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Likelihood function has significant advantages in the fields of statistical inference. Based on this theory, Yager proposed a soft likelihood function to make it more widely used. However, Yager’s method can only deal with probabilities expressed by crisp values, and has strict restrictions on the form of data. Due to human subjectivity and lack of effective information, it is inevitable that data uncertainty will be involved. In order to deal with the uncertain data more flexibly and intuitively and solve the complex problems faced in real-world applications, a generalized soft likelihood function in combining multi-source belief distribution functions is proposed in this paper. Different from other existing methods, this paper uses a distribution function to represent uncertain information, which can retain more original information and improve the credibility of the results. The expectation and variance are used to rank the obtained evidences, and the evidence that contributes more to the results is ranked higher. Finally, the reliable likelihood results are obtained. The proposed method extends the method of Yager and can work well in more uncertain environment. Several numerical examples and comparative experimental simulation are used to illustrate the efficiency of the proposed soft likelihood function.
Pengdan Zhang; Ruonan Zhu; Jiaqi Chen; Bingyi Kang. A generalized soft likelihood function in combining multi-source belief distribution functions. Applied Intelligence 2021, 1 -18.
AMA StylePengdan Zhang, Ruonan Zhu, Jiaqi Chen, Bingyi Kang. A generalized soft likelihood function in combining multi-source belief distribution functions. Applied Intelligence. 2021; ():1-18.
Chicago/Turabian StylePengdan Zhang; Ruonan Zhu; Jiaqi Chen; Bingyi Kang. 2021. "A generalized soft likelihood function in combining multi-source belief distribution functions." Applied Intelligence , no. : 1-18.
Information fusion has traditionally been a concern. In the fusion process, how to effectively take care of the ambiguity and uncertainty of data is a fascinating problem. Dempster–Shafer evidence theory shows powerful functions in dealing with uncertainty information, and Z-number can comprehensively model the ambiguity and reliability of information. Inspired by this, this paper proposed a new information fusion method based on Dempster–Shafer theory and K-means clustering and it established the reliability evaluation criterion based on Z-number. Comparison and discussion verify the rationality of the proposed method, which also illustrates the method has better robustness and sensitivity than existing methods, some critical issues in DST, e.g., conflict management, evidence stuck, are well investigated and overcome by the proposed method. Number examples and the application further shows the application potential of the proposed method in a data-driven intelligent system.
Ye Tian; Xiangjun Mi; Huizi Cui; Pengdan Zhang; Bingyi Kang. Using Z-number to measure the reliability of new information fusion method and its application in pattern recognition. Applied Soft Computing 2021, 111, 107658 .
AMA StyleYe Tian, Xiangjun Mi, Huizi Cui, Pengdan Zhang, Bingyi Kang. Using Z-number to measure the reliability of new information fusion method and its application in pattern recognition. Applied Soft Computing. 2021; 111 ():107658.
Chicago/Turabian StyleYe Tian; Xiangjun Mi; Huizi Cui; Pengdan Zhang; Bingyi Kang. 2021. "Using Z-number to measure the reliability of new information fusion method and its application in pattern recognition." Applied Soft Computing 111, no. : 107658.
In Dempster–Shafer evidence theory, how to use the basic probability assignment (BPA) in decision-making is a significant issue. The transformation of BPA into a probability distribution function is one of the common and feasible schemes. To overcome the problems of the existing methods, we propose a marginal probability transformation method based on the Shapley value approach. The proposed method allocates BPA values in terms of how much an element contributes to a set, which is an equitable and effective distribution mechanism. Furthermore, we use probabilistic information content to evaluate the effect of each transformation method. Moreover, some numerical examples are used to demonstrate the efficiency and feasibility of the proposed method. Further, two applications, target recognition, fault diagnosis are used to verify the superiority and effectiveness of the proposed method in practice.
Chongru Huang; Xiangjun Mi; Bingyi Kang. Basic probability assignment to probability distribution function based on the Shapley value approach. International Journal of Intelligent Systems 2021, 36, 4210 -4236.
