Abstract
In this paper, we propose an intuitively straightforward extension of the vague soft set model called the vague parameterized vague soft set (vp-VSS). This model generalizes the vague soft set by including the opinions of an expert or a moderator regarding the values of the membership function for the parameters that are considered, in the form of a vague set. The values provided by the experts indicate the threshold values for the membership functions of the elements, i.e., the minimum values that must be ideally satisfied by all the elements for each parameter. This provides a clear indication to the users of these information, and forms a pertinent component of the model, particularly in the decision-making process. Subsequently, we define some operations for this model and examine its properties. Subsequently, we introduce two algorithms based on a modified TOPSIS approach and a weighted aggregation operator approach, both of which are based on our proposed vp-VSS model. These algorithms are then applied in two multi-attribute decision-making problems involving supplier selection and the evaluation of supplier performance. The performance and utility of these algorithms are compared and contrasted in terms of the computational complexity and discriminative power of the algorithms.
Similar content being viewed by others
References
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Molodtsov D (1999) Soft set theory—first results. Comput Math Appl 37(4–5):19–31
Cagman N, Citak F, Enginoglu S (2011) Fuzzy parameterized soft set theory and its applications. Ann Fuzzy Math Inform 2(2):219–226
Cagman N, Citak F, Enginoglu S (2010) Fuzzy parameterized fuzzy soft set theory and its applications. Turk J Fuzzy Syst 1(1):21–35
Alkhazaleh S, Salleh AR, Hassan N (2011) Fuzzy parameterized interval-valued fuzzy soft sets. Appl Math Sci 5(67):3335–3346
Bashir M, Salleh AR (2012) Fuzzy parameterized soft expert set. Abstr Appl Anal 2012:1–15. https://doi.org/10.1155/2012/258361
Selvachandran G, Salleh AR (2016) Fuzzy parameterized intuitionistic fuzzy soft expert set theory and its application in decision making. Int J Soft Comput 11(2):52–63
Deli I, Cagman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28:109–113
Karaaslan F (2016) Intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets with applications in decision making. Ann Fuzzy Math Inform 11(4):607–619
Hwang C-L, Yoon K (1981) Multiple attribute decision making. Methods and applications: a state-of-the-art survey. Springer, Berlin
Mayyas A, Omar MA, Hayajneh MT (2016) Eco-material selection using fuzzy TOPSIS method. Int J Sustain Eng 9(5):292–304
Solanki R, Gulati G, Tiwari A, Lohani QMD (2016) A correlation based intuitionistic fuzzy TOPSIS method on supplier selection problem. In: Proceedings of the IEEE international conference on fuzzy systems (FUZZ-IEEE), Vancouver, Canada. http://doi.org/10.1109/CCDC.2010.5499018
Eraslan S, Cagman N (2017) A decision making method by combining TOPSIS and grey relation method under fuzzy soft sets. Sigma J Eng Nat Sci 8(1):53–64
Chaharsooghi SK, Ashrafi M (2014) Sustainable supplier performance evaluation and selection with neofuzzy TOPSIS method. Int Sch Res Not 2014:1–10. https://doi.org/10.1155/2014/434168
Ren F, Kong M, Pei Z (2017) A new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making. Symmetry 9(289):1–19
Onat NC, Gumus S, Kucukvar M, Tatari O (2016) Application of the TOPSIS and intuitionistic fuzzy approaches for ranking the life cycle sustainability performance of alternative vehicle technologies. Sustain Prod Consum 6:12–25
Ye J (2015) An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. J Intell Fuzzy Syst 28:247–255
Liang W, Zhang X, Liu M (2015) The maximizing deviation based on interval-valued Pythagorean fuzzy weighted aggregating operator for multiple criteria group decision analysis. Discrete Dyn Nat Soc 2015:1–15. https://doi.org/10.1155/2015/746572
Biswas P, Pramanik S, Giri BC (2016) TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment. Neural Comput Appl 27(3):727–737
Buyukozkan G, Guleryuz S (2016) Multi-criteria group decision making approach for smart phone selection using intuitionistic fuzzy TOPSIS. Int J Comput Intell Syst 9(4):709–725
Yang W, Chen Z, Zhang F (2017) New group decision making method in intuitionistic fuzzy setting based on TOPSIS. Technol Econ Dev Econ 23(3):441–461
Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23(2):610–614
