Z -number is an effective model to describe uncertainty in the real world. Under the condition that uncertainty reasoning is an important issue to process information, how to achieve Z -valuation uncertainty reasoning is a problem. As a Z -number involves both fuzzy and probabilistic uncertainty, main difficulty in the problem to be solved is accomplishing both two uncertainties’ reasoning. In this paper, a novel Z -network model and its associated reasoning algorithm are proposed to overcome the difficulty. Structure of the proposed Z -network that contains three basic structures is directed acyclic graph, and this is similarly with Bayesian network (BN). Process of reasoning algorithm involves two parts: first, Bayesian reasoning is applied to establish an optimization model for probabilistic uncertainty reasoning in a Z -number; second, the arithmetic approach of discrete Z -number on if–then rule and maximum entropy approach are proposed for fuzzy uncertainty reasoning. Z -network is essentially an extended model on the basis of BN and properties of a Z -number for Z -valuation uncertainty reasoning. In application, a novel framework of dependence assessment in human reliability analysis is proposed based on Z -network, and a case study demonstrates its effectiveness.

A Novel Z -Network Model Based on Bayesian Network and Z -Number

An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges

The q‐rung orthopair fuzzy set (q‐ROFS), originally developed by Yager, is more capable than that of Pythagorean fuzzy set to deal uncertainty in real life. The main goal of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for q‐ROFSs. The primary purpose of the study is to develop the systematic transformation of information measures (distance measure, similarity measure, entropy, and inclusion measure) for q‐ROFSs. For obtaining this goal, some new formulae for information measures of q‐ROFSs are presented. To show the validity of the explored similarity measure, we apply it to pattern recognition, clustering analysis, and medical diagnosis. Some illustrative examples are given to support the findings, and also demonstrate their practicality and availability of similarity measure between q‐ROFSs.

Information measures for q‐rung orthopair fuzzy sets

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.

Environmental assessment under uncertainty using Dempster–Shafer theory and Z-numbers

Investment risk evaluation for new energy resources: An integrated decision support model based on regret theory and ELECTRE III

Z -number is the general representation of real-life information with reliability, and it has adequate description power from the point of view of human perception. This study develops an innovative method for addressing multicriteria group decision-making (MCGDM) problems with Z -numbers under the condition that the weight information is completely unknown. Processing Z -numbers requires effective support of reliable tools. Then, the normal cloud model can be employed to analyze the Z -number construct. First, the potential information involved in Z -numbers is invoked, and a novel concept of normal Z +-value is proposed with the aid of the normal cloud model. The operations, distance measurement, and power aggregation operators of normal Z +-values are defined. Moreover, an MCGDM method is developed by incorporating the defined distance measurement and power aggregation operators into the MultiObjective Optimization by Ratio Analysis plus the Full Multiplicative Form. Finally, an illustrative example concerning air pollution potential evaluation is provided to demonstrate the proposed method. Its feasibility and validity are further verified by a sensitivity analysis and comparison with other existing methods.

Hong-Gang Peng

Papers

A Multicriteria Group Decision-Making Method Based on the Normal Cloud Model With Zadeh's Z -Numbers