MADA problem: A new scheme based on D numbers and aggregation functions

2021 ◽  
pp. 1-25
Author(s):  
Xiangjun Mi ◽  
Ye Tian ◽  
Bingyi Kang
Keyword(s):  
Likelihood Function ◽  
Evidence Theory ◽  
Decision Makers ◽  
Uncertain Information ◽  
Excellent Performance ◽  
Likelihood Functions ◽  
Aggregation Functions ◽  
Reliability Characteristics ◽  
Novel Model ◽  
D Numbers

Describing and processing complex as well as ambiguous and uncertain information has always been an inescapable and challenging topic in multi-attribute decision analysis (MADA) problems. As an extension of Dempster-Shafer (D-S) evidence theory, D numbers breaks through the constraints of the constraint framework and is a new way of expressing uncertainty. The soft likelihood function based on POWA operator is one of the most useful tools recently developed for dealing with uncertain information, since it provides a more excellent performance for the aggregation of multiple compatible evidence. Recently, a new MADA model based on D numbers has been proposed, called DMADA. In this paper, inspired by the above mentioned theories, based on soft likelihood functions, POWA aggregation and D numbers we design a novel model to improve the performance of representing and processing uncertain information in MADA problems as an improvement of the DMADA approach. In contrast, our advantages include mainly the following. Firstly, the proposed method considers the reliability characteristics of each initial D number information. Secondly, the proposed method empowers decision makers with the possibility to express their perceptions through attitudinal features. In addition, an interesting finding is that the preference parameter in the proposed method can clearly distinguish the variability between candidates by adjusting the space values between adjacent alternatives, making the decision results clearer. Finally, the effectiveness and superiority of this model are proved through analysis and testing.

A New Soft Likelihood Function Based on D Numbers in Handling Uncertain Information

2020 ◽  
Vol 22 (7) ◽  
pp. 2333-2349 ◽  
Author(s):  
Ye Tian ◽  
Xiangjun Mi ◽  
Lili Liu ◽  
Bingyi Kang
Keyword(s):  
Likelihood Function ◽  
Uncertain Information ◽  
D Numbers

scholarly journals Health Monitoring and Diagnosis of Equipment Based on Multi-sensor Fusion

2018 ◽  
Vol 14 (04) ◽  
pp. 4
Author(s):  
Xuemei Yao ◽  
Shaobo Li ◽  
Yong Yao ◽  
Xiaoting Xie
Keyword(s):  
Evidence Theory ◽  
Sensor Data ◽  
Uncertain Information ◽  
Fusion Algorithm ◽  
Monitoring And Diagnosis ◽  
Multi Sensor Data Fusion ◽  
Basic Probability ◽  
Optimal Fusion ◽  
Single Sensor ◽  
Mechanical Devices

As the information measured by a single sensor cannot reflect the real situation of mechanical devices completely, a multi-sensor data fusion based on evidence theory is introduced. Evidence theory has the advantage of dealing with uncertain information. However, it produces unreasonable conclusions when the evidence conflicts. An improved fusion method is proposed to solve this problem. Basic probability assignment of evidence is corrected according to evidence and sensor weights, and an optimal fusion algorithm is selected by comparing an introduced threshold and a conflict factor. The effectiveness and practicability of the algorithm are tested by simulating the monitoring and diagnosis of rolling bearings. The result shows that the method has better robustness.

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 Evidence Theory in Picture Fuzzy Set Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Harish Garg ◽  
R. Sujatha ◽  
D. Nagarajan ◽  
J. Kavikumar ◽  
Jeonghwan Gwak
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Evidence Theory ◽  
Belief Function ◽  
Uncertain Information ◽  
Interval Probability ◽  
Dempster Shafer Theory ◽  
Effective Manner ◽  
Picture Fuzzy Set ◽  
Shafer Theory

Picture fuzzy set is the most widely used tool to handle the uncertainty with the account of three membership degrees, namely, positive, negative, and neutral such that their sum is bound up to 1. It is the generalization of the existing intuitionistic fuzzy and fuzzy sets. This paper studies the interval probability problems of the picture fuzzy sets and their belief structure. The belief function is a vital tool to represent the uncertain information in a more effective manner. On the other hand, the Dempster–Shafer theory (DST) is used to combine the independent sources of evidence with the low conflict. Keeping the advantages of these, in the present paper, we present the concept of the evidence theory for the picture fuzzy set environment using DST. Under this, we define the concept of interval probability distribution and discuss its properties. Finally, an illustrative example related to the decision-making process is employed to illustrate the application of the presented work.

