A new interactive design approach for concept selection based on expert opinion

Abstract

Effective identification of the optimal design in the early stages of product development is critical in order to obtain the best chances of eventual customer satisfaction. Currently, the advancements in prototyping techniques offer unique chances to evaluate the features of different design candidates by means of product experts acting as assessors and/or customers enrolled as testers. In this paper, the candidate identification using virtual and physical prototypes is described and a practical fuzzy approach toward the evaluation of the optimal design is presented. The proposed methodology is tested on a full case study, namely the choice of optimal design for the traditional Neapolitan coffeemaker, inspired by the prototypes of the Italian designer Riccardo Dalisi. Several concepts are developed in a virtual environment and four alternatives among them are realized using Additive Manufacturing. By allowing experts to interact with virtual and physical prototypes, they were able to express their opinion on a custom fuzzy evaluation scale (i.e. they were freely choosing more or less coarse linguistic scales as well as the related shapes of fuzzy sets to adequately represent the level of fuzziness of their judgments). Once the opinions are collected, the set of best candidate(s) is easily identified and useful suggestion can be obtained for further developing the product.

Appendix

Once the m experts rated the n alternatives by linguistic performance values, as in the $m\times n$ Table 6, the need for obtaining a collective performance evaluation for each alternative requires deploying a two steps process: making the multi-granular information uniform and suitably aggregate the ratings.

• 1. The linguistic performance value is translated into the BLTS ( $S_T \left\{ c_0, c_1, \dots , c_g \right\}$ choosen as the scale with the greatest number of grades among the linguistic term sets $S_j \left\{ l_0, l_1, \dots , l_{p_j} \right\}$ expressed by the experts $p_j \le g$) via a multi-granularity transformation $\tau _{S_jS_T}$ so defined as:

  $$\begin{aligned}&\tau _{S_{j}S_{T}}: S_{j} \rightarrow F\left( {S_{T}} \right) \end{aligned}$$

  (3)
  $$\begin{aligned}&\tau _{S_{j}S_{T}}\left( {l_{ij}} \right) =\left\{ {\left( {c_{k}, b_k^{ij}} \right) } \right\} \end{aligned}$$

  (4)

  where:

  $$\begin{aligned}&b_k^{ij}= \underset{y}{\max } \min \left\{ {\mu _{l_{ij}}\left( {y} \right) ,\mu _{c_k}\left( {y} \right) } \right\} \\&i=1,2, \ldots , n; \quad j=1,2, \ldots , m; \quad k=0,1, \ldots , g \end{aligned}$$

  Therefore, the linguistic performance values are homogenized onto the BLTS as:

  $$\begin{aligned} r_{ij}=\left( {b_0^{ij}, b_1^{ij}, \ldots , b_g^{ij}} \right) \end{aligned}$$

  (5)

• 2. The linguistic performance values are aggregated into collective linguistic performance values as:

  $$\begin{aligned} r_i={\left( { b_0^{i}, b_1^{i}, \ldots , b_g^{i}} \right) } \end{aligned}$$

  (6)

  by means of a OWA generated by a regular increasing monotone, RIM, linguistic quantifier.

Since the experts evaluated the alternantives whit reference to different dimensions, all needed for a successful design, the chosen quantifier is as many as possible and the resulting OWA weights are calculated accordingly ($w_j : [0, 0, 0.2, 0.4, 0.4]$, orness: 0.2, entropy: 1.05); therefore the $n\times \left( g +1 \right)$ matrix in Table 7 represent the profile of each alternative onto the BLTS.

Having all the alternatives rated on the BLTS as fuzzy sets, a fuzzy preference relation can be computed and a suitable choice method to rank the alternatives and identify the best one(s) applied. Following the approach of possibility of dominance, the matrix $D = \left[ d_{ih}\right]$ is calculated by pairwise comparing any alternative i to the other $h \ne i$, where:

$$\begin{aligned} d_{ih}= \underset{c_k}{\max } ~\underset{c_k,c_l}{\min } \left\{ {\mu _r^i\left( {c_k} \right) ,\mu _r^h\left( {c_l} \right) } \right\} \end{aligned}$$

(7)

so as to obtain the $d_{ih}$ values collected in Table 8.

Table 8 Values $d_{ih}$ of the matrix D

Table 9 Values $\delta _{ih}$ of the matrix $\varDelta$ and index on non-dominance $\mu _{ND}$

Finally, the non-dominance choice degree (i.e. the membership of each alternative to the set of non dominated ones ND, $\mu _{ND}$) is easily computed from the strict non dominance scores $\delta$, obtained by matrix D as:

$$\begin{aligned} \delta _{ih}= & {} \max \{d_{ih} - d_{hi} , 0 \} \end{aligned}$$

(8)

$$\begin{aligned} \mu _{ND}= & {} \underset{a_h}{\min }\left\{ {1-\delta _{ih}, h\ne i} \right\} \end{aligned}$$

(9)

which yields to the matrix $\varDelta = \left[ \delta _{ih}\right]$ and finally to the $\mu _{ND}$ vector, as reported in Table 9.