Generalized Neutrosophic Soft Expert Set for Multiple-Criteria Decision-Making
Abstract
:1. Introduction
2. Preliminaries
3. Generalized Neutrosophic Soft Expert Set
- i.
- , and
- ii.
- is a generalized neutrosophic soft expert subset, for all
- 1.
- 2.
- 3.
- 1.
- 2.
- .
- 1.
- 2.
- .
- 1.
- .
- 2.
- .
- 1.
- 2.
4. GNSES-Aggregation Operator
5. An Application of Generalized Neutrosophic Soft Expert Set
- Step 1—Choose a feasible subset of the set of parameters.
- Step 2—Construct the GNSES tables for each opinion (agree, disagree) of experts.
- Step3—Compute the aggregation operator GNSES of and the reduced fuzzy set of .
- Step 4—Score.
- Step 5—Choose the element of that has maximum score. This will be the optimal solution.
6. Comparison Analysis
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Set Syst. 1986, 20, 87–96. [Google Scholar] [CrossRef]
- Molodtsov, D. Soft set theory-first results. Comput. Math. Appl. 1999, 37, 19–31. [Google Scholar] [CrossRef]
- Smarandache, F. Neutrosophy: Neutrosophic Probability, Set, and Logic; American Research Press: Rehoboth, IL, USA, 1998. [Google Scholar]
- Smarandache, F. Neutrosophic set—A generalization of the intuitionistic fuzzy set. J. Def. Resour. Manag. 2010, 1, 107–116. [Google Scholar]
- Alkhazaleh, S.; Salleh, A.R.; Hassan, N. Possibility fuzzy soft set. Adv. Decis. Sci. 2011, 479756. [Google Scholar] [CrossRef]
- Alkhazaleh, S.; Salleh, A.R.; Hassan, N. Soft multisets theory. Appl. Math. Sci. 2011, 5, 3561–3573. [Google Scholar]
- Salleh, A.R.; Alkhazaleh, S.; Hassan, N.; Ahmad, A.G. Multiparameterized soft set. J. Math. Stat. 2012, 8, 92–97. [Google Scholar] [CrossRef]
- Alhazaymeh, K.; Halim, S.A.; Salleh, A.R.; Hassan, N. Soft intuitionistic fuzzy sets. Appl. Math. Sci. 2012, 6, 2669–2680. [Google Scholar]
- Adam, F.; Hassan, N. Q-fuzzy soft matrix and its application. AIP Conf. Proc. 2014, 1602, 772–778. [Google Scholar] [CrossRef]
- Adam, F.; Hassan, N. Q-fuzzy soft set. Appl. Math. Sci. 2014, 8, 8689–8695. [Google Scholar] [CrossRef]
- Adam, F.; Hassan, N. Operations on Q-fuzzy soft set. Appl. Math. Sci. 2014, 8, 8697–8701. [Google Scholar] [CrossRef]
- Adam, F.; Hassan, N. Multi Q-fuzzy parameterized soft set and its application. J. Intell. Fuzzy Syst. 2014, 27, 419–424. [Google Scholar] [CrossRef]
- Adam, F.; Hassan, N. Properties on the multi Q-fuzzy soft matrix. AIP Conf. Proc. 2014, 1614, 834–839. [Google Scholar] [CrossRef]
- Adam, F.; Hassan, N. Multi Q-fuzzy soft set and its application. Far East J. Math. Sci. 2015, 97, 871–881. [Google Scholar] [CrossRef]
- Fatimah, F.; Rosadi, D.; Hakim, R.F.; Alcantud, J.C.R. N-soft sets and their decision making algorithms. Soft Comput. 2018, 22, 3829–3842. [Google Scholar] [CrossRef]
- Akram, M.; Adeel, A.; Alcantud, J.C.R. Group decision-making methods based on hesitant N-soft sets. Expert Syst. Appl. 2019, 115, 95–105. [Google Scholar] [CrossRef]
- Akram, M.; Adeel, A.; Alcantud, J.C.R. Fuzzy N-soft sets: A novel model with applications. J. Intell. Fuzzy Syst. 2018, 1–15. [Google Scholar] [CrossRef]
- Varnamkhasti, M.J.; Hassan, N. A hybrid of adaptive neuro-fuzzy inference system and genetic algorithm. J. Intell. Fuzzy Syst. 2013, 25, 793–796. [Google Scholar] [CrossRef]
- Varnamkhasti, M.J.; Hassan, N. Neurogenetic algorithm for solving combinatorial engineering problems. J. Appl. Math. 2012, 2012, 253714. [Google Scholar] [CrossRef]
- Maji, P.K. Neutrosophic soft set. Comput. Math. Appl. 2013, 45, 555–562. [Google Scholar] [CrossRef]
- Alhazaymeh, K.; Hassan, N. Generalized interval-valued vague soft set. Appl. Math. Sci. 2013, 7, 6983–6988. [Google Scholar] [CrossRef]
- Alhazaymeh, K.; Hassan, N. Vague soft multiset theory. Int. J. Pure Appl. Math. 2014, 93, 511–523. [Google Scholar] [CrossRef]
