BIPOLAR PICTURE FUZZY DOMBI WEIGHTED GEOMETRIC OPERATOR AND ITS APPLICATION

2020 ◽  
Vol 7 (10) ◽  
Keyword(s):  
2017 ◽  
Vol 59 (3) ◽  
pp. 743-751
Author(s):  
SHOUWEN FANG ◽  
FEI YANG ◽  
PENG ZHU

AbstractLet (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Ricci flow. In the paper, we prove that the eigenvalues of geometric operator −Δφ + $\frac{R}{2}$ are non-decreasing under the Ricci flow for manifold M with some curvature conditions, where Δφ is the Witten Laplacian operator, φ ∈ C2(M), and R is the scalar curvature with respect to the metric g(t). We also derive the evolution of eigenvalues under the normalized Ricci flow. As a consequence, we show that compact steady Ricci breather with these curvature conditions must be trivial.


2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Muhammad Akram ◽  
Naveed Yaqoob ◽  
Ghous Ali ◽  
Wathek Chammam

An m-polar fuzzy set is a powerful mathematical model to analyze multipolar, multiattribute, and multi-index data. The m-polar fuzzy sets have appeared as a useful tool to portray uncertainty in multiattribute decision making. The purpose of this article is to analyze the aggregation operators under the m-polar fuzzy environment with the help of Dombi norm operations. In this article, we develop some averaging and geometric aggregation operators using Dombi t-norm and t-conorm to handle uncertainty in m-polar fuzzy (mF, henceforth) information, which are mF Dombi weighted averaging (mFDWA) operator, mF Dombi ordered weighted averaging (mFDOWA) operator, mF Dombi hybrid averaging (mFDHA) operator, mF Dombi weighted geometric (mFDWG) operator, mF Dombi weighted ordered geometric operator, and mF Dombi hybrid geometric (mFDHG) operator. We investigate properties, namely, idempotency, monotonicity, and boundedness, for the proposed operators. Moreover, we give an algorithm to solve multicriteria decision-making issues which involve mF information with mFDWA and mFDWG operators. To prove the validity and feasibility of the proposed model, we solve two numerical examples with our proposed models and give comparison with mF-ELECTRE-I approach (Akram et al. 2019) and mF Hamacher aggregation operators (Waseem et al. 2019). Finally, we check the effectiveness of the developed operators by a validity test.


Author(s):  
Lihua Liu ◽  
Jing Huang ◽  
Huimin Wang

In the real decision-making process, there are so many time series values that need to be aggregated. In this paper, a visibility graph power geometric (VGPG) aggregation operator is developed, which is based on the complex network and power geometric operator. Time series data are converted into a visibility graph. A visibility matrix is developed to denote the links among different time series values. A new support function based on the distance of two values are proposed to measure the support degree of each other when the two time series values have visibility. The VGPG operator considers not only the relationship but also the similarity degree between two values. Meanwhile, some properties of the VGPG operator are also investigated. Finally, a case study for water, energy, and food coupling efficiency evaluation in China is illustrated to show the effectiveness of the proposed operator. Comparative analysis with the existing research is also offered to show the advantages of the proposed method.


Author(s):  
Z. S. XU

Linguistic information aggregation has received great attention from researchers, and a variety of operators have been developed for aggregating linguistic information. All the existing linguistic information aggregation operators only consider the situations where all the aggregated linguistic arguments are independent, i.e., they only consider the addition of the importance of individual linguistic arguments, however, in some actual situations, the considered linguistic arguments may be correlative. In this paper, we focus on this issue. Motivated by the idea of the well-known Choquet integrals,1 we propose two new linguistic information aggregation operators called the linguistic correlated averaging operator and linguistic correlated geometric operator. In the special cases where the aggregated linguistic arguments are independent, the linguistic correlated averaging operator can be reduced to a variety of traditional linguistic averaging aggregation operators; while the linguistic correlated geometric operator can be reduced to a variety of the traditional linguistic geometric aggregation operators. Furthermore, we extend the above results to accommodate uncertain linguistic environments, and illustrate them with a practical problem.


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