Abstract

     The weight and reliability of an individual assessment are two important concepts considered in the evidential reasoning (ER) approach. Through analyzing the existing studies on the combination of individual assessments with both their weights and reliabilities considered in the ER context, their deficiencies are identified in accordance with two principles. One principle is developed in the situation where a specific individual assessment is fully unreliable and the other is developed in the situation where all individual assessments are fully reliable. To address the deficiencies, this paper proposes a new method. In the method, a combination process that takes into account both the weights and reliabilities of individual assessments simultaneously is developed to generate the overall assessment. It is theoretically proven that the combination process satisfies the two principles. Three ways are designed to help a decision maker to flexibly provide individual assessments and determine their reliabilities. A strategic project evaluation problem for an enterprise located in Changzhou, Jiangsu, China is analyzed using the proposed method as a case study to demonstrate its validity and applicability. These are highlighted by its comparison with two existing methods.

Introduction

     When facing real world problems or challenges, people usually need to take into account multiple diverse or conflicting perspectives to make satisfactory decisions. To facilitate the analysis of problems, multiple criteria decision making (MCDM) methods have been applied (Hafezalkotob et al., 2019; Liao et al., 2020; Ma et al., 2018). Representative applications include the selection of sustainable suppliers (Girubha et al., 2016), the evaluation of new product pricing strategies (Baykaso ˘glu et al., 2017), the selection of socially responsible investments (Bilbao-Terol et al., 2016), the evaluation of logistics performance in hospitals (Longaray et al., 2018), and the evaluation of photovoltaic cells (García-Cascales et al., 2012). In studies on MCDM, criterion weights are commonly considered although their meanings may be different. They are generally used to make trade-offs among criteria (Butler et al., 1997, 2001).

     There is another important concept associated with each criterion as implied in the work of Yang and Xu (2013), which is reliability. Reliability is a very common concept usually associated with specific meanings in different contexts. For example, in the context of system, reliability is evaluated to improve system performance or safety (Wang et al., 2011); while in the context of underground structures, reliability is measured by the probability that the structures have been safe over a period of time (Wang & Fang, 2018). Differently, in the context of MCDM, the reliability of a criterion means the reliability of the individual assessment on the criterion. When all data are available and the judgments of a decision maker are not explicitly required, most MCDM methods can find a solution by comprehensively considering all data. However, when the judgments of a decision maker are necessary, many MCDM methods may be able to generate a solution that is consistent with what is anticipated by the decision maker. This paper focuses on the second type of situations. In such cases, the reliability of an individual assessment should be explicitly considered in the analysis of the MCDM problems. Unfortunately, in existing studies, criterion weights are usually considered to make tradeoffs among criteria under the assumption that all individual assessments are fully reliable and thus reliabilities of criteria are not explicitly considered in MCDM processes. This assumption may not be valid in many practical cases and may result in a solution that is not satisfactory or acceptable to a decision maker. An example of breast cancer screening is provided to demonstrate this.

Conclusions

     To focus on MCDM problems modeled by belief functions with the consideration of the weights and reliabilities of individual assessments, the deficiencies of existing studies in two extreme situations and general situations are analyzed. To overcome the deficiencies, a new MCDM method with belief functions is proposed. In the method, a new process is designed to combine individual assessments with their weights and reliabilities. The process is theoretically proven to be correct in two extreme situations and is numerically demonstrated to be correct in general situations. To make the new process applicable, three ways are designed to help a decision maker flexibly provide individual assessments and correspondingly obtain their reliabilities. The generation of a solution is then presented. The proposed method is applied to solve the SPE problem for an enterprise that primarily provides high-quality gear boxes for high-speed trains. Through the data in the SPE problem, the main contributions of the proposed method are highlighted by its comparison with existing studies.