Decision-Making Method of Qualitative and Quantitative Comprehensive Evaluation of Talents Based on Probability Hesitation Fuzzy Language

A scientific, reasonable, and novel talent evaluation index system is the foundation of talent training and selection. Based on the novel “Man-Machine-Environment System Engineering” (hereinafter referred to as MMESE) theory, this paper proposes a novel talent evaluation index system that considers the ontological attributes and the external environment of the object comprehensively for talent evaluation, which could help the evaluator obtain more accurate evaluation results. Since the comprehensive evaluation of MMESE talents is a complex decision-making problem that is both qualitative and quantitative, a corresponding decision-making method that integrates qualitative and quantitative approaches is proposed here based on probabilistic language entropy and the possibility of superior order relationships. First, the weights of quantitative and qualitative attributes are calculated based on entropy theory and probabilistic fuzzy language. Second, the standard weight vectors of qualitative and quantitative attributes are obtained by adjusting the weight integration coefficients, and the change intervals of the pros and cons between the objects to be evaluated are calculated. Third, the pros and cons of the objects to be evaluated are compared to obtain the possibility degree matrix that describes the priority relationships among the objects, and a ranking vector is derived from the possibility degree matrix to reflect the rankings of the objects’ pros and cons. Finally, this system and the decision-making methods have been verified as scientific and effective.

A α -Spectral Characterizations of Some Joins

Let G be a graph with n vertices. For every real α ∈ 0,1 , write A α G for the matrix A α G = α D G + 1 − α A G , where A G and D G denote the adjacency matrix and the degree matrix of G , respectively. The collection of eigenvalues of A α G together with multiplicities are called the A α -spectrum of G . A graph G is said to be determined by its A α -spectrum if all graphs having the same A α -spectrum as G are isomorphic to G . In this paper, we show that some joins are determined by their A α -spectra for α ∈ 0 , 1 / 2 or 1 / 2 , 1 .

A Note on Some Bounds of the α-Estrada Index of Graphs

Let G be a simple graph with n vertices. Let A~αG=αDG+1−αAG, where 0≤α≤1 and AG and DG denote the adjacency matrix and degree matrix of G, respectively. EEαG=∑i=1neλi is called the α-Estrada index of G, where λ1,⋯,λn denote the eigenvalues of A~αG. In this paper, the upper and lower bounds for EEαG are given. Moreover, some relations between the α-Estrada index and α-energy are established.

A tutorial and tool for exploring feature similarity gradients with MRI data

There has been an increasing interest in examining organisational principles of the cerebral cortex (and subcortical regions) using different MRI features such as structural or functional connectivity. Despite the widespread interest, however, an introductory and intuitive review on the underlying technique for the neuroimaging community is lacking in the literature.Articles that investigate “neural gradients” have increased in popularity. Thus, we believe that it is opportune to discuss what is generally meant by “gradient analysis”. We introduce basics concepts in graph theory, such as graphs themselves, the degree matrix, and the adjacency matrix. We discuss how one can think about gradients of feature similarity using graph theory and we extend this to explore such gradients across the whole MRI scale; from the voxel level to the whole brain level. We proceed to introduce a measure for quantifying the level of similarity in regions of interest. We propose the term “the Vogt-Bailey index” for such quantification to pay homage to our history as a brain mapping community.We run through the techniques on a sample brain MRI dataset as an example of theapplication of the techniques on real data and we provide several appendices that expand upon details. To maximise intuition, the appendices contain a didactic example describing how one could use these techniques to solve a particularly pernicious problem that one may encounter at a wedding. Accompanying the article is a tool, available in both MATLAB and Python, that enables readers to perform the analysis described in this article on their own data.We refer readers to the graphical abstract as an overview of the analysis pipeline presented in this work.

Divisor Degree Energy of Some Graphs using Mat Lab Programme

In this paper, we find the divisor degree matrix of wheel, fan, complete bipartite and splitting graph of star graph and generate their divisor degree energy. Also, we obtain the divisor degree matrix of a tree graphs such as path, star and comb graph and their divisor degree energy by using MAT LAB programme.

Generalized Permanental Polynomials of Graphs

The search for complete graph invariants is an important problem in graph theory and computer science. Two networks with a different structure can be distinguished from each other by complete graph invariants. In order to find a complete graph invariant, we introduce the generalized permanental polynomials of graphs. Let G be a graph with adjacency matrix A ( G ) and degree matrix D ( G ) . The generalized permanental polynomial of G is defined by P G ( x , μ ) = per ( x I − ( A ( G ) − μ D ( G ) ) ) . In this paper, we compute the generalized permanental polynomials for all graphs on at most 10 vertices, and we count the numbers of such graphs for which there is another graph with the same generalized permanental polynomial. The present data show that the generalized permanental polynomial is quite efficient for distinguishing graphs. Furthermore, we can write P G ( x , μ ) in the coefficient form ∑ i = 0 n c μ i ( G ) x n − i and obtain the combinatorial expressions for the first five coefficients c μ i ( G ) ( i = 0 , 1 , ⋯ , 4 ) of P G ( x , μ ) .

Bounds of Laplacian Energy of a Hypercube Graph

Let Qn denote the n – dimensional hypercube with order 2n and size n2n-1. The Laplacian L is defined by L = D where D is the degree matrix and A is the adjacency matrix with zero diagonal entries. The Laplacian is a symmetric positive semidefinite. Let µ1 ≥ µ2 ≥ ....µn-1 ≥ µn = 0 be the eigen values of the Laplacian matrix. The Laplacian energy is defined as LE(G) = . In this paper, we defined Laplacian energy of a Hypercube graph and also attained the lower bounds.