AMA StyleChongru Huang, Xiangjun Mi, Bingyi Kang. Basic probability assignment to probability distribution function based on the Shapley value approach. International Journal of Intelligent Systems. 2021; 36 (8):4210-4236.
Chicago/Turabian StyleChongru Huang; Xiangjun Mi; Bingyi Kang. 2021. "Basic probability assignment to probability distribution function based on the Shapley value approach." International Journal of Intelligent Systems 36, no. 8: 4210-4236.
It is a common case that Wireless Sensor Networks are attacked by malware in the real world. According to the game theory, the action of attack–defense between Wireless Sensor Network(WSN) and malware can be regarded as a game. While substantial efforts have been made to address this issue, most of these efforts have predominantly focused on the analysis of attack–defense game in the known environment. Given that the process of gaming in real world often contains a lot of fuzzy information, we extend the focus in this line by considering the fuzzy exterior environment. Specifically, we assume the WSN attack–defense Stackelberg game is in the fuzzy environment by using fuzzy variable. Then Stackelberg game theory is utilized to calculate the equilibrium solutions of the introduced maximax chance-constrained model and minimax chance-constrained model. Based on the simulation data, this study demonstrates the confidence levels and decision perspectives affect the optimal strategy of WSN and the reliability of WSN. Finally, the novel analytical method is compared with the non-fuzzy WSN attack–defense game method. The analysis shows that the novel approach is optimal in terms of predicting the behavior of malware in resisting the attack of malware.
Yingfu Wu; Bingyi Kang; Hao Wu. Strategies of attack–defense game for wireless sensor networks considering the effect of confidence level in fuzzy environment. Engineering Applications of Artificial Intelligence 2021, 102, 104238 .
AMA StyleYingfu Wu, Bingyi Kang, Hao Wu. Strategies of attack–defense game for wireless sensor networks considering the effect of confidence level in fuzzy environment. Engineering Applications of Artificial Intelligence. 2021; 102 ():104238.
Chicago/Turabian StyleYingfu Wu; Bingyi Kang; Hao Wu. 2021. "Strategies of attack–defense game for wireless sensor networks considering the effect of confidence level in fuzzy environment." Engineering Applications of Artificial Intelligence 102, no. : 104238.
As the core mechanism of intelligent systems, decision-making has received widespread attention in recent years. As decision-making environments become more complex, large amounts of data are fuzzy and partially reliable. Zadeh proposed the concept of the Z-numbers, this more anthropomorphic fuzzy set representation framework describes the simultaneous existence of probability measures and probability measures of random variables, and it is regarded as a very powerful tool for modeling uncertain information. However, the representation of Z-numbers still has limitations. Therefore, we propose a new extended Z-numbers, ZE=((A,B),E), E is the credibility. As the objective reliability of (A,B), it restricts the original Z-numbers. At the same time, the conversion function between them is also defined. Based on this, we proposed a multi-attribute group decision-making (MAGDM) method considering the attitudes of decision-makers. Application examples show the rationality and effectiveness of the proposed methodology, and the superiority of this method is further illustrated through comparison and discussion with other methods.
Ye Tian; Xiangjun Mi; Yunpeng Ji; Bingyi Kang. ZE-numbers: A new extended Z-numbers and its application on multiple attribute group decision making. Engineering Applications of Artificial Intelligence 2021, 101, 104225 .
AMA StyleYe Tian, Xiangjun Mi, Yunpeng Ji, Bingyi Kang. ZE-numbers: A new extended Z-numbers and its application on multiple attribute group decision making. Engineering Applications of Artificial Intelligence. 2021; 101 ():104225.
Chicago/Turabian StyleYe Tian; Xiangjun Mi; Yunpeng Ji; Bingyi Kang. 2021. "ZE-numbers: A new extended Z-numbers and its application on multiple attribute group decision making." Engineering Applications of Artificial Intelligence 101, no. : 104225.
