# Conceptual Design Evaluation Considering Confidence Based on Z-AHP-TOPSIS Method
###### Abstract  
In concept design, effective decision making and management of schemes can shorten the design cycle and improve product quality. The decision maker (DM)'s confidence is one of the critical factors affecting the conceptual design evaluation. Although many studies use quantitative linguistic evaluation for design scheme decision-making, which improves product conceptual design decision-making efficiency and effectiveness, few studies consider the confidence level of a decision. A conceptual design evaluation method based on Z-numbers is proposed to solve this problem, considering the customer requirements and the DM's confidence. Firstly, the evaluation criteria are determined by analyzing customer requirements; then, the fuzzy analytic hierarchy process in the Z-numbers environment (Z-AHP) is used to determine the criteria weight; Finally, the fuzzy technique for order preference by similarity to ideal solution method in the Z-numbers environment (Z-TOPSIS) is used to evaluate the design schemes to obtain the optimal scheme. The proposed method is applied to the selection of the design scheme of the waste containers in the kitchen. The results show that considering the DM's self-confidence can achieve a more reasonable and practical evaluation of the conceptual design scheme, and it is easier to obtain the best scheme. conceptual design evaluation; Z-numbers; fuzzy AHP; fuzzy TOPSIS; confidence +
Footnote †: journal: Applied  
11 July 202110 August 202111 July 202110 August 202111 July 202110 August 202111 July 202110 August 202111 July 202110 August 202111 July 202110 August  
design stage, this area will become smaller and may become irreparable or correctable in the product design stage. In conceptual design evaluation, decision-makers (DMs) prefer to use natural language to express judgment and preference with the increase of reference factors or evaluation indicators. For example, define an evaluation scale set as (good, poor, very poor) to evaluate the practicability of a product. In this case, the linguistic terms in the evaluation scale set are linguistic variables [4]. The traditional scoring method maps linguistic variables to a precise value (such as good = 2, very poor = 0) to quantify linguistic terms, which is classical logic (also known as binary logic or Boolean logic) [5]. However, in the evaluation process, semantic concepts are often uncertain, and whether an element belongs to a semantic concept is often a gradual process rather than a mutation process. For example, if the concept with a score of more than five is defined as \"good\" then \"good\" is classical logic, and the score of 5 is \"good\" while 4.9 is not \"good\". Its set representation is shown in Figure 1(a). In fact, in people's understanding there is no big difference between 5 and 4.9 (more than five belongs to \"good\", but 4.9 also belongs to \"good\"). In order to better model semantic concepts, [PERSON] [6] proposed fuzzy set theory. It extends the representation of classical sets and expresses the membership degree of each element in the set as [0, 1], which is usually used to describe the value of linguistic variables. Using fuzzy sets can grasp the inherent fuzziness of human evaluation better, more accurately, and more meaningfully. Figure 1(b) is a fuzzy set corresponding to the semantic concept of \"good\". The scores between 4.5 and 5 are also \"good\", but they have different degrees of membership. Compared with classical logic, fuzzy sets can better  
Figure 1: Opportunity in conceptual design. Figure 2: Different representations of “good”. (**a**) Classical set (**b**) Fuzzy set. model the uncertainty of people's understanding of semantic concepts. Therefore, the fuzzy linguistic quantification method is a very suitable method of modelling and processing the relevant information of conceptual design evaluation [7]. To formalize the uncertainty, [PERSON] proposed the Z-number method [8]. Z-number is an ordered pair (\(A\), \(B\)), where \(A\) is a fuzzy value and \(B\) is \(A\)'s reliability.