# Conceptual Design Evaluation Considering Confidence Based on Z-AHP-TOPSIS Method
## 2 Literature Review  
Due to the increasing diversification of consumer demand in new product development (NPD), enterprises want to obtain products that meet the expected results and need to adopt modern methods, technologies, and tools to reduce production costs [12]. As conceptual design evaluation plays an essential role in NPD, it has attracted the attention of many researchers [13; 14]. Conceptual design evaluation is the process of determining design criteria and selecting the best scheme from the possible options, which can be considered a multi-attribute decision-making (MADM) problem. MADM deals with finding the best solution from a limited number of solutions, which usually have the characteristics of large number and conflict. With the increase in the number of alternatives available for evaluation and the decrease in available time, it is difficult for DMs to make the objective decision because of the imprecise information regarding alternatives. Some related studies consider statistical methods to complete the new design conceptual evaluation such as SWOT (strength/weakness/opportunity/threat) analysis [15], Pugh matrix [16], balanced scorecard [17], etc. Although the statistical evaluation method is simple and suitable for applications, its evaluation efficiency is significantly reduced for complex NPD. Another more general evaluation method is to utilize various MADM models, such as the analytic hierarchical process (AHP) [18], the analytic network process (ANP) [19], the technique for order preference by similarity to ideal solution (TOPSIS) [20], and weighted aggregated sum product assessment (WASPAS) [21], have been utilized to evaluate design options and select the best design concept. In addition, the application of the stochastic multicriteria acceptability analysis (SMAA) in MADM also achieved good results [22; 23]. The above methods are deterministic models. Because DMs are faced with fuzzy information in the early stage of product design, they prefer to use natural language for evaluation. The deterministic model cannot fully capture the fuzzy and subjective judgment and preference in the design evaluation process. The fuzzy set theory effectively solves these problems and has been applied in many fields. [PERSON] et al. [24] proposed a novel adaptive mask generating algorithm based on the fuzzy set theory to automatically calculate an optimal threshold. [PERSON] et al. [25] presented a new method based the fuzzy set theory to measure the level of maintenance sustainability. Therefore, it is beneficial to combine the deterministic method with the fuzzy evaluation method. For instance, [PERSON] et al. [26] proposed a framework of financial performance evaluation based on fuzzy TOPSIS. [PERSON] et al. [27] proposed the fuzzy ANP method using fuzzy triangular numbers to represent linguistic variables and calculated the critical metrics of significant and export cities. [PERSON] et al. [28] proposed a hybrid fuzzy model for evaluation to converge upon product design concepts associated with lesser supply chain risks. When the subjective judgment of DM is transformed into a fuzzy number, there may be potential problems because the confidence of DMs, that is, the information about how sure the DM is of the evaluation, is not included in this transformation. Unlike the classical fuzzy set theory, once the Z-number is used, DM can add the reliability related to judgment into decision-making to eliminate ambiguity and enhance the objectivity of evaluation information. The successful application of Z-number in MADM also appears in the literature. [PERSON] et al. [29] proposed a method based on a multilevel fuzzy cognitive map and Z-number theory to evaluate the risk of the production process by considering both reliability and uncertainty. [PERSON] [30] proposed a mathematical model of the portfolio problem based on Z-number and gave the best portfolio in all deterministic and non-deterministic formulas under bubble conditions. [PERSON] et al.