Abstract
The fuzzy set theory plays an important role in the modeling of the problems involving uncertain data. Some extensions of the fuzzy sets are needed due to the variety of problems encountered in real life. The concept of a hesitant fuzzy set is one of these extensions. Also, soft set theory, which is free from the difficulties of determining the membership function in fuzzy sets, plays an important role in dealing with uncertainty. In this study, we introduce the concept of hesitant fuzzy parameterized soft set as a generalization of the fuzzy parameterized soft sets. Then we define set-theoretical operations of the hesitant fuzzy parameterized soft sets and obtain some of their properties. We also improve a decision-making algorithm under the hesitant fuzzy parameterized soft environment and give an example to show the process of the algorithm. Finally, we compare the proposed decision-making algorithm with methods existing in the literature.
Similar content being viewed by others
References
Akram M, Adeel A, Alcantud JCR (2019) Hesitant fuzzy N-soft sets: a new model with applications in decision-making. J Intell Fuzzy Syst 36(6):6113–6127
Akram M, Ilyas F, Garg H (2020) Multi-criteria group decision making based on ELECTRE I method in Pythagorean fuzzy information. Soft Comput 24(5):3425–3453
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Set Syst 20:87–96
Borah MJ, Hazarika B, Zhang X (2016) Some aspects on hesitant fuzzy soft set. Cogent Math 3(1):1–11
Boumi S, Deli I, Smarandache F (2014) Interval valued neutrosophic parameterized soft set theory and its decision making. J New Result Sci 7:58–71
Çağman N, Çıtak F, Enginoğlu S (2010) Fuzzy parameterized fuzzy soft set theory and its applications. Turk J Fuzzy Syst 1(1):21–35
Çağman N, Enginoğlu S, Çıtak F (2011) Fuzzy soft set theory and its applications. Iran J Fuzzy Syst 8(3):137–147
Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211
Das S, Malakar D, Kar S, Pal T (2019) Neural Comput Appl 31:1023–1039
Deli İ, Çağman N (2015) Intuitionistic fuzzy parameterized soft set theory and its decision making. Appl Soft Comput 28:109–113
Deli I, Karaaslan F (2019) Bipolar FPSS-theory with applications in decision making. Afr Mat. https://doi.org/10.1007/s13370-019-00738-4
Hao J, Chiclana F (2020) Attitude quantifier based possibility distribution generation method for hesitant fuzzy linguistic group decision making. Inform Sci 518:341–360
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
Karaaslan F (2016) Intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets with applications in decision making. Ann Fuzzy Math Inform 11(4):607–619
Li C, Li D, Jin J (2019) Generalized hesitant fuzzy soft sets and its application to decision making. Int J Pattern Recogn 33(12):1950019
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602
Molodtsov DA (1999) Soft set theory-first results. Comput Math Appl 37:19–31
Morente-Molinera JA, Pèrez IJ, Ureña MR, Herrera-Viedma E (2015) On multi-granular fuzzy linguistic modeling in group decision making problems: a systematic review and future trends. Knowl Based Syst 74:49–60
Morente-Molinera JA, Ríos-Aguilar S, González-Crespo R, Herrera-Viedma E (2019) Dealing with group decision-making environments that have a high amount of alternatives using card-sorting techniques. Expert Syst Appl 127:187–198
Morente-Molinera JA, Wu X, Morfeq A, Al-Hmouz R, Herrera-Viedma E (2020) A novel multi-criteria group decision-making method for heterogeneous and dynamic contexts using multi-granular fuzzy linguistic modelling and consensus measures. Inform Fusion 53:240–250
Ozlu S, Karaaslan F (2019) Some distance measures for type 2 hesitant fuzzy sets and their applications to multi-criteria group decision-making problems. Soft Comput. https://doi.org/10.1007/s00500-019-04509-y
Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11(5):341–356
Pei Z, Yi L (2015) A note on operations of hesitant fuzzy sets. Int J Comput Int Sys 8(2):226–239
Smarandache F (1999) A unifying field in logics. Neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539
Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: The 18th IEEE international conference on fuzzy systems, Jeju Island, Korea, pp 1378–1382
Wang F, Li X, Chen X (2014) Hesitant fuzzy soft set and its applications in multicriteria decision making. J Appl Math Article ID 643785:10
Xia MM, Xu ZS (2010) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52(3):395–407
Xu Z, Xia M (2011) Distance and similarity measures for hesitant fuzzy sets. Inform Sci 181:2128–2138
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zhang C, Liao H, Luo L, Xu Z (2020) Distance-based consensus reaching process for group decision making with intuitionistic multiplicative preference relations. Appl Soft Comput 88:106045
Acknowledgements
An earlier version of this paper was presented at 14. Ankara Mathematics Days (AMG-2019), Ankara, Turkey, Jun 28–29, 2019.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Karamaz, F., Karaaslan, F. Hesitant fuzzy parameterized soft sets and their applications in decision making. J Ambient Intell Human Comput 12, 1869–1878 (2021). https://doi.org/10.1007/s12652-020-02258-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-020-02258-7