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.

scholarly journals Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xihua Li ◽  
Fuqiang Wang ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Value Function ◽  
Cumulative Prospect Theory ◽  
Intuitionistic Fuzzy Numbers ◽  
Attribute Weight ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Fuzzy Environment ◽  
Shafer Theory

With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight function are used to calculate prospect values of attributes for each alternative. Then considering uncertain attribute weight information, Dempster-Shafer theory is used to aggregate prospect values for each alternative, and overall prospect values are obtained and thus the alternatives are sorted consequently. Finally, an illustrative example shows the feasibility of the proposed method.

A NON-SPECIFICITY MEASURE FOR CONVEX SETS OF PROBABILITY DISTRIBUTIONS

2000 ◽  
Vol 08 (03) ◽  
pp. 357-367 ◽  
Author(s):  
JOAQUIN ABELLAN ◽  
SERAFIN MORAL
Keyword(s):  
Convex Sets ◽  
Probability Distributions ◽  
Belief Functions ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Specificity Measure ◽  
Lack Of Knowledge

In belief functions, there are two types of uncertainty which are due to lack of knowledge: randomness and non-specificity. In this paper, we present a non-specificity measure for convex sets of probability distributions that generalizes Dubois and Prade's non-specificity measure in the Dempster-Shafer theory of evidence.

scholarly journals Multimodel Approach Based on Evidence Theory for Forecasting Tropical Cyclone Tracks

2010 ◽  
Vol 138 (2) ◽  
pp. 405-420 ◽  
Author(s):  
Svetlana V. Poroseva ◽  
Nathan Lay ◽  
M. Yousuff Hussaini
Keyword(s):  
Tropical Cyclone ◽  
Evidence Theory ◽  
Dempster Shafer Theory ◽  
South Indian ◽  
Cyclone Tracks ◽  
Environmental Prediction ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Year 2000 ◽  
Tropical Cyclone Tracks

Abstract In this paper a new multimodel approach for forecasting tropical cyclone tracks is presented. The approach is based on the Dempster–Shafer theory of evidence. At each forecast period, the multimodel forecast is given as an area where the tropical cyclone position is likely to occur. Each area includes a quantitative assessment of the credibility (degree of belief) of the prediction. The multimodel forecast is obtained by combining individual model forecasts into a single prediction by Dempster’s rule. Mathematical requirements associated with the Dempster’s rule are discussed. Particular attention is given to the requirement of independence of evidence sources, which, for tropical cyclone track forecasting, are the model and best-track data. The origin of this requirement is explored, and it is shown that for forecasting tropical cyclone tracks, this requirement is excessive. The influence of the number of models included in the multimodel approach on the forecasting ability is also studied. Data produced by the models of the Navy Operational Global Atmospheric Prediction System, the European Centre for Medium-Range Weather Forecasts, and the National Centers for Environmental Prediction are used to produce two-, three-, and four-model forecasts. The forecasting ability of the multimodel approach is evaluated using the best-track database of the tropical cyclones that occurred in the eastern and western North Pacific and South Indian Ocean basins in the year 2000.

scholarly journals Pipe burst diagnostics using evidence theory

2010 ◽  
Vol 13 (4) ◽  
pp. 596-608 ◽  
Author(s):  
Josef Bicik ◽  
Zoran Kapelan ◽  
Christos Makropoulos ◽  
Dragan A. Savić
Keyword(s):  
Distribution System ◽  
Water Distribution ◽  
Information Sources ◽  
Water Distribution System ◽  
Evidence Theory ◽  
Dempster Shafer Theory ◽  
Pipe Burst ◽  
The Individual ◽  
Shafer Theory ◽  
Theory Of Evidence

This paper presents a decision support methodology aimed at assisting Water Distribution System (WDS) operators in the timely location of pipe bursts. This will enable them to react more systematically and promptly. The information gathered from various data sources to help locate where a pipe burst might have occurred is frequently conflicting and imperfect. The methodology developed in this paper deals effectively with such information sources. The raw data collected in the field is first processed by means of several models, namely the pipe burst prediction model, the hydraulic model and the customer contacts model. The Dempster–Shafer Theory of Evidence is then used to combine the outputs of these models with the aim of increasing the certainty of determining the location of a pipe burst within a WDS. This new methodology has been applied to several semi-real case studies. The results obtained demonstrate that the method shows potential for locating the area of a pipe burst by capturing the varying credibility of the individual models based on their historical performance.

scholarly journals Translating Islamic identity into numbers

2021 ◽  
Vol 5 (S1) ◽  
pp. 139-159
Author(s):  
Andino Maseleno ◽  
Miftachul Huda ◽  
Mazdi Marzuki ◽  
Fauziah Che Leh ◽  
Azmil Hashim ◽  
...  
Keyword(s):  
Evidence Theory ◽  
Theory Model ◽  
Ordinal Scale ◽  
Average Level ◽  
Dempster Shafer Theory ◽  
Islamic Identity ◽  
Specific Individual ◽  
Shafer Theory ◽  
Theory Of Evidence

