1 **Affiliation :
**Dept. Math, University of Management and Technology, Johar Town Campus, Lahore, 54000, Pakistan and COMSATS University Islamabad, Lahore Campus, Department of Mathematics, Lahore, 54000, Pakistan

** Email : **shaziaranams@gmail.com

2 **Affiliation :
**Dept. Math, University of Management and Technology, Johar Town Campus, Lahore, 54000, Pakistan

** Email : **Muhammad.Saeed22@gmail.com

3 **Affiliation :
**COMSATS University Islamabad, Lahore Campus, Department of Mathematics, Lahore, 54000, Pakistan

** Email : **mqayyum17@gmail.com

4 **Affiliation :
**Dept. Math and Sciences, University of New Mexico, Gallup, NM 87301, USA

** Email : ** smarand@unm.edu

**Abstract : **

In this paper, we initially introduce a novel type of matrix representation of Plithogenic Crisp/Fuzzy/Intuitionistic/Neutrosophic Hypersoft Set named as **Plithogenic Crisp/Fuzzy/Intuitionistic/Neutrosophic Hypersoft Matrix, **which is** **generated by multiple parallel sheets of matrices. Furthermore, these parallel sheets are representing parallel universes or parallel realities (a combination of attributes and sub-attributes w.r.t. subjects). We represent cross-sectional cuts of these hyper-soft matrices as parallel sheets (images of the expanded universe). Later, we utilize these Hypersoft matrices to formulate** Plithogenic Subjective Crisp/Fuzzy/Intuitionistic/Neutrosophic Hyper-Super-Soft Matrix. **These matrices are framed by the generalization of Whole Hyper-Soft Set to Subjective Whole Hyper-Soft Set and then their representation in such** hyper-super-soft-matrix (**parallel sheets of matrices) whose elements are matrices. The Hypersoft matrices and hyper-super-soft matrices are tensors of rank three and four, respectively, having three and four indices of variations. Later we provide an application of these Plithogenic Hyper super soft matrices in the form of **Local, Global, Universal Subjective Ranking Model. **The specialty of this model is that it offers precise classification of the universe from micro-universe to macro-universe levels by observing them through several angles of visions in many environments having several ambiguities and hesitation levels. This model provides optimal and neutral values of universes and can compact the expanded universe to a single point in such a way that the compacted universe reflects the cumulative effect of the whole universe. It further offers a transparent ranking by giving a percentage authenticity measure of the ranking. Finally, we provide an application of the model as a numerical example.

**Keywords : **

Plithogenic Hyper-Super-Soft matrices , Sheets of matrices , Expanded Universe , Compacted Universe , Subjective , Local , Global , Universal Ranking ,

**References : **

[1] Smarandache, F. "A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability: Neutrsophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. Infinite Study", pp. 443-458, 2005.

[2] Atanassov , K. T, "Intuitionistic fuzzy sets. Fuzzy Sets and Systems", 20(1), pp. 87-96, 1986.

[3] Atanassov, K. T, "Applications of intuitionistic fuzzy sets”, In Intuitionistic Fuzzy Set, Series Studies in Fuzziness and Soft Computing", 35(1), pp. 237-238, 1999.

[4] Cagman N, Enginoglu S, Citak F,” Fuzzy soft set theory and its applications”, Iranian journal of fuzzy systems", 18,8(3), pp. 137-147, 2011.

[5] Molodtsov, D. "Soft set theory-First results, Computers and mathematics with applications", 37, pp.19-31, 1999.

[6] Pie, D and Miao, D, "From soft sets to informations systems”, In:Proceedings of Granular computing IEEE, 2, pp. 617-621, 2005.

[7] Zadeh, L. A "Fuzzy sets”, Inform and Control, 8(3), pp. 338-353, 1965.

[8] Kandasamy, W. V., & Smarandache, F, "Superbimatrices and their generalizations”, Infinite Study", 2009.

[9] Kandasamy, W. V., & Smarandache, F, "DSm Super Vector Space of Refined Labels”, Zip Publishing, 2011.

[10] Herrera, F., & Martínez, L, "A 2-tuple fuzzy linguistic representation model for computing with words”, IEEE Transactions on fuzzy systems, 8(6), pp. 746-752, 2000.

[11] Horst, P, "Matrix algebra for social scientists”, Holt, Rinehart and Winston, 1963.

[12] Onyeozili, I.A.,Gwary T.M, "A Study of The Fundamentals of Soft Set Theory”, International Journal of Scientific & Technology Research, (3), pp. 2277-8616, 2014.

[13] Nye, J. F, "Physical properties of crystals: their representation by tensors and matrices”, Oxford university press, 1985.

[14] Rana S, Qayyum M, Saeed M, Smarandache F, Khan BA," Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique”, Neutrosophic Sets and Systems, Vol. 28, pp.34-50, 2019.

[15] Smarandache, F,”Neutrosophic logic and set, mss”, 1995.

[16] Smarandache, F," Extension of soft Set to hypersoft Set, and then to plithogenic hypersoft Set”, Neutrosophic Sets and Systems, Vol. 22 ,pp.168-170, 2018.

[17] Smarandache, "Neutrosophic Set is a Generalization of Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set (Picture Fuzzy Set, Ternary Fuzzy Set), Pythagorean Fuzzy Set, Spherical Fuzzy Set, and q-Rung Orthopair Fuzzy Set, while Neutrosophication is a Generalization of Regret Theory, Grey System Theory, and Three-Ways Decision (revisited)”, Journal of New Theory, (29), pp. 1-31 , 2019

[18] de Sáa, S. D. L. R., Gil, M. Á., González-Rodríguez, G., López, M. T., & Lubiano, M. A, “Fuzzy rating scale-based questionnaires and their statistical analysis”, IEEE Transactions on Fuzzy Systems, 23(1), pp.111-126, 2014.

[19] Wang, W. P, "A fuzzy linguistic computing approach to supplier evaluation”, Applied Mathematical Modelling, 34(10), pp. 3130-3141, 2010.

[20] Khalid M, Khalid NA, Khalid H, Broumi S. “Multiplicative Interpretation of Neutrosophic Cubic Set on B-Algebra”, International Journal of Neutrosophic Science, Vol1, issue1.pp, 64-73, 2020.

[21] Smarandache F. "NeutroAlgebra is a Generalization of Partial Algebra”, International Journal of Neutrosophic Science, Volume 2 , Issue 1, pp. 08-17, 2020

[22] Prem. K , "Plithogenic set for multi-variable data analysis”, International Journal of Neutrosophic Science, Vol1, issue 2, pp, 82-89, 2020

[23] Deli I, Broumi S. "Neutrosophic soft matrices and NSM-decision making”, Journal of Intelligent & Fuzzy Systems, 1;28(5),pp.2233-2241, 2015.

[24] Deli I, Çağman N. "Intuitionistic fuzzy parameterized soft set theory and its decision making”, Applied Soft Computing, Vol1, issue, 28, pp.109-113, 2015.

[25] Broumi S., Dey A., Talea M., Bakali A., Smarandache F., Nagarajan D., Lathamaheswari M. and Kumar R., “Shortest Path Problem using Bellman Algorithm under Neutrosophic Environment”, Complex & Intelligent Systems, 5, pp.409–416, 2019. https://doi.org/10.1007/s40747-019-0101-8,

[26] Broumi S. , Talea M., Bakali A. , Smarandache F. , Nagarajan D., Lathamaheswari M. and Parimala M., “Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview”, Complex & Intelligent Systems, 5, pp.371–378, 2019.https://doi.org/10.1007/s40747-019-0098-z