1 Affiliation : Department of Mathematics, Arul Anandar College (Autonomous), Karmathur, India
Email : firstname.lastname@example.org
2 Affiliation : Department of Mathematics, PKN Arts and Science College, Thirumangalam, India
Email : email@example.com
3 Affiliation : Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
Email : firstname.lastname@example.org
Neutrosophic overset, neutrosophic underset and neutrosophic offset introduced by Smarandache are the special kinds of neutrosophic sets with values beyond the range [0,1] and these sets are pragmatic in nature as it represents the real life situations. This paper introduces the concept of saturated refined neutrosophic sets and extends the same to the special kinds of neutrosophic sets. The proposed concept is applied in decision making on Teacher’s adaptation to cybergogy. The decision making environment is characterized by different types of teachers, online teaching skills and various training methods. Fuzzy relation is used to match the most suitable method to the different kinds of teachers with the intervention of saturated interval valued neutrosophic refined oversets, offsets and undersets. The results obtained by applying the notion of saturated refined sets using various distance measures represent the effect of training methods on teacher’s adaptation to learner-centred teaching methods, which certainly give space to gain many insights on the relationship between quality of training and teacher’s adaptation rate. The proposed concept has wide scope and few limitations.
neutrosophic oversets , neutrosophic offsets , neutrosophic offsets , refined sets , saturated , interval-valued sets , cybergogy
 Zadeh,L.A., “ Fuzzy sets”, Information and Control, vol. 8, pp. 338–353, 1965.
 Atanassov,K.T., “Intuitionistic fuzzy sets”, Fuzzy sets system, vol. 20, pp.87-96,1983.
 Khan .,Saleem Abdullah., “ Interval‐valued Pythagorean fuzzy GRA method for multiple‐attribute decision making with incomplete weight information”, International journal of Intelligent systems,Vol.33, pp .1689-1716, 2018.
 Zhuosheng Jia,Yingjun Zhang., “Interval valued Intuitionistic fuzzy multiple attribute group decision making with uncertain weights”, Mathematical Problems in Engineering, Special Issue, pp 1-9,2019.
 Smarandache,F., “Neutrosophic set, a generalization of the Intuitionistic Fuzzy Sets”, International Journal of Pure and Applied Mathematics, vol 24, pp.287-297, 2005.
 Abdel-Baset, M., Chang, V., & Gamal, A., “Evaluation of the green supply chain management practices: A novel neutrosophic approach” Computers in Industry, vol.108, pp. 210-220, 2019.
 Abdel-Baset, M., Chang, V., Gamal, A., &Smarandache, F., “An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in importing field”, Computers in Industry, vol.106, pp.94-110,2019.
 Hu.J,Pan.L, and Chen.X, “An interval neutrosophic projection-based VIKOR method for selecting doctors”. Cognitive Computation, vol.9, pp.801-816,2017.
 Nada A., Nabeeh, Ahmed Abdel-Monem and Ahmed Abdelmouty., “A Hybrid Approach of Neutrosophic with MULTIMOORA in Application of Personnel Selection”, Neutrosophic Sets and Systems, vol. 30, pp. 1-21,2019.
 Ajay, D., Aldring, J., Abirami, S., and Martina, D. J. S., “A SVTrN-number approach of multi-objective optimisation on the basis of simple ratio analysis based on MCDM method”, International Journal of Neutrosophic Science, vol .5, pp.16-28, 2020
 Sahidul Islam and Sayan Chandra Deb., “Neutrosophic Goal Programming Approach to A Green Supplier Selection Model with Quantity Discount”, Neutrosophic Sets and Systems, vol. 30, pp. 98-112 ,2019.
 Mullai,M., Broumi, S., Surya,R., and Madhan Kumar,G., “ Neutrosophic Intelligent Energy Efficient Routing for Wireless ad-hoc Network Based on Multi-criteria Decision Making”, Neutrosophic Sets and Systems, vol. 30,pp. 113-121,2019.
 Abdel Nasser H, Zaied., Abduallah Gamal, Mahmoud Ismail., “An Integrated Neutrosophic and TOPSIS for Evaluating Airline Service Quality”, Neutrosophic Sets and Systems, vol. 29, pp. 30-39, 2019.
