# Conceptual Design Evaluation Considering Confidence Based on Z-AHP-TOPSIS Method
###### Abstract
Since Z-number describes both the limit of value and the reliability of the limit, it describes human knowledge more comprehensively than general fuzzy numbers. When the influence of uncertainty is significant, the uncertainty can be accurately modeled by using a Z-number. The traditional method of conceptual design evaluation is to think that the information is reliable or definite. However, knowledge or information in the real world contains various types of uncertainty. When the reliability of information is ignored, we need to consider the potential information loss and its impact. According to the literature [9], there are two main types of information imperfection: uncertainty and imprecision. Due to the influence of professional background, knowledge level, experience, and other factors, DM will produce different degrees of hesitation and uncertainty in different evaluation indexes. This phenomenon is accessible to causes deviation in scheme evaluation and may not obtain the product design scheme to meet the market demand and enterprise profit demand. At present, the research of conceptual design evaluation focuses on combining the existing decision-making methods and adding fuzzy methods to improve the authenticity of evaluation information, mainly using a fuzzy set, rough number, or rough set evaluation without considering the reliability of decision-making related information (that is, the degree of hesitation and uncertainty of DM) [10; 11]. If we do not consider DM's confidence in the evaluation index, the evaluation may be too subjective, or the result may be unreasonable. Given the above problems, we propose different DMs to use different evaluation confidence scales for conceptual design evaluation to make up for the lack of quantitative information reliability when using the fuzzy method. When the available information is qualitative, fuzzy sets are used to model semantics in conceptual design evaluation. Then, a Z-number is used to supplement these fuzzy sets with additional fuzzy sets, representing the reliability of the previous fuzzy set, that is, the certainty of DM for information evaluation. First, DM evaluates the concept and shows the degree of self-confidence. Constructing and using different confidence linguistic term sets to express the situation from self-confidence to non-self-confidence can reflect the knowledge level and experience differences of different DMs. Then, the Z-number is used to represent the evaluation information of DMs, and it is transformed into a regular fuzzy number. Next, fuzzy AHP in the Z-number environment (Z-AHP) is used to determine the weight of customer requirements. Finally, fuzzy TOPSIS in the Z-number environment (Z-TOPSIS) is used to sort the design schemes. The rest of this paper is structured as follows. The second section summarizes the literature on concept selection methods. Section 3 introduces some basic concepts and methods. The fourth section is a case study that proves the proposed framework's feasibility through a new design task. The fifth section is the discussion and the sixth section is the conclusion.