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

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.

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Probabilistic Inference from Arbitrary Uncertainty using Mixtures of Factorized Generalized Gaussians

Journal of Artificial Intelligence Research ◽

10.1613/jair.533 ◽

1998 ◽

Vol 9 ◽

pp. 167-217 ◽

Cited By ~ 7

Author(s):

A. Ruiz ◽

P. E. Lopez-de-Teruel ◽

M. C. Garrido

Keyword(s):

Mixture Models ◽

Likelihood Function ◽

Finite Mixture Models ◽

Probabilistic Inference ◽

Joint Probability ◽

Alternative Methods ◽

Uncertain Information ◽

Wide Range ◽

Training Examples ◽

Comparative Results

This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both the joint probability density of the variables and the likelihood function of the (objective or subjective) observation are approximated by a special mixture model, in such a way that any desired conditional distribution can be directly obtained without numerical integration. We have developed an extended version of the expectation maximization (EM) algorithm to estimate the parameters of mixture models from uncertain training examples (indirect observations). As a consequence, any piece of exact or uncertain information about both input and output values is consistently handled in the inference and learning stages. This ability, extremely useful in certain situations, is not found in most alternative methods. The proposed framework is formally justified from standard probabilistic principles and illustrative examples are provided in the fields of nonparametric pattern classification, nonlinear regression and pattern completion. Finally, experiments on a real application and comparative results over standard databases provide empirical evidence of the utility of the method in a wide range of applications.

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Evidential Estimation of an Uncertain Mixed Exponential Distribution under Progressive Censoring

Entropy ◽

10.3390/e22101106 ◽

2020 ◽

Vol 22 (10) ◽

pp. 1106

Author(s):

Kuang Zhou ◽

Yimin Shi

Keyword(s):

Exponential Distribution ◽

Mixture Models ◽

Censored Data ◽

Likelihood Function ◽

Finite Mixture Models ◽

Expectation Maximization Algorithm ◽

Estimation Method ◽

Optimization Method ◽

Uncertain Information ◽

Mixed Exponential Distribution

In this paper, the evidential estimation method for the parameters of the mixed exponential distribution is considered when a sample is obtained from Type-II progressively censored data. Different from the traditional statistical inference methods for censored data from mixture models, here we consider a very general form where there is some uncertain information about the sub-class labels of units. The partially specified label information, as well as the censored data are represented in a united frame by mass functions within the theory of belief functions. Following that, the evidential likelihood function is derived based on the completely observed failures and the uncertain information included in the data. Then, the optimization method using the evidential expectation maximization algorithm (E2M) is introduced. A general form of the maximal likelihood estimates (MLEs) in the sense of the evidential likelihood, named maximal evidential likelihood estimates (MELEs), can be obtained. Finally, some Monte Carlo simulations are conducted. The results show that the proposed estimation method can incorporate more information than traditional EM algorithms, and this confirms the interest in using uncertain labels for the censored data from finite mixture models.

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The Improved Combination Rule of D Numbers and Its Application in Radiation Source Identification

Mathematical Problems in Engineering ◽

10.1155/2018/6025680 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 8

Author(s):

Xin Guan ◽

Haiqiao Liu ◽

Xiao Yi ◽

Jing Zhao

Keyword(s):

Source Identification ◽

Radiation Source ◽

Uncertain Information ◽

Practical Application ◽

Combination Rule ◽

Improved Method ◽

Dempster Shafer Theory ◽

Novel Theory ◽

Shafer Theory ◽

D Numbers

The D numbers theory is a novel theory to express uncertain information. It successfully overcomes some shortcomings of Dempster-Shafer theory, such as the conditions of exclusiveness hypothesis and completeness constraint. However, the combination rule of D numbers does not satisfy the associative property, which leads to limitations in practical application for D numbers. In this paper, the improved D numbers theory is proposed to overcome the weakness based on the analysis of D numbers’ combination rule. A new algorithm is constructed with the strict proof to simplify the combination rule. The similarities and differences among DS theory, D numbers, and the improved D numbers are introduced with the numerical analysis. An illustrative example of the radiation source identification is presented to demonstrate the effectiveness of the improved method.

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A hybrid multi-criteria decision making approach for assessing health-care waste management technologies based on soft likelihood function and D-numbers

Applied Intelligence ◽

10.1007/s10489-020-02148-7 ◽

2021 ◽

Author(s):

Xiangjun Mi ◽

Ye Tian ◽

Bingyi Kang

Keyword(s):

Health Care ◽

Decision Making ◽

Waste Management ◽

Likelihood Function ◽

Multi Criteria Decision Making ◽

Health Care Waste ◽

D Numbers

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New Failure Mode and Effects Analysis based on D Numbers Downscaling Method

International Journal of Computers Communications & Control ◽

10.15837/ijccc.2018.2.2990 ◽

2018 ◽

Vol 13 (2) ◽

pp. 205-220 ◽

Cited By ~ 12

Author(s):

Baoyu Liu ◽

Yong Hu ◽

Yong Deng

Keyword(s):

Risk Factors ◽

Risk Assessment ◽

Computational Complexity ◽

Failure Mode ◽

High Efficiency ◽

Uncertain Information ◽

Risk Priority Number ◽

Mutual Exclusivity ◽

Downscaling Method ◽

D Numbers

Failure mode and effects analysis (FMEA) is extensively applied to process potential faults in systems, designs, and products. Nevertheless, traditional FMEA, classical risk priority number (RPN), acquired by multiplying the ratings of occurrence, detection, and severity, risk assessment, is not effective to process the uncertainty in FMEA. Many methods have been proposed to solve the issue but deficiencies exist, such as huge computing quality and the mutual exclusivity of propositions. In fact, because of the subjectivity of experts, the boundary of two adjacent evaluation ratings is fuzzy so that the propositions are not mutually exclusive. To address the issues, in this paper, a new method to evaluate risk in FMEA based on D numbers and evidential downscaling method, named as D numbers downscaling method, is proposed. In the proposed method, D numbers based on the data are constructed to process uncertain information and aggregate the assessments of risk factors, for they permit propositions to be not exclusive mutually. Evidential downscaling method decreases the number of ratings from 10 to 3, and the frame of discernment from 2^{10} to 2^3 , which greatly reduce the computational complexity. Besides, a numerical example is illustrated to validate the high efficiency and feasibility of the proposed method.

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AN EVALUATION FOR SUSTAINABLE MOBILITY EXTENDED BY D NUMBERS

Technological and Economic Development of Economy ◽

10.3846/tede.2019.10293 ◽

2019 ◽

Vol 25 (5) ◽

pp. 802-819 ◽

Cited By ~ 33

Author(s):

Hongming Mo ◽

Yong Deng

Keyword(s):

Decision Making ◽

Multiple Criteria Decision Making ◽

New Method ◽

Uncertain Information ◽

Mathematical Tool ◽

Sustainable Mobility ◽

Numerical Example ◽

Open Issue ◽

The Impact ◽

D Numbers

How to evaluate the impact of transport measures on city sustainability effectively is still an open issue, and it can be abstracted as one of the multiple criteria decision making problems. In this paper, a new method based on D numbers is proposed to evaluate the sustainable mobility of city. D number is a new mathematical tool to represent and deal uncertain information. The property of integration of D numbers is employed to fusion information. A numerical example of carsharing demonstrates the effectiveness of the proposed method.

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