How lower approximation and discernibility matrix are computed in fuzzy model of Rough set?

More Arnab Sadhu's questions See All

F statistics v/s the number of clusters

In a dataset, F-statistics is inversely proportional to the number of clusters. It suggests that within cluster variance gets increased with the number of clusters. What does it suggests??

04 May 2016 1,624 3 View

Basis set and input instruction to calculate HOMO and LUMO using Orca for Imidazolium based organic salts?

Hey there, As a synthetic chemist delving into theoretical calculations for my imidazolium-based organic molecules, I would greatly appreciate any guidance on the appropriate input instructions...

09 August 2024 5,444 7 View

How to define an anisotropic material with asymmetric elastic compliance/stiffness matrix in ANSYS APDL?

I need to model an anisotropic material in which the Poisson's ratio ν_12 ≠ ν_21 and so on. Therefore, the elastic compliance matrix wouldn't be a symmetric one. In ANSYS APDL, for TB,ANEL...

09 August 2024 5,048 2 View

Is it true that $\det(V(A))$ may be only $\pm 1$, depending on $n$, for the last symmetric tridiagonal matrix $A$?

One can try to generalize the Vandermonde determinant in the following direction: Let $A$ be any symmetric $n$-order square matrix. Consider its powers' diagonal elements $(A^k)_{ii}$ and...

08 August 2024 6,690 1 View

Usage of internal standards in LC-MS/MS analysis?

Have you ever seen a LC-MS/MS method uses both internal standards and external standards (in matrix matching purpose) but the concentrations of internal standards are outside the calibration curve...

05 August 2024 3,084 6 View

Request a single Lecture notes for math as detailed as this that I can find in one place?

- The Existence/Uniqueness of Solutions to Higher Order Linear Differential Equations - Higher Order Homogenous Differential Equations - Wronskian Determinants of $n$ Functions - Wronskian...

03 August 2024 2,366 0 View

Tissue homogenization in mouse with FastPrep-24™ 5G - is the D matrix system useful?

I need to lyse and homogenise mouse tissues. So far I have experimented with liver and lung tissue, using matrix D. The liver was completely lysed with 6 repetitions of the standard program, but...

31 July 2024 9,186 0 View

Is it true that science is leaving the era of mathematics and entering the era of matrix mechanics?

We assume this to be true. Science leaves the era of mathematics and enters the era of matrix mechanics and the turning point is the discovery of numerical statistical theory called Cairo...

31 July 2024 3,900 2 View

Help on understanding the implementation of Mori Tanaka method on MATLAB?

I am new to Micromechanics and having similar problem with understanding the implementation of the formula's. I would appreciate if anyone can guide me on how to go about getting a scalar value...

30 July 2024 969 0 View

Difficulty with permittivitt and Magnetic Permeability Calculations?

Difficulty with permittivitt and Magnetic Permeability Calculations Hello everyone, I have all the parameters related to the calculations of the permittivitty and magnetic permeability...

30 July 2024 5,206 1 View

How to use Desmond in HPC ?

Our department has recently acquired an HPC (High-Performance Computing) system, and I'm thrilled to take my molecular dynamics calculations to the next level using Desmond. I used to run my...

28 July 2024 6,553 1 View

James F Peters

This is a very good question.

For an overview of research on rough sets that includes questions, research projects and publications that include a fuzzy approach, see

https://www.researchgate.net/topic/Rough-Set-Theory

Arnab Sadhu

Thanks, Prof. J F Peters, for the response. Actually, I wanted to know how exactly the lower approximation of similarity, i.e. Sim(R)_(A)(x) is calculated from Sim(R)(xi,xj) in the paper attached.