A Multi-Criteria Intuitionistic Fuzzy Group Decision Making Method for Supplier Selection with VIKOR Method

2012 ◽  
pp. 967-983
Author(s):  
Razieh Roostaee ◽  
Mohammad Izadikhah ◽  
Farhad Hosseinzadeh Lotfi ◽  
Mohsen Rostamy-Malkhalifeh
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Supplier Selection ◽  
Group Decision ◽  
Decision Makers ◽  
Uncertain Information ◽  
Vikor Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Right

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain, and is typically a multi-criteria group decision problem. In many practical situations, there usually exists incomplete and uncertain information, and the decision makers cannot easily express their judgments on the candidates with exact and crisp values. Therefore, in this paper an extended VIKOR method for group decision making with intuitionistic fuzzy numbers is proposed to solve the supplier selection problem under incomplete and uncertain information environment. In other researches in this area, the weights of each decision makers and in many of them the weights of criteria are pre-determined, but these weights have been calculated in this paper by using the decision matrix of each decision maker. Also, normalized Hamming distance is proposed to calculate the distance between intuitionistic fuzzy numbers. Finally, a numerical example for supplier selection is given to clarify the main results developed in this paper.

“World of Uncertainty” Game for Decision-Makers

2012 ◽  
pp. 46-51
Author(s):  
Jyldyz Tabyldy Kyzy
Keyword(s):  
Learning Effect ◽  
Computer Game ◽  
Decision Makers ◽  
Uncertain Information ◽  
Online Game ◽  
Subjective Uncertainty ◽  
The World ◽  
More Care ◽  
To Receive ◽  
Explicit Feedback

Decisions on both personal and public matters benefit significantly if uncertainties and risks are handled with more care and accuracy. It is crucial to refine and express degrees of confidence and subjective probabilities of various outcomes. Experience, intuition, and skills help make the most of uncertain information. This paper proposes a concept and design of a computer game which aims to train and enhance some of these skills. It is an online game, which allows players to indicate their subjective uncertainty on a numerical scale and to receive explicit feedback. The accuracy of the player is conditioned and motivated by the incentives based on proper scoring rules. The game aims to train accuracy and better calibration in estimating probabilities and expressing degrees of confidence. The “World of Uncertainty” (n.d.) project researched the learning effect of the game and its impact on players’ attitudes towards uncertainty. The concept of this game can be adopted as part of an advanced and complex game in the future.

scholarly journals Incomplete Information Management Using an Improved Belief Entropy in Dempster-Shafer Evidence Theory

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 993 ◽  
Author(s):  
Bin Yang ◽  
Dingyi Gan ◽  
Yongchuan Tang ◽  
Yan Lei
Keyword(s):  
Data Fusion ◽  
Incomplete Information ◽  
Information Fusion ◽  
Evidence Theory ◽  
Sensor Data ◽  
Uncertain Information ◽  
Open World ◽  
Belief Entropy ◽  
Open World Assumption ◽  
Deng Entropy

Quantifying uncertainty is a hot topic for uncertain information processing in the framework of evidence theory, but there is limited research on belief entropy in the open world assumption. In this paper, an uncertainty measurement method that is based on Deng entropy, named Open Deng entropy (ODE), is proposed. In the open world assumption, the frame of discernment (FOD) may be incomplete, and ODE can reasonably and effectively quantify uncertain incomplete information. On the basis of Deng entropy, the ODE adopts the mass value of the empty set, the cardinality of FOD, and the natural constant e to construct a new uncertainty factor for modeling the uncertainty in the FOD. Numerical example shows that, in the closed world assumption, ODE can be degenerated to Deng entropy. An ODE-based information fusion method for sensor data fusion is proposed in uncertain environments. By applying it to the sensor data fusion experiment, the rationality and effectiveness of ODE and its application in uncertain information fusion are verified.

scholarly journals A New Evaluation Methodology for Quality Goals Extended by D Number Theory and FAHP

