Derive knowledge of Z-number from the perspective of Dempster-Shafer evidence theory

Abstract Z-number, combined with constraint and reliability of the information, is an effective frame to simulate the thinking of humans. How to derive knowledge of Z-numbers, especially from the objective data may become a fascinating and open issue. In this paper, a method of deriving knowledge of Z-numbers from the perspective of Dempster–Shafer theory is proposed. The proposed method considers the Z-number generating from objective and subjective data using Dempster–Shafer theory. Some numerical examples and experimental simulations are used to illustrate the effectiveness of the proposed methodology.

[1]  Jian-Bo Yang,et al.  On the centroids of fuzzy numbers , 2006, Fuzzy Sets Syst..

[2]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[3]  Yi Zhao,et al.  Z-Differential Equations , 2020, IEEE Transactions on Fuzzy Systems.

[4]  Rafik A. Aliev,et al.  The arithmetic of discrete Z-numbers , 2015, Inf. Sci..

[5]  Rafik A. Aliev,et al.  The Arithmetic of Z-Numbers - Theory and Applications , 2015, The Arithmetic of Z-Numbers.

[6]  Shyi-Ming Chen.  FUZZY SYSTEM RELIABILITY-ANALYSIS USING FUZZY NUMBER ARITHMETIC OPERATIONS (VOL 64, PG 31, 1994) , 1994 .

[7]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[8]  Yong Deng,et al.  Performer selection in Human Reliability analysis: D numbers approach , 2019, Int. J. Comput. Commun. Control.

[9]  Liguo Fei,et al.  A new vector valued similarity measure for intuitionistic fuzzy sets based on OWA operators , 2019 .

[10]  Wei Zheng,et al.  Failure Mode and Effects Analysis by Using the House of Reliability-Based Rough VIKOR Approach , 2018, IEEE Transactions on Reliability.

[11]  Witold Pedrycz,et al.  Functions defined on a set of Z-numbers , 2018, Inf. Sci..

[12]  Xinyang Deng,et al.  Analyzing the monotonicity of belief interval based uncertainty measures in belief function theory , 2017, Int. J. Intell. Syst..

[13]  邓勇,et al.  Determination of Basic Probability Assignment Based on Interval Numbers and Its Application , 2012 .

[14]  Yong Deng,et al.  A hybrid intelligent model for assessment of critical success factors in high-risk emergency system , 2018, Journal of Ambient Intelligence and Humanized Computing.

[15]  Yu Yang,et al.  SMAA-based model for decision aiding using regret theory in discrete Z-number context , 2018, Appl. Soft Comput..

[16]  Yong Deng,et al.  An enhanced fuzzy evidential DEMATEL method with its application to identify critical success factors , 2018, Soft Computing.

[17]  Lotfi A. Zadeh,et al.  A note on web intelligence, world knowledge and fuzzy logic , 2004, Data Knowl. Eng..

[18]  Zhen Li,et al.  A novel evidential FMEA method by integrating fuzzy belief structure and grey relational projection method , 2019, Eng. Appl. Artif. Intell..

[19]  Tofigh Allahviranloo,et al.  Z-Advanced numbers processes , 2019, Inf. Sci..

[20]  Yong Deng,et al.  The Negation of Basic Probability Assignment , 2019, IEEE Access.

[21]  Yong Deng,et al.  An interval-valued Pythagorean prioritized operator-based game theoretical framework with its applications in multicriteria group decision making , 2019, Neural Computing and Applications.

[22]  Shi Wen-kang,et al.  Combining belief functions based on distance of evidence , 2004 .

[23]  Yong Deng,et al.  AN EVALUATION FOR SUSTAINABLE MOBILITY EXTENDED BY D NUMBERS , 2019, Technological and Economic Development of Economy.

[24]  Zhiyong Gao,et al.  A novel framework for the reliability modelling of repairable multistate complex mechanical systems considering propagation relationships , 2018, Qual. Reliab. Eng. Int..

[25]  Fuyuan Xiao,et al.  A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on D numbers , 2018, Eng. Appl. Artif. Intell..

[26]  Yong Deng,et al.  A New Method to Determine Generalized Basic Probability Assignment in the Open World , 2019, IEEE Access.

[27]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[28]  Xinyang Deng,et al.  D-AHP method with different credibility of information , 2017, Soft Computing.

[29]  Witold Pedrycz,et al.  Hukuhara difference of Z-numbers , 2018, Inf. Sci..

[30]  Shahram Rahimi,et al.  Integration of Z-numbers and Bayesian decision theory: A hybrid approach to decision making under uncertainty and imprecision , 2018, Appl. Soft Comput..

[31]  Rahib H. Abiyev,et al.  Control of Omnidirectional Robot Using Z-Number-Based Fuzzy System , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[32]  Yong Deng,et al.  A novel matrix game with payoffs of Maxitive Belief Structure , 2018, Int. J. Intell. Syst..

[33]  Fuyuan Xiao,et al.  Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy , 2019, Inf. Fusion.

[34]  Dong-Ling Xu,et al.  Evidential reasoning rule for evidence combination , 2013, Artif. Intell..

[35]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[36]  Lotfi A. Zadeh,et al.  PRUF—a meaning representation language for natural languages , 1978 .

[37]  Fuyuan Xiao,et al.  An improved distance-based total uncertainty measure in belief function theory , 2017, Applied Intelligence.

[38]  Jerry M. Mendel,et al.  Similarity Measures for Closed General Type-2 Fuzzy Sets: Overview, Comparisons, and a Geometric Approach , 2019, IEEE Transactions on Fuzzy Systems.