Xu W, Ma J, Wang S, Hao G (2010) Vague soft sets and their properties. Comput Math Appl 59:787–794
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 3(9):589–602
Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692
Yang X, Lin TY, Yang J, Li Y, Yu D (2009) Combination of interval-valued fuzzy set and soft set. Comput Math Appl 58:521–527
Jiang Y, Tang Y, Chen Q, Liu H, Tang J (2010) Interval-valued intuitionistic fuzzy soft sets and their properties. Comput Math Appl 60:906–918
Shaw K, Shankar R, Yadav SS, Thakur LS (2012) Supplier selection using fuzzy AHP and fuzzy multi-objective linear programming for developing low carbon supply chain. Expert Syst Appl 39(9):8182–8192
Rouyendegh BD, Saputro TE (2014) Supplier selection using fuzzy TOPSIS and MCGP: a case study. Proc Soc Behav Sci 116:3957–3970
Dargi A, Anjomshoae A, Galankashi MR, Memari A, Tap MBM (2014) Supplier selection: a fuzzy-ANP approach. Proc Comput Sci 31:691–700
Kaur P (2014) Selection of vendor based on intuitionistic fuzzy analytical hierarchy process. Adv Oper Res 2014:1–10. https://doi.org/10.1155/2014/987690
Kaur P, Rachana KNL (2016) An intuitionistic fuzzy optimization approach to vendor selection problem. Perspect Sci 8:348–350
Dweiri F, Kumar S, Khan SA, Jain V (2016) Designing an integrated AHP based decision support system for supplier selection in automotive industry. Expert Syst Appl 62:273–283
Junior FRL, Osiro L, Carpinetti LCR (2014) A comparison between fuzzy AHP and fuzzy TOPSIS methods to supplier selection. Appl Soft Comput 21:194–209
Wang YM (1997) Using the method of maximizing deviations to make decision for multiindices. Syst Eng Electron 8:21–26
Hadi-Venchen A, Mirjaberi M (2014) Fuzzy inferior ratio method for multiple attribute decision making problems. Inf Sci 277:263–272
Peng X, Yang Y (2015) Interval-valued hesitant fuzzy soft sets and their application in decision making. Fundam Inform 141:71–93
Agarwal M, Biswas KK, Hanmandlu M (2013) Generalized intuitionistic fuzzy soft sets with applications in decision-making. Appl Soft Comput 13:3552–3566. https://doi.org/10.1016/j.asoc.2013.03.015
Zhu K, Zhan J (2016) Fuzzy parameterized fuzzy soft sets and decision making. Int J Mach Learn Cybern 7(6):1207–1212. https://doi.org/10.1007/s13042-015-0449-z
Garg H (2016) A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int J Intell Syst 31(12):1234–1252. https://doi.org/10.1002/int.21827
Singh P (2015) Correlation coefficients for picture fuzzy sets. J Intell Fuzzy Syst 28:591–604. https://doi.org/10.3233/IFS-141338
Yang Y, Tan X, Meng C (2013) The multi-fuzzy soft set and its application in decision making. Appl Math Model 37:4915–4923
Zhang XH (2014) On interval soft sets with applications. Int J Comput Intell Syst 7:186–196
Chetia B, Das PK (2011) Application of vague soft sets in students’ evaluation. Adv Appl Sci Res 2(6):418–423
Zhang H, Xiong L, Ma W (2015) On interval-valued hesitant fuzzy soft sets. Math Probl Eng 2015:1–17. https://doi.org/10.1155/2015/254764
Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp 57–61
Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28:436–452
Cuong BC (2013) Picture fuzzy sets—first results, Part 1. Seminar “Neuro-fuzzy systems with applications”, Preprint 03/2013, Institute of Mathematics, Hanoi
Cuong BC (2013) Picture fuzzy sets—first results, Part 2. Seminar “Neuro-fuzzy systems with applications”, Preprint 04/2013, Institute of Mathematics, Hanoi
Cuong BC (2014) Picture fuzzy sets. J Comput Sci Cybern 30(4):409–420
Acknowledgements
The authors would like to express their gratitude to the anonymous reviewers, the editor in charge of this paper, and the Editor-in-Chief for their constructive comments which has helped to improve the quality of this paper. In addition, the first author Ganeshsree Selvachandran would like to gratefully acknowledge the financial assistance received from the Ministry of Education, Malaysia, under Grant No. FRGS/1/2017/STG06/UCSI/03/1 and UCSI University, Kuala Lumpur, Malaysia, under Grant No. Proj-In-FOBIS-014.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Rights and permissions
About this article
Cite this article
Selvachandran, G., Peng, X. A modified TOPSIS method based on vague parameterized vague soft sets and its application to supplier selection problems. Neural Comput & Applic 31, 5901–5916 (2019). https://doi.org/10.1007/s00521-018-3409-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-018-3409-1