Information ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 206
Author(s):  
Hongming Mo
Keyword(s):  
Number Theory ◽  
Process Management ◽  
Evidence Theory ◽  
Evaluation Methodology ◽  
Uncertain Information ◽  
Mathematical Tool ◽  
Analytic Hierarchy ◽  
Multi Attribute Decision Making ◽  
Hierarchy Process ◽  
Evaluation Information

Evaluation of quality goals is an important issue in process management, which essentially is a multi-attribute decision-making (MADM) problem. The process of assessment inevitably involves uncertain information. The two crucial points in an MADM problem are to obtain weight of attributes and to handle uncertain information. D number theory is a new mathematical tool to deal with uncertain information, which is an extension of evidence theory. The fuzzy analytic hierarchy process (FAHP) provides a hierarchical way to model MADM problems, and the comparison analysis among attributes is applied to obtain the weight of attributes. FAHP uses a triangle fuzzy number rather than a crisp number to represent the evaluation information, which fully considers the hesitation to give a evaluation. Inspired by the features of D number theory and FAHP, a D-FAHP method is proposed to evaluate quality goals in this paper. Within the proposed method, FAHP is used to obtain the weight of each attribute, and the integration property of D number theory is carried out to fuse information. A numerical example is presented to demonstrate the effectiveness of the proposed method. Some necessary discussions are provided to illustrate the advantages of the proposed method.

scholarly journals The estimation of the uncertainty associated with rating curves of the river Ivinhema in the state of Paraná/Brazil

2018 ◽  
Vol 40 ◽  
pp. 06029
Author(s):  
Luiz Henrique Maldonado ◽  
Daniel Firmo Kazay ◽  
Elio Emanuel Romero Lopez
Keyword(s):  
Bayesian Inference ◽  
Likelihood Function ◽  
The State ◽  
Likelihood Estimator ◽  
Likelihood Functions ◽  
Important Impact ◽  
Rating Curves

The estimation of the uncertainty associated with stage-discharge relations is a challenge to the hydrologists. Bayesian inference with likelihood estimator is a promissory approach. The choice of the likelihood function has an important impact on the capability of the model to represent the residues. This paper aims evaluate two likelihood functions with DREAM algorithm to estimate specific non-unique stage-discharge rating curves: normal likelihood function and Laplace likelihood function. The result of BaRatin is also discussed. The MCMC of the DREAM and the BaRatin algorithm have been compared and its results seem consistent for the studied case. The Laplace likelihood function presented as good results as normal likelihood function for the residues. Other gauging stations should be evaluated to attend more general conclusions.

Objective Inference for Climate Parameters: Bayesian, Transformation-of-Variables, and Profile Likelihood Approaches

2014 ◽  
Vol 27 (19) ◽  
pp. 7270-7284 ◽  
Author(s):  
Nicholas Lewis
Keyword(s):  
Climate Sensitivity ◽  
Bayesian Methods ◽  
Likelihood Function ◽  
Profile Likelihood ◽  
Likelihood Method ◽  
Jeffreys Prior ◽  
Bayesian Approaches ◽  
Noninformative Priors ◽  
Likelihood Functions ◽  
Transformation Of Variables

Abstract Insight is provided into the use of objective-Bayesian methods for estimating climate sensitivity by considering their relationship to transformations of variables in the context of a simple case considered in a previous study, and some misunderstandings about Bayesian inference are discussed. A simple model in which climate sensitivity (S) and effective ocean heat diffusivity (Kυ) are the only parameters varied is used, with twentieth-century warming attributable to greenhouse gases (AW) and effective ocean heat capacity (HC) being the only data-based observables. Probability density functions (PDFs) for AW and HC are readily derived that represent valid independent objective-Bayesian posterior PDFs, provided the error distribution assumptions involved in their construction are justified. Using them, a standard transformation of variables provides an objective joint posterior PDF for S and Kυ; integrating out Kυ gives a marginal PDF for S. Close parametric approximations to the PDFs for AW and HC are obtained, enabling derivation of likelihood functions and related noninformative priors that give rise to the objective posterior PDFs that were computed initially. Bayes’s theorem is applied to the derived AW and HC likelihood functions, demonstrating the effect of differing prior distributions on PDFs for S. Use of the noninformative Jeffreys prior produces an identical PDF to that derived using the transformation-of-variables approach. It is shown that similar inference for S to that based on these two alternative objective-Bayesian approaches is obtained using a profile likelihood method on the derived joint likelihood function for AW and HC.

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