Health-care waste (HCW) management is an important issue, especially in developing countries. How to choose the best management technology is a challenging and open subject in this issue. Limited work has been done, but there is still a lack of a technical approach that not only takes into account multi-granular linguistic terminology, but also considers the attitude characters of decision makers (DMs). To adress the above problem, in this paper a hybrid multi-criteria decision making scheme is proposed based on soft likelihood function and D-numbers. First, the D-numbers is used to characterize complex multi-grained decision information. Secondly, a novel soft likelihood function based on power ordered weighted averaging operator (POWA) is designed to effectively take into account the DMs’ preferences, which is then integrated into the proposed HCW management approach. Eventually, the effectiveness and superiority of the proposed approach is demonstrated through an application example. In particular, an intuitive advantage has been confirmed that the proposed method can adjust the gap between adjacent alternatives through decision preference to distinguish differences. This is expected to provide a reliable fault-tolerant interval for decision-making in HCW management, and further improve the reliability of the algorithm. In addition, the analysis and evaluation also confirm the reliability and practicality of the proposed technology.
Xiangjun Mi; Ye Tian; Bingyi Kang. A hybrid multi-criteria decision making approach for assessing health-care waste management technologies based on soft likelihood function and D-numbers. Applied Intelligence 2021, 1 -20.
AMA StyleXiangjun Mi, Ye Tian, Bingyi Kang. A hybrid multi-criteria decision making approach for assessing health-care waste management technologies based on soft likelihood function and D-numbers. Applied Intelligence. 2021; ():1-20.
Chicago/Turabian StyleXiangjun Mi; Ye Tian; Bingyi Kang. 2021. "A hybrid multi-criteria decision making approach for assessing health-care waste management technologies based on soft likelihood function and D-numbers." Applied Intelligence , no. : 1-20.
Multi-sensor data fusion plays an irreplaceable role in actual production and application. Dempster–Shafer theory (DST) is widely used in numerous fields of information modeling and information fusion due to the flexibility and effectiveness of processing uncertain information and dealing with uncertain information without prior probabilities. However, when highly contradictory evidence is combined, it may produce results that are inconsistent with human intuition. In order to solve this problem, a hybrid method for combining belief functions based on soft likelihood functions (SLFs) and ordered weighted averaging (OWA) operators is proposed. More specifically, a soft likelihood function based on OWA operators is used to provide the possibility to fuse uncertain information compatible with each other. It can characterize the degree to which the probability information of compatible propositions in the collected evidence is affected by unknown uncertain factors. This makes the results of using the Dempster’s combination rule to fuse uncertain information from multiple sources more comprehensive and credible. Experimental results manifest that this method is reliable. Example and application show that this method has obvious advantages in solving the problem of conflict evidence fusion in multi-sensor. In particular, in target recognition, when three pieces of evidence are fused, the target recognition rate is 96.92%, etc.
Xiangjun Mi; Tongxuan Lv; Ye Tian; Bingyi Kang. Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system. ISA Transactions 2020, 112, 137 -149.
AMA StyleXiangjun Mi, Tongxuan Lv, Ye Tian, Bingyi Kang. Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system. ISA Transactions. 2020; 112 ():137-149.
Chicago/Turabian StyleXiangjun Mi; Tongxuan Lv; Ye Tian; Bingyi Kang. 2020. "Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system." ISA Transactions 112, no. : 137-149.
In this paper, we proposed a notion of belief universal gravitation (BUG) in the Dempster-Shafer (D-S) evidence theory, of which the notion of mass of a belief function is newly addressed using evidence quality coding (EQC) method. The proposed BUG aims to discuss the process of information fusion from the perspective of Newton’s mechanics, which may provide us a new insight to address the issues of D-S evidence theory. A key issue in D-S evidence theory, i.e., conflict management, is solved better than previous methods using the proposed BUG. An application in fault diagnosis is used to illustrate the effectiveness of the proposed BUG. Some further work is also summarized to present the potentials of the proposed BUG.
