A Method of Measuring Uncertainty for Z-Number

Self Cite

Dempster‐Shafer is widely used to address the problems of uncertainty. One assumption mentioned in this theory is that the distribution of information should be independent. In practice, the requirement cannot be fulfilled. One of the efficient methods to deal with dependent evidence is to calculate the correlation discounting. However, existing coefficient can only be applied to show the direct relation between evidence A and B but do not take the indirect relationship into consideration. To address this issue, in this paper, a new method to combine dependent evidence based on decision‐making trial and evaluation laboratory is presented, not only considering the relation between evidence A and B and the relation between evidence B and C, but also considering the transitive influence between evidence A and C. Finally, the experiments on some benchmark data sets are illustrated to show the efficiency of the proposed method.

Section: Preliminariesmentioning

confidence: 99%

Dependent evidence combination based on decision‐making trial and evaluation laboratory method

Deng

2019

Self Cite

“…Fuzzy logic was developed by Zadeh and Mamdani and Assilian, based on which the concept of approximate reasoning was introduced and showed that vague logical statements enable the formation of algorithms that can use vague data to derive vague inferences. Many theories have been promoted by this method, such as Dempster‐Shafer theory, Z‐numbers, and fuzzy reasoning . The definition of fuzzy sets is given as follows:…”

Section: Fuzzy Sets and Ivfssmentioning

confidence: 99%

“…Fuzzy logic was developed by Zadeh 26 and Mamdani and Assilian, 27 based on which the concept of approximate reasoning was introduced and showed that vague logical statements enable the formation of algorithms that can use vague data to derive vague inferences. Many theories have been promoted by this method, such as Dempster-Shafer theory, [28][29][30][31] Z-numbers, [32][33][34] and fuzzy reasoning. [35][36][37] The definition of fuzzy sets is given as follows: Note that the membership function can take any value from the closed interval [0, 1], and the greater μ x ( ) A is, the greater the truth of the statement that element x belongs to set A is.…”

Section: Fuzzy Sets and Ivfssmentioning

confidence: 99%

On interval‐valued fuzzy decision‐making using soft likelihood functions

Fei

2019

Multicriteria decision‐making approaches have been studied very widely in recent years and are frequently used in many real‐life applications. To select the optimal alternative that satisfies the multicriteria, effective aggregation methods are crucial in the decision‐making process. The soft likelihood functions (SLF) developed by Yager is introduced as preliminaries of our research, which is a flexible aggregation approach of probabilistic evidence in the context of forensic crime investigations. Motivated by SLF, in this study, a novel aggregation method is proposed based on ordered weighted averaging operator under interval‐valued fuzzy environments. To improve the performance of the new aggregation method, the reliability is taken into account in the decision‐making process from two perspectives. The first is the reliability of assessment value, including certainty and compatibility, for discounting assessment information; the second is human reliability for redefining SLF. Some numerical examples are given to demonstrate the proposed decision approach. And the reliability‐based aggregation method is illustrated more reasonable than the one without considering reliability.

“…Two primary approaches have been presented to solve this issue. The first is to modify Dempster's rule of combination, based on which varieties of new rules have been proposed in Fei, Feng, and Liu, Li and Deng, Jiang, and Fei, Xia, Feng, and Liu and the second one focuses on improving the sources of evidence without modifying the combination rule . From other perspectives, such as divergence measure and evolutionary game theory, many approaches were put forward.…”

Section: Introductionmentioning

confidence: 99%

“…The first is to modify Dempster's rule of combination, based on which varieties of new rules have been proposed in and the second one focuses on improving the sources of evidence without modifying the combination rule. [14][15][16] From other perspectives, such as divergence measure 7 and evolutionary game theory, 17 many approaches were put forward.The combination of bodies of evidence could be employed in plenty of contexts where the knowledge of experts needs to be aggregated. One crucial application is environmental impact assessment (EIA), 18 which focuses on the recognition and assessment of possible influencing factors, including physical-chemistry, biology, culture, etc.…”

mentioning

confidence: 99%

On combination rule in Dempster–Shafer theory using OWA‐based soft likelihood functions and its applications in environmental impact assessment

Fei

2019

Dempster–Shafer theory (DST) was presented as an effective mathematical tool to represent uncertainty. Its significant innovation is to allow the allocation of the belief of mass to sets or intervals, and it becomes a valuable method in the field of decision making and evaluation when accurate information is not available or when knowledge is expressed subjectively by humans. A crucial research issue in DST is the combination of multi‐sources of evidence. In this paper, a novel combination rule for Dempster–Shafer structures is developed based on ordered weighted average (OWA)‐based soft likelihood functions proposed by Yager. First, the belief intervals, including the belief measures and plausibility measures, of all the hypotheses in the frame of discernment (FOD) are calculated. Second, the representative value of belief interval is defined based on golden rule introduced by Yager. Third, the soft likelihood value of each hypothesis is calculated based on the proposed OWA‐based soft likelihood function for belief interval, which can be considered as the combined evidence. The final evaluation results can be employed for practical applications, such as decision making and evaluation. In addition, the improved evidence combination rule is presented which takes into account the weight of evidence. Several illustrative examples are conducted to manifest the use of the developed methods. Finally, an application for environmental impact assessment is given to demonstrate the usefulness of the developed combination rule in DST.