This research aims to define various Islamic based identity profile to different individuals by identifying the various degrees of Islamic based identity profile. A scale of measurement in ordinal scale has been used to determine an Islamic based identity profile. The scale is subdivided into three main subsections, namely very rarely, average level and very frequently. By using the scale of measurement on an ordinal scale, it assists in developing a numerical hypothesis that is then used to determine an individual's Islamic based identity profile using the Dempster-Shafer theory of evidence. Using twenty-four set of questions, the research used the evidence presented to support a given Islamic based identity profile of a specific individual and filtered it using various degrees of probabilities of the evidence theory model, which have aided in proving or validating a particular hypothesis. The questions are divided into three types  based on Islamic identity profile which include Fitrah, Khalifah and Din. The conclusion made is that we may be able to easily diagnose an individual’s Islamic based identity profile using Dempster-Shafer theory of evidence.

scholarly journals Plato's Cave in the Dempster-Shafer land--the Link between Pignistic and Plausibility Transformations

2017 ◽  
Author(s):  
Chunlai Zhou ◽  
Biao Qin ◽  
Xiaoyong Du
Keyword(s):  
Statistical Inference ◽  
Belief Function ◽  
Belief Functions ◽  
Reasoning Under Uncertainty ◽  
Function Model ◽  
Probability Functions ◽  
Degree Of Belief ◽  
Dempster Shafer Theory ◽  
Shafer Theory ◽  
Theory Of Evidence

In reasoning under uncertainty in AI, there are (at least) two useful and different ways of understanding beliefs: the first is as absolute belief or degree of belief in propositions and the second is as belief update or measure of change in belief. Pignistic and plausibility transformations are two well-known probability transformations that map belief functions to probability functions in the Dempster-Shafer theory of evidence. In this paper, we establish the link between pignistic and plausibility transformations by devising a belief-update framework for belief functions where plausibility transformation works on belief update while pignistic transformation operates on absolute belief. In this framework, we define a new belief-update operator connecting the two transformations, and interpret the framework in a belief-function model of parametric statistical inference. As a metaphor, these two transformations projecting the belief-update framework for belief functions to that for probabilities are likened to the fire projecting reality into shadows on the wall in Plato's cave.

scholarly journals Temporal and Causal Relations on Evidence Theory: an Application on Adverse Drug Reactions

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Luiz Alberto Pereira Afonso Ribeiro ◽  
Ana Cristina Bicharra Garcia ◽  
Paulo Sérgio Medeiros Dos Santos
Keyword(s):  
Information Fusion ◽  
Evidence Theory ◽  
Mass Function ◽  
Data Sources ◽  
Drug Reactions ◽  
Clinical Notes ◽  
Dempster Shafer Theory ◽  
Multisensor Information Fusion ◽  
Shafer Theory ◽  
Theory Of Evidence

The use of big data and information fusion in electronichealth records (EHR) allowed the identification of adversedrug reactions(ADR) through the integration of heteroge-neous sources such as clinical notes (CN), medication pre-scriptions, and pathological examinations. This heterogene-ity of data sources entails the need to address redundancy,conflict, and uncertainty caused by the high dimensionalitypresent in EHR. The use of multisensor information fusion(MSIF) presents an ideal scenario to deal with uncertainty,especially when adding resources of the theory of evidence,also called Dempster–Shafer Theory (DST). In that scenariothere is a challenge which is to specify the attribution of be-lief through the mass function, from the datasets, named basicprobability assignment (BPA). The objective of the presentwork is to create a form of BPA generation using analy-sis of data regarding causal and time relationships betweensources, entities and sensors, not only through correlation, butby causal inference.

EVIDENCE THEORY BASED ON GENERAL CONSEQUENCE RELATIONS

1995 ◽  
Vol 06 (02) ◽  
pp. 119-135 ◽  
Author(s):  
PHILIPPE BESNARD ◽  
JÜRG KOHLAS
Keyword(s):  
Infinite Order ◽  
Evidence Theory ◽  
Consequence Relations ◽  
Support Functions ◽  
Consequence Relation ◽  
Dempster Shafer Theory ◽  
Duality Relations ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Usual Duality

The Dempster-Shafer theory of evidence can be conceived as a theory of probability of provability. In fact, it has been shown that evidence theory can be developed on the basis of assumption-based reasoning. Taking this approach, reasoning is modeled in this paper by a consequence relation in the sense of Tarski. It is shown that it is possible to construct evidence theory on top of the very general logics defined by these consequence relations. Support functions can be derived which are, as usual, set functions, monotone of infinite order. Furthermore, plausibility functions can also be defined. However, as negation need not be defined in these general logics, the usual duality relations between support and plausibility functions of Dempster-Shafer theory do not hold in general. Nonetheless, this symmetry can be installed progressively by considering logics that enjoy more and more “structural properties”.

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