Xiangjun Mi; Bingyi Kang. On the belief universal gravitation (BUG). Computers & Industrial Engineering 2020, 148, 106685 .
AMA StyleXiangjun Mi, Bingyi Kang. On the belief universal gravitation (BUG). Computers & Industrial Engineering. 2020; 148 ():106685.
Chicago/Turabian StyleXiangjun Mi; Bingyi Kang. 2020. "On the belief universal gravitation (BUG)." Computers & Industrial Engineering 148, no. : 106685.
How to effectively deal with uncertain information has traditionally been a concern. The D numbers theory overcomes the limitations of Dempster–Shafer theory and further strengthens the ability of uncertainty modeling. Recently, Yager et al. proposed a soft likelihood function which can effectively combine probability information. Related research has enriched and expanded its connotation, but there are still problems to be solved. This paper conducted further research and proposed a new soft likelihood function based on D numbers. Comparison and discussion illustrate the rationality and superiority of the proposed methodology.
Ye Tian; Xiangjun Mi; Lili Liu; Bingyi Kang. A New Soft Likelihood Function Based on D Numbers in Handling Uncertain Information. International Journal of Fuzzy Systems 2020, 22, 1 -17.
AMA StyleYe Tian, Xiangjun Mi, Lili Liu, Bingyi Kang. A New Soft Likelihood Function Based on D Numbers in Handling Uncertain Information. International Journal of Fuzzy Systems. 2020; 22 (7):1-17.
Chicago/Turabian StyleYe Tian; Xiangjun Mi; Lili Liu; Bingyi Kang. 2020. "A New Soft Likelihood Function Based on D Numbers in Handling Uncertain Information." International Journal of Fuzzy Systems 22, no. 7: 1-17.
The negation of a problem provides a new perspective for information representation. However, existing negation method has limitations since it can only be applied to the accurately expressed knowledge. Real-world information is imperfect and imprecise. It usually describes in natural language. In view of this, Prof. Zadeh suggested the concept of Z-number as a more adequate way for description of real world information. As Z-number involves both fuzzy and probabilistic uncertainty, a novel method for the negation of Z-number in combination of probability and fuzziness is proposed from the reliability of probability transmission in this paper. Moreover, several examples are used to describe the negation process and result. As far as our latest knowledge is concerned, the negation of Z-number has not been covered by researchers, so this may be another door for us to process Z-number-based information.
Qing Liu; Huizi Cui; Ye Tian; Bingyi Kang. On the Negation of discrete Z-numbers. Information Sciences 2020, 537, 18 -29.
AMA StyleQing Liu, Huizi Cui, Ye Tian, Bingyi Kang. On the Negation of discrete Z-numbers. Information Sciences. 2020; 537 ():18-29.
Chicago/Turabian StyleQing Liu; Huizi Cui; Ye Tian; Bingyi Kang. 2020. "On the Negation of discrete Z-numbers." Information Sciences 537, no. : 18-29.
How to generate Z-number is an important and open issue in the uncertain information processing of Z-number. In Kang et al. (Int J Intell Syst 33(8):1745–1755, 2018), a method of generating Z-number using OWA weight and maximum entropy is investigated. However, the meaning of the method in Kang et al. (2018) is not clear enough according to the definition of Z-number. Inspired by the methodology in Kang et al. (2018), we modify the method of determining Z-number based on OWA weights and maximum entropy, which is more clear about the meaning of Z-number. In addition, the model of generating Z-number under the environment of group decision making is well investigated based the modified model. Some numerical examples are used to illustrate the effectiveness of the proposed methodology.
Ye Tian; Bingyi Kang. A modified method of generating Z-number based on OWA weights and maximum entropy. Soft Computing 2020, 24, 15841 -15852.
AMA StyleYe Tian, Bingyi Kang. A modified method of generating Z-number based on OWA weights and maximum entropy. Soft Computing. 2020; 24 (20):15841-15852.
