The arithmetic of discrete Z-numbers

Best Worst Method (BWM) has recently been proposed as a method for Multi Criteria Decision Making (MCDM). Studies show that BWM compared with other methods such as Analytic Hierarchy Process (AHP), leads to lower inconsistency of the results while reducing the number of required pairwise comparisons. MCDM methods such as BWM require accurate information. However, it often happens in practice that a level of uncertainty accompanies the information. The main aim of this paper is to address this problem and provide an integration of BWM and Z-numbers, namely ZBWM. Providing BWM with Z-numbers enables the BWM method to handle the uncertainty of information of a multi-criteria decision. Additionally, the capabilities of the proposed method in the process of utilizing the linguistic information dealing with big data are highlighted. The proposed method is examined to address a supplier development problem. By experimental results, we show that ZBWM results lower inconsistency when compared with BWM. A Z-number contains subjectivity in its fuzzy part, which can be addressed in future applications of ZBWM.

https://openresearch-repository.anu.edu.au/bitstream/1885/212341/1/ZBWM_AAM.pdf

ZBWM: The Z-number extension of Best Worst Method and its application for supplier development

Z-numbers are a new concept considering both the description of cognitive information and the reliability of information. Linguistic terms are useful tools to adequately and effectively model real-life cognitive information, as well as to characterize the randomness of events. However, a form of Z-numbers, in which their two components are in the form of linguistic terms, is rarely studied, although it is common in decision-making problems. In terms of Z-numbers and linguistic term sets, we provided the definition of linguistic Z-numbers as a form of Z-numbers or a subclass of Z-numbers. Then, we defined some operations of linguistic Z-numbers and proposed a comparison method based on the score and accuracy functions of linguistic Z-numbers. We also presented the distance measure of linguistic Z-numbers. Next, we developed an extended TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method based on the Choquet integral for multi-criteria decision-making (MCDM) problems with linguistic Z-numbers. Finally, we provided an example concerning the selection of medical inquiry applications to demonstrate the feasibility of our proposed approach. We then verified the applicability and superiority of our approach through comparative analyses with other existing methods. Illustrative and comparative analyses indicated that the proposed approach was valid and feasible for different decision-makers and cognitive environments. Furthermore, the final ranking results of the proposed approach were closer to real decision-making processes. Linguistic Z-numbers can flexibly characterize real cognitive information as well as describe the reliability of information. This method not only is a more comprehensive reflection of the decision-makers’ cognition but also is more in line with expression habits. The proposed method inherited the merits of the classical TODIM method and considers the interactivity of criteria; therefore, the proposed method was effective for dealing with real-life MCDM problems. Consideration about bounded rational and the interactivity of criteria made final outcomes convincing and consistent with real decision-making.

Multi-Criteria Decision-Making Method Based on Distance Measure and Choquet Integral for Linguistic Z-Numbers

The arithmetic of continuous Z-numbers

This paper introduces hesitant uncertain linguistic Z-numbers (HULZNs) based on Z-numbers and linguistic models. HULZNs can serve as a reliable tool to depict complex and uncertain decision-making information and reflect the hesitancy of DMs. This paper focuses on the development of an innovative method to address multi-criteria group decision-making (MCGDM) problems in which the weight information is incompletely known. Handling qualitative information requires the effective support of quantitative tools, after which the linguistic scale function is employed to deal with linguistic information. First, the operations and distance of HULZNs are defined. Then, two power aggregation operators for HULZNs are proposed. Subsequently, a new MCGDM approach is developed by incorporating the power aggregation operators and the VIKOR model. Finally, an illustrative example of ERP system selection is provided for demonstration, and the feasibility and validity of the proposed method are further verified by sensitivity analysis and comparison with an existing method.

Hesitant Uncertain Linguistic Z-Numbers and Their Application in Multi-criteria Group Decision-Making Problems

Multi-criteria decision making (MCDM) under uncertain environment is still an open issue. Recently, Znumber has been developed by Zadeh to model fuzzy numbers with the confidence degree. In this paper, a new MCDM method based on Z-number is proposed to deal with linguistic decision making problems. The decision making process can be easily realized step by step with the arithmetic operations on Znumbers. A numerical example on MCDM is used to illustrate the efficiency of the proposed method.

Ya Li

Papers

Decision Making Using Z-numbers under Uncertain Environment