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The selection of plant location plays a very important role in minimizing cost and maximizing the use of resources for many companies. In this paper, a new TOPSIS approach for selecting plant location under linguistic environments is presented, where the ratings of various alternative locations under various criteria, and the weights of various criteria are assessed in linguistic terms represented by fuzzy numbers. To avoid complicated fuzzy arithmetic operations, the linguistic variables, which are represented by triangular fuzzy numbers, are transformed into crisp numbers based on graded mean representation. The canonical representation of multiplication operations on triangular fuzzy numbers is used to obtain the "positive ideal solution" and the "negative ideal solution". The closeness efficient is defined to determine the ranking order of all alternatives by calculating the distance to both the "positive-ideal solution" and the "negative-ideal solution" simultaneously. Compared with existing fuzzy TOPSIS methods, the proposed method can deal with group decision-making problems in a more efficient manner. A numerical example of plant location selection is used to illustrate the efficiency of the proposed method.

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As an extension of probability theory, evidence theory is able to better handle unknown and imprecise information. Owing to its advantages, evidence theory has more flexibility and effectiveness for modeling and processing uncertain information. Uncertainty measure plays an essential role both in evidence theory and probability theory. In probability theory, Shannon entropy provides a novel perspective for measuring uncertainty. Various entropies exist for measuring the uncertainty of basic probability assignment (BPA) in evidence theory. However, from the standpoint of the requirements of uncertainty measurement and physics, these entropies are controversial. Therefore, the process for measuring BPA uncertainty currently remains an open issue in the literature. Firstly, this paper reviews the measures of uncertainty in evidence theory followed by an analysis of some related controversies. Secondly, we discuss the development of Deng entropy as an effective way to measure uncertainty, including introducing its definition, analyzing its properties, and comparing it to other measures. We also examine the concept of maximum Deng entropy, the pseudo-Pascal triangle of maximum Deng entropy, generalized belief entropy, and measures of divergence. In addition, we conduct an analysis of the application of Deng entropy and further examine the challenges for future studies on uncertainty measurement in evidence theory. Finally, a conclusion is provided to summarize this study.

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Failure mode and effects analysis (FMEA) is a widely used technique for assessing the risk of potential failure modes in designs, products, processes, system, and services. One of the main problems with FMEA is the need to address a variety of assessments given by FMEA team members and the sequence of the failure modes according to the degree of risk factors. Many different methods have been proposed to improve the traditional FMEA, which is impractical when the risk assessments given by multiple experts to one failure mode are imprecise, incomplete, or inconsistent. However, the existing methods cannot adequately handle these types of uncertainties. In this paper, a new risk priority model based on D numbers and technique for the order of preference by similarity to ideal solution (TOPSIS) is proposed to evaluate the risk in FMEA. In the proposed model, the assessments given by the FMEA team members are represented by D numbers, where a new feasible and effective method can effectively represent the uncertain information. The TOPSIS method, a multicriteria decision‐making method is presented to rank the preference of failure modes with respect to risk factors. Finally, an application of the failure modes of the rotor blades of an aircraft turbine is provided to illustrate the efficiency of the proposed method.