TWO GENERALIZATIONS OF AGGREGATED UNCERTAINTY MEASURE FOR EVALUATION OF DEZERT–SMARANDACHE THEORY

2012 ◽  
Vol 11 (01) ◽  
pp. 119-142 ◽  
Author(s):  
MAHDI KHODABANDEH ◽  
ALIREZA MOHAMMAD-SHAHRI
Keyword(s):  
Decision Making ◽  
Belief Function ◽  
Localization Problem ◽  
Uncertainty Measure ◽  
Total Uncertainty ◽  
Dempster Shafer Theory ◽  
Uncertainty Measures ◽  
The Difference ◽  
Shafer Theory

Generality of the model which is used in Dezert–Smarandache Theory (DSmT) rather than other fusion algorithms such as Dempster–Shafer theory and capability of DSmT for dealing with highly conflict problems are two main reasons to prefer DSmT for decision-making systems. Aggregated uncertainty measure, which is called AU measure, has been introduced for Dempster–Shafer theory as one of the best presented ways to quantify the total uncertainty or the ambiguity of a belief function. Since AU cannot be applied to DSmT, two generalized aggregated uncertainty measures for DSmT, which are called GAU1 measure and GAU2 measure, are proposed in this paper. The GAU1 measure is developed by extension of the frame of discernment with distinct sub-events. The GAU2 measure is developed by considering new conditions on probability assignments which are used in the uncertainty measure. The new conditions are the difference of this measure with AU measure. A rigorous discussion is presented to validate that the proposed uncertainty measures holds on the requirements for an uncertainty measure. Finally evaluation of uncertainty in a DSmT-based localization problem is presented to show how to apply the generalized uncertainty measures, GAU1 and GAU2.

scholarly journals An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1122 ◽  
Author(s):  
Yonggang Zhao ◽  
Duofa Ji ◽  
Xiaodong Yang ◽  
Liguo Fei ◽  
Changhai Zhai
Keyword(s):  
Belief Function ◽  
Total Uncertainty ◽  
Probability Assignment ◽  
Basic Probability Assignment ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Shafer Theory ◽  
Deng Entropy

It is still an open issue to measure uncertainty of the basic probability assignment function under Dempster-Shafer theory framework, which is the foundation and preliminary work for conflict degree measurement and combination of evidences. This paper proposes an improved belief entropy to measure uncertainty of the basic probability assignment based on Deng entropy and the belief interval, which takes the belief function and the plausibility function as the lower bound and the upper bound, respectively. Specifically, the center and the span of the belief interval are employed to define the total uncertainty degree. It can be proved that the improved belief entropy will be degenerated to Shannon entropy when the the basic probability assignment is Bayesian. The results of numerical examples and a case study show that its efficiency and flexibility are better compared with previous uncertainty measures.

scholarly journals A New Total Uncertainty Measure from A Perspective of Maximum Entropy Requirement

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1061
Author(s):  
Yu Zhang ◽  
Fanghui Huang ◽  
Xinyang Deng ◽  
Wen Jiang
Keyword(s):  
Maximum Entropy ◽  
Information Fusion ◽  
Uncertainty Measure ◽  
Total Uncertainty ◽  
Numerical Examples ◽  
Dempster Shafer Theory ◽  
Basic Probability ◽  
Open Issue ◽  
Shafer Theory ◽  
Fusion Framework

The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, the existing methods have some limitations. In this paper, a new total uncertainty measure from a perspective of maximum entropy requirement is proposed. The proposed method can measure both dissonance and non-specificity in BPA, which includes two components. The first component is consistent with Yager’s dissonance measure. The second component is the non-specificity measurement with different functions. We also prove the desirable properties of the proposed method. Besides, numerical examples and applications are provided to illustrate the effectiveness of the proposed total uncertainty measure.

scholarly journals Multi-Attribute Decision Making Based on Intuitionistic Fuzzy Power Maclaurin Symmetric Mean Operators in the Framework of Dempster-Shafer Theory

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 807 ◽  
Author(s):  
Gao ◽  
Zhang ◽  
Liu
Keyword(s):  
Decision Making ◽  
Hamming Distance ◽  
Intuitionistic Fuzzy Set ◽  
Semantic Framework ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Maclaurin Symmetric Mean ◽  
Multi Attribute Decision Making ◽  
The Difference ◽  
Shafer Theory

It is well known that there are some unfavorable shortcomings in the ordinary operational rules (OORs) of intuitionistic fuzzy number (IFN), and there exists a close and forceful connection between the intuitionistic fuzzy set (IFS) and Dempster-Shafer Theory (DST). We can utilize this relationship to present a transparent and fruitful semantic framework for IFS in terms of DST. In the framework of DST, an IFN can be converted into a basic probability assignment (BPA) and operations on IFNs can be represented as operations on a belief interval (BI), which can break away from the revealed shortcomings of the OORs of the IFN. Although there are many operators to aggregate the IFN, the operator to aggregate the BPA is rare. The Maclaurin symmetric mean (MSM) operator has the advantage of considering interrelationships among any number of attributes. The power average (PA) operator can reduce the influences of extreme evaluation values. In addition, for measuring the difference between IFNs, we replace the Hamming distance and Euclidean distance with the Jousselme distance (JD). In this paper, we develop an intuitionistic fuzzy power MSM (IFPMSMDST) operator and an intuitionistic fuzzy weighted power MSM (IFPWMSMDST) operator in the framework of the DST and provide their favorable properties. Then, we propose a novel method based on the proposed operators to solve multi-attribute decision-making (MADM) problems without intermediate defuzzification when their attributes and weights are both IFNs. Finally, some examples are utilized to demonstrate that the proposed methods outperform the previous ones.

scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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.

Belief Function Approach to Evidential Reasoning in Causal Maps

2005 ◽  
pp. 109-141
Author(s):  
Rajendra P. Srivastava ◽  
Mari W. Buche ◽  
Tom L. Roberts
Keyword(s):  
Job Satisfaction ◽  
Information Technology ◽  
Belief Function ◽  
Evidential Reasoning ◽  
Belief Functions ◽  
Causal Maps ◽  
Dempster Shafer Theory ◽  
Evidential Reasoning Approach ◽  
Theory Of Belief Functions ◽  
Shafer Theory

The purpose of this chapter is to demonstrate the use of the evidential reasoning approach under the Dempster-Shafer (D-S) theory of belief functions to analyze revealed causal maps (RCM). The participants from information technology (IT) organizations provided the concepts to describe the target phenomenon of Job Satisfaction. They also identified the associations between the concepts. This chapter discusses the steps necessary to transform a causal map into an evidential diagram. The evidential diagram can then be analyzed using belief functions technique with survey data, thereby extending the research from a discovery and explanation stage to testing and prediction. An example is provided to demonstrate these steps. This chapter also provides the basics of Dempster-Shafer theory of belief functions and a step-by-step description of the propagation process of beliefs in tree-like evidential diagrams.

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