Chicago/Turabian StyleYe Tian; Bingyi Kang. 2020. "A modified method of generating Z-number based on OWA weights and maximum entropy." Soft Computing 24, no. 20: 15841-15852.
In Dempster-Shafer (D-S) evidence theory, how to deal with conflict is an important and open topic. Two key strategies for resolving conflicts of evidence are considered, namely information averaging and information focus. How to balance this relationship is still a question worth considering. Recently, Ma et al. studied evidence conflicts from the perspective of complete conflict set and proposed a flexible rule for conflict evidence combination. The proposed combination rule seems to take into account the above two strategies. However, through analysis, we find that Ma et al.’s method tends to use the average method to solve conflicting propositions, while Dempster’s combined rule has a weak focusing function. In this paper, based on the concept of non-conflict element set, a new conflict handling method is proposed. First, the similarity between the evidences is characterized by the correlation coefficient; based on this, a new weighting scheme of evidence is developed. In addition, the propositional support is reasonably allocated through discounts.Through numerical examples, the applicability and superiority of the method are compared and analyzed. The results show that the proposed method takes two strategies of averaging and focusing into consideration, and the information variance is small.
Xiangjun Mi; Bingyi Kang. A Modified Approach to Conflict Management From the Perspective of Non-Conflicting Element Set. IEEE Access 2020, 8, 73111 -73126.
AMA StyleXiangjun Mi, Bingyi Kang. A Modified Approach to Conflict Management From the Perspective of Non-Conflicting Element Set. IEEE Access. 2020; 8 (99):73111-73126.
Chicago/Turabian StyleXiangjun Mi; Bingyi Kang. 2020. "A Modified Approach to Conflict Management From the Perspective of Non-Conflicting Element Set." IEEE Access 8, no. 99: 73111-73126.
Deng entropy is a novel and efficient uncertainty measure to deal with imprecise phenomenon, which is an extension of Shannon entropy. In this paper, power law and dimension of the maximum value for belief distribution with the max Deng entropy are presented, which partially uncover the inherent physical meanings of Deng entropy from the perspective of statistics. This indicated some work related to power law or scale-free can be analyzed using Deng entropy. The results of some numerical simulations are used to support the new views.
Ruonan Zhu; Jiaqi Chen; Bingyi Kang. Power Law and Dimension of the Maximum Value for Belief Distribution With the Maximum Deng Entropy. IEEE Access 2020, 8, 47713 -47719.
AMA StyleRuonan Zhu, Jiaqi Chen, Bingyi Kang. Power Law and Dimension of the Maximum Value for Belief Distribution With the Maximum Deng Entropy. IEEE Access. 2020; 8 (99):47713-47719.
Chicago/Turabian StyleRuonan Zhu; Jiaqi Chen; Bingyi Kang. 2020. "Power Law and Dimension of the Maximum Value for Belief Distribution With the Maximum Deng Entropy." IEEE Access 8, no. 99: 47713-47719.
Dempster-Shafer evidence theory has been widely applied to solving data fusion problems. However, it is still an open issue about how to combine the evidences effectively when the high conflict evidences are collected. Many scholars have made improvements to solve this problem, but there are new problems such as violation of the theoretical attributes of D-S combination rules and limitations of application scope of improvement methods. Considering these shortcomings, a new evidence synthesis formula based on correlation coefficient of belief functions is proposed in this paper. Our contribution is that the proposed formula can solve the highly conflict issues mentioned above effectively. Moreover, the various types of evidences collected can be well combined. One of the advantages of the proposed model is that conflict coefficient Kr is the coefficient of the fusion formula which represents the degree of conflict about evidences. So the fusion process is more flexible and useful. Several examples and comparative experimental simulation are used to illustrate the effectiveness of the proposed methodology.
Pengdan Zhang; Ye Tian; Bingyi Kang. A New Synthesis Combination Rule Based on Evidential Correlation Coefficient. IEEE Access 2020, 8, 39898 -39906.
