compromise ranking method for supervisor selection: A multi-criteria decision making (MCDM) approach. Int J Vocat Tech Educ 1: 7-13.

De S.K., Biswas R., Roy A.R. (2000). Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114: 477-484.

Deschrijver G.,  Kerre E.E. (2004). On the representation of intuitionistic fuzzy t-norms and t-conorms. IEEE Trans Fuzzy Syst 12: 45–61.

Devi, K. (2011). Extension of VIKOR method in intuitionistic fuzzy environment for robot selection. Expert Systems with Applications, 38(11), 14163-14168.

Devi, K., & Yadav, S. P. (2013). A multicriteria intuitionistic fuzzy group decision making for plant location selection with ELECTRE method. The International Journal of Advanced Manufacturing Technology, 66(9-12), 1219-1229.

Gumus A.T. (2009) Evaluation of hazardous waste transportation firms by using a two step fuzzy-AHP and TOPSIS methodology. Expert Syst Appl 36: 4067-4074.

Gürkan E., Erkmen I., Erkmen A.M. (2002) Two-way fuzzy adaptive identification and control of a flexible-joint robot arm. Info Sci 145: 13–43.

Hernandez E.A., Uddameri V. (2010) Selecting agricultural best management practices for water conservation and quality improvements using Atanassov’s intuitionistic fuzzy sets. Water Resour Manage 24: 4589–4612.

Hwang C.L., Yoon K. (1992) Fuzzy multiple attribute decision making. Springer-Verlag, Berlin Heidberg.

Hwang, C. L., & Yoon, K. (2012). Multiple attribute decision making: methods and applications a state-of-the-art survey (Vol. 186). Springer Science & Business Media.

─░Ntepe, G., Bozdag, E., &Koc, T. (2013). The selection of technology forecasting method using a multi-criteria interval-valued intuitionistic fuzzy group decision making approach. Computers & Industrial Engineering, 65(2), 277-285.

Kaklauskas A., Zavadskas E.K., Raslanas S., Ginevicius R., Komka A., Malinauskas P. (2006) Selection of low-e windows in retrofit of public buildings by applying multiple criteria method COPRAS: A Lithuanian case. Energ Build 38: 454–462.

Li D.-F. (2005) Multiattribute decision making models and methods using intuitionistic fuzzy sets. J Comput Syst Sci 70: 73–85.

Li D.-F., Chen G.-H., Huang, Z.-G. (2010) Linear programming method for multiattribute group decision making using IF sets. Inform Sci 180: 1591–1609.

Lin L., Yuan X.H., Xia Z.Q. (2007) Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J Comput Syst Sci 73: 84–88.

Malekly H., Mousavi S.M., Hashemi H. (2010). A fuzzy integrated methodology for evaluating conceptual bridge design. Expert Syst Appl 37: 4910–4920.

Mousavi S.M., Jolai F., Tavakkoli-Moghaddam R. (2011) A fuzzy stochastic multi-attribute group decision-making approach for selection problems. Group DecisNegot, Article in press, DOI: 10.1007/s10726-011-9259-1.

Nguyen, H. (2016). A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition. Expert Systems with Applications, 45, 97-107.

Ölçer A.I., Odabasi A.Y. (2005) A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem. Eur J Oper Res 166: 93–114.

Onar, S. C., Oztaysi, B., Otay, ─░., &Kahraman, C. (2015). Multi-expert wind energy technology selection using interval-valued intuitionistic fuzzy sets. Energy, 90, 274-285.

Peng, X., &Selvachandran, G. (2017). Pythagorean fuzzy set: state of the art and future directions. Artificial Intelligence Review, 1-55.

Shu M.S., Cheng C.H., Chang J.R. (2006) Using intuitionistic fuzzy sets for fault tree analysis on printed circuit board assembly. Microelectron Reliab46(12): 2139–2148.

Szmidt E., Kacprzyk J. (2002) Using intuitionistic fuzzy sets in group decision making. ContrCybern31: 1037–1053.

TuranogluBekar, E., Cakmakci, M., &Kahraman, C. (2016). Fuzzy COPRAS method for performance measurement in total productive maintenance: a comparative analysis. Journal of Business Economics and Management, 17(5), 663-684.

Vahdani B., Hadipour H. (2010) Extension of the ELECTRE method based on interval-valued fuzzy sets. Soft Comput, Article in press, DOI: 10.1007/s00500-010-0563-5.

Vahdani B., Hadipour H., Tavakkoli-Moghaddam R. (2010) Soft computing based on interval valued fuzzy ANP-A novel methodology. J IntellManuf, Article in press, DOI 10.1007/s10845-010-0457-5.

Wan, S. P., & Li, D. F. (2015). Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees. Information Sciences, 325, 484-503.

Wan, S. P., Wang, F., & Dong, J. Y. (2016). A novel group decision making method with intuitionistic fuzzy preference relations for RFID technology selection. Applied Soft Computing, 38, 405-422.

Wu, Y., Geng, S., Xu, H., & Zhang, H. (2014). Study of decision framework of wind farm project plan selection under intuitionistic fuzzy set and fuzzy measure environment. Energy Conversion and Management, 87, 274-284.

Xu Z.S. (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15: 1179–1187.

Xu Z.S., Yager R.R. (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35: 417–433.

Xu, G. L., Wan, S. P., Wang, F., Dong, J. Y., & Zeng, Y. F. (2016). Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations. Knowledge-Based Systems, 98, 30-43.

Ye J. (2010) Multicriteria group decision-making method using vector similarity measures for trapezoidal intuitionistic fuzzy numbers. Group DecisNegot, Article in press, DOI: 10.1007/s10726-010-9224-4.

Zadeh L.A. (1965) Fuzzy sets. InformContr 8: 338–353.

Zavadskas E., Kaklauskas, A. (1996) Multiple criteria analysis of buildings (in Lithuanian). Vilnius: Technika.

Zheng, Y., Xu, Z., He, Y., & Liao, H. (2018). Severity Assessment of Chronic Obstructive Pulmonary Disease Based on Hesitant Fuzzy Linguistic COPRAS Method. Applied Soft Computing.

Zimmerman H.J. (2001). Fuzzy set theory and its applications (4th ed.). Boston, Dordrecht, London: Kluwer Academic Publishers.