 Muhammad Saqlain, Muhammad Saeed, Muhammad Rayees Ahmad, Smarandache,F., “Generalization of TOPSIS for Neutrosophic Hypersoft set using Accuracy Function and its Application”, Neutrosophic Sets and Systems, vol. 27, pp. 131-137, 2019.
 Surapati Pramanik, Partha Pratim Dey., “Multi-level linear programming problem with neutrosophic numbers: A goal programming strategy”, Neutrosophic Sets and Systems, vol. 29, pp. 242-254, 2019.
 Ajay, D., & Aldring, J., “ A Decision Making Technique Based on Similarity Measure and Entropy of Bipolar Neutrosophic Sets”.The International journal of analytical and experimental modal analysis,vol. 1, pp.520-529 , 2019.
 Ajay, D., Broumi, S., & Aldring, J., “An MCDM Method under Neutrosophic Cubic Fuzzy Sets with Geometric Bonferroni Mean Operator”, Neutrosophic Sets and Systems, vol-32, pp.187, 2020.
 Chakraborty A, Mondal, Alam, Mahata, “Cylindrical Neutrosophic Single-Valued Numberand its Application in Networking problem, Multi Criterion Decision Making Problem and Graph Theory”,2020 CAAI Transactions on Intelligence Technology; DOI: 10.1049/trit.2019.0083.
 Chakraborty.A, Banik.B, Mondal and Alam, “Arithmetic and Geometric Operators of Pentagonal Neutrosophic Number and its Application in Mobile Communication Based MCGDM Problem”, Vol 32, 2020.DOI: 10.5281/zenodo.3723145.
 Deli, I., & Şubaş, Y., “ Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems” Journal of Intelligent & Fuzzy Systems, vol.32, pp.291-301, 2017.
 Deli, I., & ozturk, E. K., “ Two Centroid Point for SVTN-Numbers and SVTrN-Numbers: SVN-MADM Method”, In Neutrosophic Graph Theory and Algorithms , pp. 279-307, pp.279-307, 2020.
 Juanjuan ding,Wenhui Bai,Chao Zhang., “A New Multi-Attribute Decision Making Method with single-valued Neutrosophic Graphs”, International journal of neutrosophic science ,vol.11 ,pp.76-86, 2020.
 Dragisa stanujkic,Darjan Karabasevic,Florentin Smarandache,Gabrijela Popovic., “A novel Approach for assessing the Reliability of Data Contained in a single valued Neutrosophic number and its application in multiple criteria decision making”, International journal of neutrosophic science, vol.11, pp.22-29, 2020.
 Shahzaib Ashraf, Saleem Abdullah., “Decision Support Modeling for agriculture land selection based on sine trigonometric single valued neutrosophic information”, International journal of Neutrosophic Science, vol.9, pp.60-73, 2020.
 Muhammad Naveed Jafar , Mushal Zia , Ayisha Saeed , Maryam Yaqoob , samreen habib, “Aggregation Operators of Bipolar Neutrosophic Soft Sets and It’s Applications In Auto Car Selection”, International journal of Neutrosophic Science, vol-9, pp.37-46, 2020.
 Philippe Schweizer, “Thinking on Thinking: The Elementary forms of Mental Life Neutrosophical representation as enabling cognitive heuristics”, International Journal of Neutrosophic Science, vol 2 , pp.63-71,2020.
 Florentin Smarandache , “Operators on single valued neutrosophic oversets, neutrosophic undersets and neutrosophic off sets”, Journal of Mathematics and Informatics, vol-5, pp.63-67, 2016.
 Irfan Deli., Said Broumi., Florentin Smarandache , “ On neutrosophic refined sets and their applications in medical diagnosis”, Journal of New Theory,vol. 6, pp.88-98, 2015.
 Said Broumi and Irfan Deli., “Correlation measure for neutrosophic refined sets and its application in medical diagnosis”, Palestine Journal of Mathematics, vol 5, pp.135-143, 2016.