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.

scholarly journals Measuring the Uncertainty in the Original and Negation of Evidence Using Belief Entropy for Conflict Data Fusion

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 402
Author(s):  
Yutong Chen ◽  
Yongchuan Tang
Keyword(s):  
Information Processing ◽  
Data Fusion ◽  
Evidence Theory ◽  
Uncertain Information ◽  
Dempster Shafer Theory ◽  
Open World ◽  
Uncertainty Measurement ◽  
Basic Probability ◽  
Shafer Theory ◽  
Deng Entropy

Dempster-Shafer (DS) evidence theory is widely used in various fields of uncertain information processing, but it may produce counterintuitive results when dealing with conflicting data. Therefore, this paper proposes a new data fusion method which combines the Deng entropy and the negation of basic probability assignment (BPA). In this method, the uncertain degree in the original BPA and the negation of BPA are considered simultaneously. The degree of uncertainty of BPA and negation of BPA is measured by the Deng entropy, and the two uncertain measurement results are integrated as the final uncertainty degree of the evidence. This new method can not only deal with the data fusion of conflicting evidence, but it can also obtain more uncertain information through the negation of BPA, which is of great help to improve the accuracy of information processing and to reduce the loss of information. We apply it to numerical examples and fault diagnosis experiments to verify the effectiveness and superiority of the method. In addition, some open issues existing in current work, such as the limitations of the Dempster–Shafer theory (DST) under the open world assumption and the necessary properties of uncertainty measurement methods, are also discussed in this paper.

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.

Evidence-Based Uncertainty Modeling

2014 ◽  
pp. 54-74
Author(s):  
Tazid Ali
Keyword(s):  
Evidence Theory ◽  
Uncertainty Modeling ◽  
Possibility Theory ◽  
Dempster Shafer Theory ◽  
Uncertainty Measurement ◽  
Frame Work ◽  
Shafer Theory ◽  
Relationship Of ◽  
Different Sources ◽  
Fuzzy Setting

Evidence is the essence of any decision making process. However in any situation the evidences that we come across are usually not complete. Absence of complete evidence results in uncertainty, and uncertainty leads to belief. The framework of Dempster-Shafer theory which is based on the notion of belief is overviewed in this chapter. Methods of combining different sources of evidences are surveyed. Relationship of probability theory and possibility theory to evidence theory is exhibited. Extension of the classical Dempster-Shafer Structure to fuzzy setting is discussed. Finally uncertainty measurement in the frame work of Dempster-Shafer structure is dealt with.

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.

Planning and Evaluation of Assurance Services for Sustainability Reporting: An Evidential Reasoning Approach

2013 ◽  
Vol 27 (2) ◽  
pp. 107-126 ◽  
Author(s):  
Rajendra P. Srivastava ◽  
Sunita S. Rao ◽  
Theodore J. Mock
Keyword(s):  
Probability Theory ◽  
Theoretical Model ◽  
Corporate Sustainability ◽  
Sustainability Reporting ◽  
Belief Function ◽  
Global Reporting Initiative ◽  
Bayesian Probability ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Different Levels

ABSTRACT This study develops a framework for planning, performing, and evaluating evidence obtained to assess and control the risks of providing assurance on sustainability reports. Sustainability reporting, or corporate sustainability reporting (CSR), provides stakeholders with important information on both financial and non-financial factors related to environmental, social, and economic performance. Importantly, the presented framework is developed from both a Bayesian (probability-based theory) and Belief Function (Dempster-Shafer theory) perspective. This facilitates application of the framework to cases where the assurance provider prefers to assess risk in terms of probability versus in terms of beliefs. To demonstrate the application of this framework we evaluate assertions, sub-assertions, and audit evidence relevant to CSR based on the G3 Reporting framework developed by the Global Reporting Initiative (GRI). The paper contributes to the literature in three main areas. First, it demonstrates how evidence-based reasoning can be used for engagements where different levels of assurance are provided for the assertions being audited. Second, it shows how various items of evidence at different levels may be aggregated. Third, it presents a generic theoretical model for assuring information based on belief-based assessments, which is then contrasted with a theoretical model based on probability theory. In contrasting the two approaches, we show that in cases where initial uncertainty is substantial, the use of Dempster-Shafer theory has advantages over probability theory in terms of efficiency in achieving a targeted low level of assurance.

scholarly journals Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Yafei Song ◽  
Xiaodan Wang
Keyword(s):  
Evidence Theory ◽  
Estimation Method ◽  
Probability Estimation ◽  
Belief Functions ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Fuzzy Environment ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Interval Valued

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.

INCORPORATING FUZZY SETS INTO DEMPSTER-SHAFER THEORY FOR DECISION FUSION

2018 ◽  
pp. 299-309
Author(s):  
Somnuek Surathong ◽  
Sansanee Auephanwiriyakul ◽  
Nipon Theera-Umpon
Keyword(s):  
Fuzzy Sets ◽  
Decision Fusion ◽  
Dempster Shafer Theory ◽  
Shafer Theory

ROUTE PLANNING BASED ON UNCERTAIN INFORMATION IN TRANSPORT NETWORKS

Transport ◽  
2012 ◽  
Vol 27 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Gábor Szűcs
Keyword(s):  
Traffic Congestion ◽  
Traffic Accidents ◽  
Decision Rules ◽  
Route Planning ◽  
Transport Network ◽  
Uncertain Information ◽  
End User ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
The Cost

The goal of this paper is to find a solution for route planning in a transport network where the network type can be arbitrary: a network of bus routes, a network of tram rails, a road network or any other type of a transport network. Furthermore, the costs of network elements are uncertain. The concept is based on the Dempster–Shafer theory and Dijkstra's algorithm which helps with finding the best routes. The paper focuses on conventional studies without considering traffic accidents or other exceptional circumstances. The concept is presented by an undirected graph. In order to model conventional real transport, the influencing factors of traffic congestion have been applied in the abstract model using uncertain probabilities described by probability intervals. On the basis of these intervals, the cost intervals of each road can be calculated. Taking into account the uncertain values of costs, an algorithm has been outlined for determining the best routes from one node to all other nodes comparing cost intervals and using decision rules that can be defined by the end user, and if necessary, node by node. The suggested solution can be applied for both one type of network as well as for a combination of a few of those.

Sign in / Sign up

Export Citation Format

Share Document