The $D$ numbers and the central factorial numbers

2011 ◽  
Vol 79 (1-2) ◽  
pp. 41-53 ◽  
Author(s):  
GUODONG LIU
Keyword(s):  
Central Factorial Numbers ◽  
D Numbers

Identities related to special polynomials and combinatorial numbers

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4833-4844 ◽  
Author(s):  
Eda Yuluklu ◽  
Yilmaz Simsek ◽  
Takao Komatsu
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Euler Numbers ◽  
Special Polynomials ◽  
Central Factorial Numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

A New Intelligent MCDM Model for HCW Management: The Integrated BWM–MABAC Model Based on D Numbers

2021 ◽  
pp. 114862
Author(s):  
Dragan Pamučar ◽  
Adis Puška ◽  
Željko Stević ◽  
Goran Ćirović
Keyword(s):  
Model Based ◽  
D Numbers

scholarly journals A MODIFIED D NUMBERS METHODOLOGY FOR ENVIRONMENTAL IMPACT ASSESSMENT

2017 ◽  
Vol 24 (2) ◽  
pp. 653-669 ◽  
Author(s):  
Ningkui WANG ◽  
Daijun WEI
Keyword(s):  
Environmental Impact ◽  
Impact Assessment ◽  
Environmental Impact Assessment ◽  
Previous Method ◽  
Combination Process ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
D Numbers ◽  
Commutative Property

Environmental impact assessment (EIA) is usually evaluated by many factors influenced by various kinds of uncertainty or fuzziness. As a result, the key issues of EIA problem are to rep­resent and deal with the uncertain or fuzzy information. D numbers theory, as the extension of Dempster-Shafer theory of evidence, is a desirable tool that can express uncertainty and fuzziness, both complete and incomplete, quantitative or qualitative. However, some shortcomings do exist in D numbers combination process, the commutative property is not well considered when multiple D numbers are combined. Though some attempts have made to solve this problem, the previous method is not appropriate and convenience as more information about the given evaluations rep­resented by D numbers are needed. In this paper, a data-driven D numbers combination rule is proposed, commutative property is well considered in the proposed method. In the combination process, there does not require any new information except the original D numbers. An illustrative example is provided to demonstrate the effectiveness of the method.

scholarly journals A Novel Integration Method for D Numbers Based on Horizontal Comparison

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 312
Author(s):  
Haiyang Hou ◽  
Chunyu Zhao
Keyword(s):  
User Experience ◽  
Integration Method ◽  
Mutual Exclusion ◽  
Evidence Theory ◽  
Uncertainty Modelling ◽  
Missing Information ◽  
New Type ◽  
Evaluation Problem ◽  
D Numbers

D numbers theory is an extension of Dempster–Shafer evidence theory. It eliminates the constraints of mutual exclusion and completeness under the frame of discernment of Dempster–Shafer evidence theory, so it has been widely used to deal with uncertainty modelling, but if it cannot effectively deal with the problem of missing information, sometimes unreasonable conclusions will be drawn. This paper proposes a new type of integration representation of D numbers, which compares the data of multiple evaluation items horizontally, and can reasonably fill in missing information. We apply this method to the user experience evaluation problem of online live course platform to verify the effectiveness of this method.

scholarly journals Distance Metrics of D Numbers

2020 ◽  
Author(s):  
Liguo Fei ◽  
Yuqiang Feng
Keyword(s):  
Number Theory ◽  
Incomplete Information ◽  
Distance Function ◽  
Distance Measure ◽  
Complete Information ◽  
Belief Function ◽  
Distance Metrics ◽  
Modeling Methods ◽  
The Difference ◽  
D Numbers

Belief function has always played an indispensable role in modeling cognitive uncertainty. As an inherited version, the theory of D numbers has been proposed and developed in a more efficient and robust way. Within the framework of D number theory, two more generalized properties are extended: (1) the elements in the frame of discernment (FOD) of D numbers do not required to be mutually exclusive strictly; (2) the completeness constraint is released. The investigation shows that the distance function is very significant in measuring the difference between two D numbers, especially in information fusion and decision. Modeling methods of uncertainty that incorporate D numbers have become increasingly popular, however, very few approaches have tackled the challenges of distance metrics. In this study, the distance measure of two D numbers is presented in cases, including complete information, incomplete information, and non-exclusive elements

scholarly journals On Central Complete and Incomplete Bell Polynomials I

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 288 ◽  
Author(s):  
Taekyun Kim ◽  
Dae Kim ◽  
Gwan-Woo Jang
Keyword(s):  
Bell Polynomials ◽  
Explicit Formulas ◽  
Central Factorial Numbers

In this paper, we introduce central complete and incomplete Bell polynomials which can be viewed as generalizations of central Bell polynomials and central factorial numbers of the second kind, and also as ’central’ analogues for complete and incomplete Bell polynomials. Further, some properties and identities for these polynomials are investigated. In particular, we provide explicit formulas for the central complete and incomplete Bell polynomials related to central factorial numbers of the second kind.

On entropy function and reliability indicator for D numbers

2019 ◽  
Vol 49 (9) ◽  
pp. 3248-3266 ◽  
Author(s):  
Jun Xia ◽  
Yuqiang Feng ◽  
Luning Liu ◽  
Dongjun Liu ◽  
Liguo Fei
Keyword(s):  
Entropy Function ◽  
Reliability Indicator ◽  
D Numbers

scholarly journals The Stellar Data File at Dearborn Observatory

1982 ◽  
Vol 64 ◽  
pp. 49-50
Author(s):  
William Buscombe
Keyword(s):  
Data File ◽  
Right Ascension ◽  
D Numbers

The majority of entries for MK Spectral Classifications in the Kennedy & Buscombe (1974) catalogue referred to stars brighter than 9th magnitude with H. D. numbers. Accordingly, the file was arranged in sequence corresponding to right ascension for 1900, although the co-ordinates were actually listed for the epoch 2000, in accordance with an earlier precept established in the IAU.

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