AMA StylePengdan Zhang, Ye Tian, Bingyi Kang. A New Synthesis Combination Rule Based on Evidential Correlation Coefficient. IEEE Access. 2020; 8 (99):39898-39906.
Chicago/Turabian StylePengdan Zhang; Ye Tian; Bingyi Kang. 2020. "A New Synthesis Combination Rule Based on Evidential Correlation Coefficient." IEEE Access 8, no. 99: 39898-39906.
Information fusion is an important research direction. In this field, there are plenty of ways to combine evidence. Initially, Yager proposed a soft‐likelihood function based on the ordered weighted average (OWA) operator to effectively fuse compatible probabilistic evidence. Recently, Song et al proposed a new soft‐likelihood function based on the power ordered weighted average (POWA) operator. However, through analysis, we find Song et al's method has the following two shortcomings: (a) The weight of POWA cannot comprehensively reflect the relation between probability and OWA operator. (b) The soft‐likelihood function does not reflect the preferences of decision makers. To overcome the above problem, we propose a modified soft‐likelihood function. The effectiveness of the proposed method is demonstrated from the perspective of theoretical analysis and numerical examples.
Xiangjun Mi; Ye Tian; Bingyi Kang. A modified soft‐likelihood function based on POWA operator. International Journal of Intelligent Systems 2020, 35, 869 -890.
AMA StyleXiangjun Mi, Ye Tian, Bingyi Kang. A modified soft‐likelihood function based on POWA operator. International Journal of Intelligent Systems. 2020; 35 (5):869-890.
Chicago/Turabian StyleXiangjun Mi; Ye Tian; Bingyi Kang. 2020. "A modified soft‐likelihood function based on POWA operator." International Journal of Intelligent Systems 35, no. 5: 869-890.
The negation of probability distribution becomes an important topic since some problems are burdensome to deal with directly. Inspired by Yager's negation of probability distribution, an extension model to measure the negation of a probability distribution is proposed using the idea of a nonextensive statistic based on Tsallis entropy. Proofs show that the proposed extension of negation of probability distribution converges to the maximum Tsallis entropy. The proposed model may extend Yager's method to consider the influences of the correlations in a system, which gives the different convergent routes. Some numerical simulation results are used to illustrate the effectiveness of the proposed methodology.
Jing Zhang; Ruqin Liu; Jianfeng Zhang; Bingyi Kang. Extension of Yager's negation of a probability distribution based on Tsallis entropy. International Journal of Intelligent Systems 2019, 35, 72 -84.
AMA StyleJing Zhang, Ruqin Liu, Jianfeng Zhang, Bingyi Kang. Extension of Yager's negation of a probability distribution based on Tsallis entropy. International Journal of Intelligent Systems. 2019; 35 (1):72-84.
Chicago/Turabian StyleJing Zhang; Ruqin Liu; Jianfeng Zhang; Bingyi Kang. 2019. "Extension of Yager's negation of a probability distribution based on Tsallis entropy." International Journal of Intelligent Systems 35, no. 1: 72-84.
Qing Liu; Ye Tian; Bingyi Kang. Derive knowledge of Z-number from the perspective of Dempster–Shafer evidence theory. Engineering Applications of Artificial Intelligence 2019, 85, 754 -764.
AMA StyleQing Liu, Ye Tian, Bingyi Kang. Derive knowledge of Z-number from the perspective of Dempster–Shafer evidence theory. Engineering Applications of Artificial Intelligence. 2019; 85 ():754-764.
Chicago/Turabian StyleQing Liu; Ye Tian; Bingyi Kang. 2019. "Derive knowledge of Z-number from the perspective of Dempster–Shafer evidence theory." Engineering Applications of Artificial Intelligence 85, no. : 754-764.
A method of constructing hierarchy organization from the perspective of the maximum Deng entropy is proposed. The organization generated from the improved method can make the system take the task more stably and flexibly. A method of obtaining the ability of the department of the hierarchy organization through the maximum Deng entropy is proposed, which is compatible with the mechanic of the complex network. Some numerical examples are used to illustrate the effectiveness of the proposed methodologies.
