*3.2. Fuzzy Theory*

The fuzzy theory was proposed by L.A. Zadeh, a researcher and professor emeritus of computer science at the University of California, U.S. He proposed the concept of fuzzy sets in 1965 and fuzzy mathematics became a new branch of mathematics.

In order to consider the influence of all factors comprehensively so that a correct evaluation result can be obtained, the fuzzy comprehensive evaluation was proposed. By including the weights of corresponding factors, the comprehensive influence of all factors is reflected in a reasonable way. Therefore, the fuzzy comprehensive evaluation table is as follows.

$$\begin{aligned} \overline{\overline{B}} &= \overline{A} \cdot \overline{R} \\ A &= (a\_1, a\_2, \cdots, a\_m) \\ R &= \begin{pmatrix} r\_{11} & r\_{12} & \cdots & r\_{1n} \\ r\_{21} & r\_{22} & \cdots & r\_{2n} \\ \vdots & \vdots & \vdots & \vdots \\ r\_{m1} & r\_{m2} & \cdots & r\_{mn} \end{pmatrix} \end{aligned} \tag{1}$$

#### **4. Results and Analysis**

#### *4.1. Selection of the Concept Schemes*

In general, there are two ways of selecting the concept schemes: (1) Using the design for functions (DFF) to build a functional structure that is based on consumer demands; and (2) Using the method of morphological chart to develop design ideas that are based on the functional structure.

#### 4.1.1. Determining Product Functions

The verb-noun approach that was proposed by Tuttle [18] among the DFF approaches was used to convert the user demands that were collected from questionnaire on stereo systems to the functional aspect of a product.

The new functions to be developed for a stereo system can be defined by adding a verb to a noun according to this approach. The results are summarized in Table 2 as follows.


**Table 2.** Definition of functions of a stereo system.

#### 4.1.2. Developing the Product Structure Tree Diagram

The product functions that are listed in Table 2 will be further described by a function structure diagram as follows. During the development stage of a concept, the most important goal of the FSD is to disassemble the main product into problems with which the details can be managed. In order to further understand product functions, a product can be defined by three abstract levels, which include functions of the whole product, functions of the subassembly and functions of the individual products.

In the FSD, basis functions are bounded by solid rectangles, secondary functions are bounded by dashed rectangles and aesthetic functions are bounded by dotted rectangles. Therefore, the FSD of a stereo system is shown in Figure 3 as follows.

**Figure 3.** Function structure diagram of a stereo system.

4.1.3. Creating Concept Schemes

After the function structure diagram of a stereo system is created, a designer can further generate design ideas. The way of generating design ideas include design by analogy, brainstorming and so forth. Each approach has its own pros and cons. In this study, the design ideas were created by the morphological chart method that was proposed by Cross [19].

As shown in Table 3, after calculating the possible answer of each row, the number of all possible concepts is 4 × 4 × 4 × 4 × 4 × 2 × 2 × 2 × 2 = 16,384.


**Table 3.** Morphological chart method.

In order to simplify the problem, the subassemblies were assembled into four concept schemes:

Idea 1. Product code: P11, P21, P32, P44, P53, P61, P72, P82, P91 Idea 2. Product code: P14, P23, P31, P41, P51, P61, P71, P82, P91 Idea 3. Product code: P12, P24, P32, P44, P52, P61, P72, P81, P91

Idea 4. Product code: P13, P24, P31, P43, P51, P61, P71, P82, P91.

#### *4.2. Process of the Usability Experiment*

Parameter models of the concept schemes that were generated in the earlier stage can be created by commercial CAD software such as Solidworks. In order to make the mechanism of those concept schemes movable, the concept schemes were disassembled into components so that the mechanism patterns can be revealed. On the other hand, the assembly efficiency and assembly time of the components were also calculated from the engineering perspective.