[39]  Yu Luo,et al.  Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers , 2017, J. Intell. Fuzzy Syst..

[40]  Wen Jiang,et al.  A new medical diagnosis method based on Z-numbers , 2017, Applied Intelligence.

[41]  Zhiyong Gao,et al.  Data Fusion Based Phase Space Reconstruction from Multi-Time Series , 2015 .

[42]  Xinyang Deng,et al.  Dependence assessment in human reliability analysis using an evidential network approach extended by belief rules and uncertainty measures , 2018, Annals of Nuclear Energy.

[43]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[44]  Jianqiang Wang,et al.  Multi-criteria PROMETHEE method based on possibility degree with Z-numbers under uncertain linguistic environment , 2020, J. Ambient Intell. Humaniz. Comput..

[45]  Amir Abbas Najafi,et al.  Portfolio Selection Using Z-Number Theory: Two Solution Methodologies , 2018, Int. J. Fuzzy Syst..

[46]  Guangquan Zhang,et al.  Learning under Concept Drift: A Review , 2019, IEEE Transactions on Knowledge and Data Engineering.

[47]  Xiao Wang,et al.  Type-2 Fuzzy Comprehension Evaluation for Tourist Attractive Competency , 2019, IEEE Transactions on Computational Social Systems.

[48]  K. Mahler,et al.  An unsolved problem on the powers of 3/2 , 1968, Journal of the Australian Mathematical Society.

[49]  Liguo Fei,et al.  A new divergence measure for basic probability assignment and its applications in extremely uncertain environments , 2017, Int. J. Intell. Syst..

[50]  Yong Deng,et al.  Dependent evidence combination based on decision‐making trial and evaluation laboratory method , 2019, Int. J. Intell. Syst..

[51]  Xinyang Deng,et al.  The Negation of a Basic Probability Assignment , 2019, IEEE Transactions on Fuzzy Systems.

[52]  Fuyuan Xiao,et al.  A Multiple-Criteria Decision-Making Method Based on D Numbers and Belief Entropy , 2019, International Journal of Fuzzy Systems.

[53]  Jian-qiang Wang,et al.  Z-VIKOR Method Based on a New Comprehensive Weighted Distance Measure of Z-Number and Its Application , 2018, IEEE Transactions on Fuzzy Systems.

[54]  Didier Dubois,et al.  A Fresh Look at Z-numbers – Relationships with Belief Functions and p-boxes , 2018 .

[55]  Yong Deng,et al.  A new method to measure the divergence in evidential sensor data fusion , 2019, Int. J. Distributed Sens. Networks.

[56]  Zhen Wang,et al.  Zero-sum polymatrix games with link uncertainty: A Dempster-Shafer theory solution , 2019, Appl. Math. Comput..

[57]  Didier Dubois,et al.  Z-numbers as Generalized Probability Boxes , 2018, SMPS.

[58]  Yong Deng,et al.  Combining conflicting evidence using the DEMATEL method , 2018, Soft Comput..

[59]  Fang Liu,et al.  Fuzzy Double C-Means Clustering Based on Sparse Self-Representation , 2018, IEEE Transactions on Fuzzy Systems.

[60]  Elizabeth Chang,et al.  ZBWM: The Z-number extension of Best Worst Method and its application for supplier development , 2018, Expert Syst. Appl..

[61]  Olgierd Hryniewicz.  Statistical properties of the fuzzy p-value , 2018, Int. J. Approx. Reason..

[62]  Xinyang Deng,et al.  Evidence Combination From an Evolutionary Game Theory Perspective , 2015, IEEE Transactions on Cybernetics.

[63]  Zhiyong Gao,et al.  Evidence fusion-based framework for condition evaluation of complex electromechanical system in process industry , 2017, Knowl. Based Syst..

[64]  Chunhe Xie,et al.  Sensor Data Fusion with Z-Numbers and Its Application in Fault Diagnosis , 2016, Sensors.

[65]  Yong Deng,et al.  A New Geometric Mean FMEA Method Based on Information Quality , 2019, IEEE Access.

[66]  Xinyang Deng,et al.  D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment , 2019, Int. J. Approx. Reason..

[67]  Lotfi A. Zadeh,et al.  A Note on Z-numbers , 2011, Inf. Sci..

[68]  P. Smets.  Data fusion in the transferable belief model , 2000, Proceedings of the Third International Conference on Information Fusion.

[69]  Yong Deng,et al.  Engine fault diagnosis based on sensor data fusion considering information quality and evidence theory , 2018, Advances in Mechanical Engineering.

[70]  R.A. Aliev,et al.  The arithmetic of continuous Z-numbers , 2016, Inf. Sci..

[71]  Yong Deng,et al.  Combination of Evidential Sensor Reports with Distance Function and Belief Entropy in Fault Diagnosis , 2019, Int. J. Comput. Commun. Control.

[72]  Witold Pedrycz,et al.  Fuzzy Rule-Based Domain Adaptation in Homogeneous and Heterogeneous Spaces , 2019, IEEE Transactions on Fuzzy Systems.

[73]  Reza Tavakkoli-Moghaddam,et al.  A hybrid Z-number data envelopment analysis and neural network for assessment of supply chain resilience: a case study , 2018, Central Eur. J. Oper. Res..

[74]  Fuyuan Xiao,et al.  A Hybrid Fuzzy Soft Sets Decision Making Method in Medical Diagnosis , 2018, IEEE Access.