Abstract
In this paper, we mention and address the limitation of an existing conversion method of intuitionistic fuzzy set (IFS) from fuzzy set (FS) and propose a novel conversion method for IFS from fuzzy set. To compare the proposed conversion method, we apply it on a TOPSIS method of MCDM problem in which criteria weights are determined using intuitionistic fuzzy entropy. We take a real example in this study to compare the ranking of four organizations of different sectors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Zadeh, L.A.: Fuzzy sets. Inf. Cont. 8(3), 338–353 (1965)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy sets Syst. 20(1), 87–96 (1986)
Atanassov, K.T.: Intuitionistic fuzzy sets. Intui. Fuzzy Sets, 1–137 (1999) (Physica-Verlag HD)
Joshi, D., Kumar, S.: Intuitionistic fuzzy entropy and distance measure based TOPSIS method for multi-criteria decision making. Egypt. Info. 15(2), 97–104 (2014)
Szmidt, E., Kacprzyk, J.: Intuitionistic fuzzy sets in group decision making. Notes IFS 2(1) (1996)
Szmidt, E., Kacprzyk, J.: Using intuitionistic fuzzy sets in group decision making. Cont. Cyber. 31, 1055–1057 (2002)
Pankowska, A., Wygralak, M.: General IF-sets with triangular norms and their applications to group decision making. Inf. Sci. 176(18), 2713–2754 (2002)
Wan, S.P., Li, D.F.: Atanassov’s intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov’s intuitionistic fuzzy truth degrees. IEEE Trans. Fuzzy Syst. 22(2), 300–312 (2014)
Wan, S.P., Yi, Z.H.: Power average of trapezoidal intuitionistic fuzzy numbers using strict t-norms and t-conorms. IEEE Trans. Fuzzy Syst. 22(2), 300–312 (2015)
Xian, S., Xue, W., Dong, Y.: Intuitionistic fuzzy induced ordered entropic weighted averaging operator for group decision making. J. Int. Fuzzy Syst. 31(3), 1189–1197 (2016)
Jurio, A., Paternain, D., Bustince, H., Guerra, C., Beliakov, G.: A construction method of Atanassov’s intuitionistic fuzzy sets for image processing. In: 5th IEEE Conference on Intelligent System, London, UK (2010)
Joshi, B.P., Kumar, S.: Intuitionistic fuzzy sets based method for fuzzy time series forecasting. Cyber. Syst. 43(1), 34–47 (2012)
Joshi, B.P., Kumar, S.: Fuzzy time series model based on intuitionistic fuzzy sets for empirical research in stock market. Inter. J. App. Evolut. Comput. (IJAEC) 3(4), 71–84 (2012)
Gangwar, S.S., Kumar, S.: Probabilistic and intuitionistic fuzzy sets-based method for fuzzy time series forecasting. Cyber. Syst. 45(4), 349–361 (2014)
Hwang, C.L., Yoon, K.S.: Multiple Attribute Decision Making Methods and Applications. Springer, Berlin (1981)
Chen, C.T.: Extension of the TOPSIS for group decision making under fuzzy Environment. J. Fuzzy Sets Syst. 114, 1–9 (2000)
Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst. 118(3), 467–477 (2001)
Grzegorzewski, P., Mrówka, E.: Some notes on (Atanassov’s) intuitionistic fuzzy sets. Fuzzy Sets Syst. 156(3), 492–495 (2005)
Hung, C.C., Chen, L.H.: A multiple criteria group decision making model with entropy weight in an intuitionistic fuzzy environment. Int. Auto. Com. Eng., pp. 17–26 (2009) (Springer, Netherlands)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Singh, A., Joshi, D.K., Kumar, S. (2019). A Novel Construction Method of Intuitionistic Fuzzy Set from Fuzzy Set and Its Application in Multi-criteria Decision-Making Problem. In: Mandal, J., Bhattacharyya, D., Auluck, N. (eds) Advanced Computing and Communication Technologies. Advances in Intelligent Systems and Computing, vol 702. Springer, Singapore. https://doi.org/10.1007/978-981-13-0680-8_7
Download citation
DOI: https://doi.org/10.1007/978-981-13-0680-8_7
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-0679-2
Online ISBN: 978-981-13-0680-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)