A Methodological Framework for New Product Development in Fuzzy Environments

where $h^{\sigma (j)}(x)$ represents the jth largest value in $h(x)$ and $0<j\le 5$.

where the larger ${\mu }_{ix}(0\le {\mu }_{ix}\le 1)$ is, the stronger is the belonging to this attribute.

where $m=\max (\left|SI\right|,\left|DI\right|)$; $SI=\frac{A+O}{A+O+M+I}$ is the satisfaction index; and $DI=-\frac{M+O}{A+O+M+I}$ is the dissatisfaction index. Avikal et al. (14) further considered the importance of attribute R to indicators and stated that $SI=\frac{A+O}{A+O+M+I+R}$ and $DI=-\frac{M+O}{A+O+M+I+R}$. In addition, based on the principle that attribute R is contrary to attribute O, the k value is set to −1.

where the k values are defined as 0, 0.5, 1, 1.5, and −1 for attributes I, M, O, A, and R, respectively.

Step 1:

Design and distribute a questionnaire. Select w indicator and then collect customer demographics and Kano model data. Linguistic variables, such as satisfaction and dissatisfaction, are adopted to collect customer satisfaction and the company’s expected satisfaction for each indicator.

Step 2:

Classify the attributes of product indicators. Use Table 1 to evaluate and classify the indicator attributes of the product from the functional and dysfunctional questions of the questionnaire.

Step 3:

Calculate the affiliation value ${\mu }_{ix}$. Determine the final attribute of the indicator using Equation (8), and then calculate the value of ${\mu }_{ix}$ for each indicator belonging to different attributes using Equation (9).

Step 4:

Calculate the value of new importance ratio ${IR}_{adji}^{″}$. Given the ${\mu }_{ix}$ value of each indicator obtained from Step 3 and the k value from Table 2, the value of ${IR}_{adji}^{″}$ for each indicator can be calculated using Equation (14).

Step 5:

Obtain the TFNs of customer satisfaction $F_{a_w}$ and the company’s expected satisfaction $F_{b_w}$. The values of customer satisfaction and the company’s expected satisfaction for each indicator can be converted into TFNs using Figure 3 and the following equations:

$$F_{a_w}=(a^{L_w},a^{M_w},a^{U_w})=\left({\displaystyle \frac{a^{L_{1w}}+a^{L_{2w}}+\cdots +a^{L_{ew}}}{g}},{\displaystyle \frac{a^{M_{1w}}+a^{M_{2w}}+\cdots +a^{M_{ew}}}{g}},{\displaystyle \frac{a^{U_{1w}}+a^{U_{2w}}+\cdots +a^{U_{ew}}}{g}}\right)$$

(15)

$$F_{b_w}=(b^{L_w},b^{M_w},b^{U_w})=\left({\displaystyle \frac{b^{L_{1w}}+b^{L_{2w}}+\cdots +b^{L_{rw}}}{r}},{\displaystyle \frac{b^{M_{1w}}+b^{M_{2w}}+\cdots +b^{M_{rw}}}{r}},{\displaystyle \frac{b^{U_{1w}}+b^{U_{2w}}+\cdots +b^{U_{rw}}}{r}}\right)$$

(16)

where g is the number of valid questionnaires and r is the number of company managers.

Step 6:

Calculate the value of information content ${IC}_i^{\prime }$. The value of ${IC}_i^{\prime }$ can be calculated using the following equation:

$${IC}_i^{\prime }={\log }_2({\displaystyle \frac{\begin{array}{ccc}fuzzy& system& range\end{array}}{\begin{array}{ccc}fuzzy& common& area\end{array}}})={\log }_2({\displaystyle \frac{fuzzy satisfaction range}{fuzzy matching area}})$$

(17)

where the fuzzy matching area is the overlapping area between the fuzzy range of customer satisfaction and the fuzzy range of the company’s expected satisfaction that satisfies customer requirements. The larger the overlapping area, the more satisfied the customer’s requirements. In other words, the smaller the ${IC}_i^{\prime }$ value, the higher the degree of satisfaction matching between customers and the company, and the better the indicator performance. Otherwise, the indicator should be improved.

Step 7:

Calculate overall performance $P_i$. The overall performance of each indicator can be obtained as follows:

$$P_i={IR}_{adji}^{″}\times {IC}_i^{\prime }$$

(18)

Step 8:

Rank alternatives. The improvement order of indicators is determined according to the $P_i$ value. The larger the $P_i$ value, the higher the priority of the indicator.

Step 1:

The 27 indicators presented in Table 3 (w = 27) were selected to investigate customer satisfaction and the satisfaction levels expected by the company. A total of 307 survey responses were received, of which 207 were valid (g = 207), representing a valid response rate of 67.42%. Among them, 42.03% were male and 57.97% were female.

Step 2:

Table 3 shows the results of the attribute classification of each indicator based on Table 1.

Step 3:

Table 4 shows the final classification results and affiliation values of each indicator. To highlight the features of the proposed method, we compared our results with those of the traditional Kano model.

Steps 4 to 8:

Table 5 shows the values of $F_{a_w}$, $F_{b_w}$, $I{C^{\prime }}_i$, ${IR}_{adji}^{″}$, and $P_i$ and lists the rank of each indicator of disposable surgical masks made by Company M. The lower the rank of the indicator is, the higher the preference for it is.