- Hassan, N.; Alhazaymeh, K. Vague soft expert set theory. AIP Conf. Proc. 2013, 1522, 953–958. [Google Scholar] [CrossRef]
- Alhazaymeh, K.; Hassan, N. Mapping on generalized vague soft expert set. Int. J. Pure Appl. Math. 2014, 93, 369–376. [Google Scholar] [CrossRef]
- Adam, F.; Hassan, N. Multi Q-Fuzzy soft expert set and its applications. J. Intell. Fuzzy Syst. 2016, 30, 943–950. [Google Scholar] [CrossRef]
- Al-Qudah, Y.; Hassan, N. Bipolar fuzzy soft expert set and its application in decision making. Int. J. Decis. Sci. 2017, 10, 175–191. [Google Scholar] [CrossRef]
- Sahin, M.; Alkhazaleh, S.; Ulucay, V. Neutrosophic soft expert sets. Appl. Math. 2015, 6, 116–127. [Google Scholar] [CrossRef]
- Al-Quran, A.; Hassan, N. Neutrosophic vague soft expert set theory. J. Intell. Fuzzy Syst. 2016, 30, 3691–3702. [Google Scholar] [CrossRef]
- Al-Quran, A.; Hassan, N. Fuzzy parameterised single valued neutrosophic soft expert set theory and its application in decision making. Int. J. Appl. Decis. Sci. 2016, 9, 212–227. [Google Scholar] [CrossRef]
- Lu, Z.; Ye, J. Cosine measures of neutrosophic cubic sets for multiple attribute decision making. Symmetry 2017, 9, 121. [Google Scholar] [CrossRef]
- Tu, A.; Ye, J.; Wang, B. Multiple attribute decision-making method using similarity measures of neutrosophic cubic sets. Symmetry 2018, 10, 215. [Google Scholar] [CrossRef]
- Cui, W.; Ye, J. Multiple-attribute decision-making method using similarity measures of hesitant linguistic neutrosophic numbers regarding least common multiple cardinality. Symmetry 2018, 10, 330. [Google Scholar] [CrossRef]
- Beg, I.; Rashid, T. Group decision making using intuitonistic hesitant fuzzy sets. Int. J. Fuzzy Logic Intell. Syst. 2014, 14, 181–187. [Google Scholar] [CrossRef]
- Medina, J.; Ojeda-Aciego, M. Multi-adjoint t-concept lattices. Inf. Sci. 2010, 180, 712–725. [Google Scholar] [CrossRef]
- Pozna, C.; Minculete, N.; Precup, R.E.; Kóczy, L.T.; Ballagi, Á. Signatures: Definitions, operators and applications to fuzzy modelling. Fuzzy Sets Syst. 2012, 201, 86–104. [Google Scholar] [CrossRef]
- Nowaková, J.; Prílepok, M.; Snášel, V. Medical image retrieval using vector quantization and fuzzy S-tree. J. Med. Syst. 2017, 41, 18. [Google Scholar] [CrossRef] [PubMed]
- Kumar, A.; Kumar, D.; Jarial, S.K. A hybrid clustering method based on improved artificial bee colony and fuzzy C-Means algorithm. Int. J. Artif. Intell. 2017, 15, 24–44. [Google Scholar]
- Liu, F.; Aiwu, G.; Lukovac, V.; Vukic, M. A multicriteria model for the selection of the transport service provider: A single valued neutrosophic DEMATEL multicriteria model. Decis. Mak. Appl. Manag. Eng. 2018, 1. [Google Scholar] [CrossRef]
- Mukhametzyanov, I.; Pamucar, D. A sensitivity analysis in MCDM problems: A statistical approach. Decis. Mak. Appl. Manag. Eng. 2018, 1. [Google Scholar] [CrossRef]
- Şahin, M.; Kargın, A. Neutrosophic triplet normed space. Open Phys. 2017, 15, 697–704. [Google Scholar] [CrossRef] [Green Version]
- Şahin, M.; Kargın, A.; Çoban, M. Fixed point theorem for neutrosophic triplet partial metric space. Symmetry 2018, 10, 240. [Google Scholar] [CrossRef]
- Abu Qamar, M.; Hassan, N. Q-neutrosophic soft relations and its application in decision making. Entropy 2018, 20, 172. [Google Scholar] [CrossRef]
- Abu Qamar, M.; Hassan, N. Entropy, measures of distance and similarity of Q-neutrosophic soft sets and some applications. Entropy 2018, 20, 672. [Google Scholar] [CrossRef]
- Hassan, N.; Ulucay, V.; Sahin, M. Q-neutrosophic soft expert set and its application in decision making. Int. J. Fuzzy Syst. Appl. 2018, 7, 37–61. [Google Scholar] [CrossRef]
- Broumi, S.; Deli, I.; Smarandache, F. Neutrosophic parametrized soft set theory and its decision making. Int. Front. Sci. Lett. 2014, 1, 1–11. [Google Scholar] [CrossRef]
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