Quantum model of mass function

Gao, Xiaozhuan; Deng, Yong

doi:10.1002/int.22208

Cited by 73 publications

(35 citation statements)

References 69 publications

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“…In the diagnostic process of medical profession, improving the processing capacity of various uncertain and inconsistent information and achieving more accurate decision-making have become the major challenges in the development of medical diagnosis [1][2][3]. Up to now, the process of medical diagnosis is driven by various theoretical studies, such as fuzzy sets theory [4][5][6], intuitionistic fuzzy sets [7][8][9][10], interval-valued intuitionistic fuzzy sets [11][12][13], and quantum decision [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

2020

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As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

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Section: Introductionmentioning

confidence: 99%

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

2020

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“…How to measure uncertainty has become a hot issue, so many theories and methods have been born to deal with uncertainty [7]- [9]. Probability theory [10]- [13], Dempster-Shafer evidence theory [14]- [17], D-numbers [18]- [20], rough sets [21], [22], fuzzy set theory [23]- [28], and Z-numbers are all well-known methods for dealing with uncertainty [29]- [32]. Among these methods, Dempster-Shafer (D-S) evidence theory is widely used [33], [34].…”

Section: Introductionmentioning

confidence: 99%

An Improved Belief Entropy in Evidence Theory

Yan

Deng

2020

IEEE Access

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Uncertainty measurement of the basic probability assignment function has always been a hot issue in Dempster-Shafer evidence. Many existing studies mainly consider the influence of the mass function itself and the size of the frame of discernment, so that the correlation between the subsets is ignored in the power set of the frame of discernment. Without making full use of the information contained in the evidence, the existing methods are less effective in some cases given in the paper. In this paper, inspired by Shannon entropy and Deng entropy, we propose an improved entropy that not only inherits the many advantages of Shannon entropy and Deng entropy, but also fully considers the relationship between subsets, which makes the improved entropy overcome the shortcomings of existing methods and have greater advantages in uncertainty measurement. Many numerical examples are used to demonstrate the validity and superiority of our proposed entropy in this paper.

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“…for divergence measure [71,72], distance measure [73], correlation coefficient [74,75], entropy measure [76][77][78], dependent evidence [79], etc. [80,81].…”

Section: Dempster-shafer Evidence Theorymentioning

confidence: 99%

Determining Weights in Multi-Criteria Decision Making Based on Negation of Probability Distribution under Uncertain Environment

Sun

Deng

2020

Mathematics

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Multi-criteria decision making (MCDM) refers to the decision making in the limited or infinite set of conflicting schemes. At present, the general method is to obtain the weight coefficients of each scheme based on different criteria through the expert questionnaire survey, and then use the Dempster–Shafer Evidence Theory (D-S theory) to model all schemes into a complete identification framework to generate the corresponding basic probability assignment (BPA). The scheme with the highest belief value is then chosen. In the above process, using different methods to determine the weight coefficient will have different effects on the final selection of alternatives. To reduce the uncertainty caused by subjectively determining the weight coefficients of different criteria and further improve the level of multi-criteria decision-making, this paper combines negation of probability distribution with evidence theory and proposes a weights-determining method in MCDM based on negation of probability distribution. Through the quantitative evaluation of the fuzzy degree of the criterion, the uncertainty caused by human subjective factors is reduced, and the subjective error is corrected to a certain extent.

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Quantum model of mass function

Cited by 73 publications

References 69 publications

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

An Improved Belief Entropy in Evidence Theory

Determining Weights in Multi-Criteria Decision Making Based on Negation of Probability Distribution under Uncertain Environment

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