Bingyi Kang. Construction of Stable Hierarchy Organization from the Perspective of the Maximum Deng Entropy. Transactions on Petri Nets and Other Models of Concurrency XV 2019, 421 -431.
AMA StyleBingyi Kang. Construction of Stable Hierarchy Organization from the Perspective of the Maximum Deng Entropy. Transactions on Petri Nets and Other Models of Concurrency XV. 2019; ():421-431.
Chicago/Turabian StyleBingyi Kang. 2019. "Construction of Stable Hierarchy Organization from the Perspective of the Maximum Deng Entropy." Transactions on Petri Nets and Other Models of Concurrency XV , no. : 421-431.
Environmental assessment and decision making is complex leading to uncertainty due to multiple criteria involved with uncertain information. Uncertainty is an unavoidable and inevitable element of any environmental evaluation process. The published literatures rarely include the studies on uncertain data with variable fuzzy reliabilities. This research has proposed an environmental evaluation framework based on Dempster–Shafer theory and Z-numbers. Of which a new notion of the utility of fuzzy number is proposed to generate the basic probability assignment of Z-numbers. The framework can effectively aggregate uncertain data with different fuzzy reliabilities to obtain a comprehensive evaluation measure. The proposed model has been applied to two case studies to illustrate the proposed framework and show its effectiveness in environmental evaluations. Results show that the proposed framework can improve the previous methods with comparability considering the reliability of information using Z-numbers. The proposed method is more flexible comparing with previous work.
Bingyi Kang; Pengdan Zhang; Zhenyu Gao; Gyan Chhipi-Shrestha; Kasun Hewage; Rehan Sadiq. Environmental assessment under uncertainty using Dempster–Shafer theory and Z-numbers. Journal of Ambient Intelligence and Humanized Computing 2019, 11, 2041 -2060.
AMA StyleBingyi Kang, Pengdan Zhang, Zhenyu Gao, Gyan Chhipi-Shrestha, Kasun Hewage, Rehan Sadiq. Environmental assessment under uncertainty using Dempster–Shafer theory and Z-numbers. Journal of Ambient Intelligence and Humanized Computing. 2019; 11 (5):2041-2060.
Chicago/Turabian StyleBingyi Kang; Pengdan Zhang; Zhenyu Gao; Gyan Chhipi-Shrestha; Kasun Hewage; Rehan Sadiq. 2019. "Environmental assessment under uncertainty using Dempster–Shafer theory and Z-numbers." Journal of Ambient Intelligence and Humanized Computing 11, no. 5: 2041-2060.
How to manage the uncertainty of the basic probability assignment accurately and efficiently is of significance and also an open issue. Plenty of functions have been established to cover the issue, especially Deng entropy recently. Deng entropy can deal with the more complex situation of the focal elements (propositions). However, Deng entropy has some limitations when the propositions are of the intersection. In this paper, a modified function is proposed by considering the scale of the frame of discernment and the influence of the intersection between statements on uncertainty. The proposed belief entropy provides a promising way to measure the uncertain information. Some numerical examples and an application in pattern recognition are used to show the efficiency and accuracy of the proposed belief entropy.
Huizi Cui; Qing Liu; Jianfeng Zhang; Bingyi Kang. An Improved Deng Entropy and Its Application in Pattern Recognition. IEEE Access 2019, 7, 18284 -18292.
AMA StyleHuizi Cui, Qing Liu, Jianfeng Zhang, Bingyi Kang. An Improved Deng Entropy and Its Application in Pattern Recognition. IEEE Access. 2019; 7 ():18284-18292.
Chicago/Turabian StyleHuizi Cui; Qing Liu; Jianfeng Zhang; Bingyi Kang. 2019. "An Improved Deng Entropy and Its Application in Pattern Recognition." IEEE Access 7, no. : 18284-18292.