N-soft sets and their decision making algorithms
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In this paper, we motivate and introduce the concept of N-soft set as an extended soft set model. Some useful algebraic definitions and properties are given. We cite real examples that prove that N-soft sets are a cogent model for binary and non-binary evaluations in numerous kinds of decision making problems. Finally, we propose decision making procedures for N-soft sets.
KeywordsN-soft set Non-binary evaluation Decision making Choice value Intersection and union
Part of this research was done, while the first author was invited at the Department of Economics and Economic History in Salamanca. Their hospitality is gratefully acknowledged. The constructive comments by an anonymous referee have helped us to improve the paper and are highly appreciated.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest regarding the publication of this article.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Abbas SE, Ibedou I (2016) Fuzzy soft uniform spaces. Soft Comput (in press)Google Scholar
- Akram M, Shahzadi S (2016) Novel intuitionistic fuzzy soft multiple-attribute decision-making methods. Neural Comput Appl (in press)Google Scholar
- Alcantud JCR (2015) Fuzzy soft set based decision making: a novel alternative approach. In: IFSA-EUSFLAT conference 2015, Atlantic Press, pp 106–111Google Scholar
- Alcantud JCR (2016a) Fuzzy soft set decision making algorithms: some clarifications and reinterpretations. In: et al OL (ed) Advances in artificial intelligence. 17th Conference of the Spanish association for artificial intelligence, CAEPIA 2016, Springer-Verlag, pp 479–488Google Scholar
- Alcantud JCR, Santos-García G (2016) Incomplete soft sets: new solutions for decision making problems. Springer, Cham, pp 9–17Google Scholar
- Alcantud JCR, Santos-García G (2017) A new criterion for soft set based decision making problems under incomplete information. Int J Comput Intell Syst 10:394–404Google Scholar
- Alcantud JCR, Santos-García G, Hernández-Galilea E (2015) Glaucoma diagnosis: a soft set based decision making procedure. Springer, Cham, pp 49–60Google Scholar
- Ali MI, Mahmood T, Rehman MMU, Aslam MF (2015) On lattice ordered soft sets. Appl Soft Comput 36:499–505Google Scholar
- Babitha KV, John SJ (2013) Hesitant fuzzy soft sets. J New Results Sci 3:98–107Google Scholar
- Deli I, Eraslan S, Çağman N (2016) ivnpiv-neutrosophic soft sets and their decision making based on similarity measure. Neural Comput Appl (in press)Google Scholar
- Fatimah F, Rosadi D, Hakim RBF, Alcantud JCR (2017a) Probabilistic soft sets and dual probabilistic soft sets in decision-making. Neural Comput Appl (in press)Google Scholar
- Fatimah F, Rosadi D, Hakim RBF, Alcantud JCR (2017b) A social choice approach to graded soft sets. 2017 IEEE Int Conf Fuzzy Syst (FUZZ-IEEE). doi: 10.1109/FUZZIEEE.2017.8015428
- Hakim RBF, Saari EN, Herawan T (2014a) On if-then multi soft sets-based decision making. In: et al L (ed) Information and communication technology, Springer Berlin Heidelberg, Berlin, No. 8407 in Lecture Notes in Computer Science, pp 306–315Google Scholar
- Hakim RBF, Saari EN, Herawan T (2014b) Soft solution of soft set theory for recommendation in decision making. In: et al TH (ed) Recent advances on soft computing and data mining, Springer International Publishing, Switzerland, No. 287 in Advances in Intelligent Systems and Computing, pp 313–324Google Scholar
- Handaga B, Deris MM (2012) Text categorization based on fuzzy soft set theory. Springer, Berlin, pp 340–352Google Scholar
- Maji PK, Biswas R, Roy AR (2001a) Fuzzy soft sets. J Fuzzy Math 9:589–602Google Scholar
- Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562Google Scholar
- Sutoyo E, Mungad M, Hamid S, Herawan T (2016) An efficient soft set-based approach for conflict analysis. PLoS ONE 13:1–31Google Scholar
- Yang Y, Song J, Peng X, (2015) Comments on “An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets” [Appl. Math. Modell. 37, (2013) 4139–4146]. Appl Math Model 39(23):7746–7748Google Scholar
- Zhan J, Ali MI, Mehmood N (2017a) On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods. Appl Soft Comput 56:446–457Google Scholar
- Zhan J, Dudek WA, Neggers J (2017d) A new soft union set: characterizations of hemirings. Int J Mach Learn Cybern 8:525–535Google Scholar
- Zhou W, Xu ZS (2017) Probability calculation and element optimization of probabilistic hesitant fuzzy preference relations based on expected consistency. IEEE Trans Fuzzy Syst PP(99):1–1Google Scholar
- Zhu P, Wen Q (2010) Probabilistic soft sets. IEEE Int Conf Granul Comput 51:635–638Google Scholar