396 238
Full Length Article
Volume 6 , Issue 2, PP: 56-79 , 2020

Title

Plithogenic Subjective Hyper-Super-Soft Matrices with New Definitions & Local, Global, Universal Subjective Ranking Model

Authors Names :   Shazia Rana   1 *     Muhammad Saeed   2     Midha Qayyum   3     Florentin Smarandache   4  

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



Doi   :  10.5281/zenodo.3841624


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 ,

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