Model for evaluating the visual design quality with 2-tuple linguistic information

Abstract

In this paper, we investigate the multiple attribute decision making problems for evaluating the visual design quality with 2-tuple linguistic information. Motivated by the ideal of generalized weighted Bonferroni mean and generalized weighted geometric Bonferroni mean, we develop the 2-tuple linguistic generalized Bonferroni mean (2TLGBM) operator for aggregating the 2-tuple linguistic information. For the situations where the input arguments have different importance, we then define the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator, based on which we develop the procedure for multiple attribute decision making under the 2-tuple linguistic environments. At last, a numerical example for evaluating the visual design quality is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

Keywords

Multiple attribute decision making 2-tuple linguistic variables generalized Bonferroni mean generalized geometric Bonferroni mean generalized weighted Bonferroni mean visual design quality

1 Introduction

Multiple attribute decision making is a usual task in human activities. It consists of finding the most preferred alternative from a given alternative set. The increasing complexity of the socio-economic environment makes it less and less possible for a single decision maker to consider all relevant aspects of a problem. As a result, many decision making processes take place in group settings in the real life situation. However, under many conditions, for the real multiple attribute decision making problems, the decision information about alternatives is usually uncertain or fuzzy due to the increasing complexity of the socio-economic environment and the vagueness of inherent subjective nature of human think, thus, numerical values are inadequate or insufficient to model real-life decision problems. Indeed, human judgments including preference information may be stated in linguistic terms [1 –30].

Along with the maturity of mobile technology and the expansion of the user requirements, smart phones with simple appearance design, convenient operation, powerful functions and personalized interface have become more and more popular among users, which have set off a global buying spree. When the technology and function of the mobile phone converge, the user’s attention will be transfer to graphic interface design, and the graphic visual design will become the decisive factor for users to buy the product. A user does not need guidance book when there is a well-designed interface. They can operate the product according to interface design elements such as color, graphics and layout, which will form a good user experience. In this paper, we investigate the multiple attribute decision making problems with 2-tuple linguistic information. Motivated by the ideal of Bonferroni mean [31] and geometric Bonferroni mean [32], we develop the 2-tuple linguistic generalized Bonferroni mean (2TLGBM) operator for aggregating the 2-tuple linguistic information. For the situations where the input arguments have different importance, we then define the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator based on which we develop the procedure for multiple attribute decision making under the 2-tuple linguistic environments. At last, a numerical example for evaluating the visual design quality is provided to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate.

2 Preliminaries

Herrera [1, 2] first introduced the 2-tuple fuzzy linguistic approach for overcoming the drawback of the classical computational models, which include the semantic model and symbolic model. The 2-tuple linguistic model is a kind of new information processing method. It takes 2-tuple to represent linguistic assessment information and carry out operation. The basic concept of linguistic 2-tuple is symbolic translation. The 2-tuple linguistic representation and computational model has received more and more attention since its appearance.

In the following, we shall introduce the definition of the 2-tuple linguistic representation and computational model.

Let S ={ s_i |i = 1, 2, ⋯ , t } be a linguistic term set with odd cardinality. Any label, s_i represents a possible value for a linguistic variable, and it should satisfy the following characteristics [1, 2]:

(1) The set is ordered: s_i > s_j, if i > j; (2) Max operator: max(s_i, s_j) = s_i, if s_i ≥ s_j; (3) Min operator: min(s_i, s_j) = s_i, if s_i ≤ s_j. For example, S can be defined as $\begin{matrix} S & = & {s_{1} = extremely poor (EP), \\ s_{2} = very poor (VP), s_{3} = poor (P), \\ s_{4} = medium (M), s_{5} = good (G), \\ s_{6} = very good (VG), \\ s_{7} = extremely good (EG)} \end{matrix}$

Herrera and Martinez [1, 2] developed the 2-tuple fuzzy linguistic representation model based on the concept of symbolic translation. It is used for representing the linguistic assessment information by means of a 2-tuple (s_i, α_i), where s_i is a linguistic label from predefined linguistic term set S and α_i is the value of symbolic translation, and α_i ∈ [- 0.5, 0.5) .

Definition 1. [1, 2] Let β be the result of an aggregation of the indices of a set of labels assessed in a linguistic term set S, i.e., the result of a symbolic aggregation operation, β ∈ [1, t], being t the cardinality of S. Let i = round (β) and α = β - i be two values, such that, i ∈ [1, t] and α ∈ [- 0.5, 0.5) then α is called a symbolic translation.

Definition 2. [1, 2] Let S ={ s₁, s₂, ⋯ , s_t } be a linguistic term set and β ∈ [1, t] is a number value representing the aggregation result of linguistic symbolic. Then the function Δ used to obtain the 2-tuple linguistic information equivalent to β is defined as: $Δ : [1, t] \to S \times [- 0.5, 0.5)$ (1) $Δ (β) = {\begin{matrix} s_{i}, i = round (β) \\ α = β - i, α \in [- 0.5, 0.5) \end{matrix}$ (2) where round(.) is the usual round operation, s_i has the closest index label to β and α is the value of the symbolic translation.

Definition 3. [1, 2] Let S ={ s₁, s₂, ⋯ , s_t } be a linguistic term set and (s_i, α_i) be a 2-tuple. There is always a function Δ^-1 can be defined, such that, from a 2-tuple (s_i, α_i) it return its equivalent numerical value β ∈ [1, t] ⊂ R, which is. $Δ^{- 1} : S \times [- 0.5, 0.5) \to [1, t]$ (3) $Δ^{- 1} (s_{i}, α) = i + α = β$ (4)

From Definitions 1 and 2, we can conclude that the conversion of a linguistic term into a linguistic 2-tuple consists of adding a value 0 as symbolic translation: $Δ (s_{i}) = (s_{i}, 0)$ (5)

Definition 4. [1, 2] Let (s_k, a_k) and (s_l, a_l) be two 2-tuple, they should have the following properties:

If k < l then (s_k, a_k) is smaller than (s_l, a_l);

If k = l then

if a_k = a_l, then (s_k, a_k), (s_l, a_l) represents the same information;

if a_k < a_l then (s_k, a_k) is smaller than (s_l, a_l); if a_k > a_l then (s_k, a_k) is bigger than (s_l, a_l).

3 Some generalized Bonferroni mean aggregating operators with 2-tuple linguistic information

Beliakov et al. [33] further extended the BM operator by considering the correlations of any three aggregated arguments instead of any two.

Definition 5. Let p, q, r ≥ 0 and a_i (i = 1, 2, ⋯ , n) be a collection of nonnegative numbers. If $\begin{array}{l} G B M^{p, q, r} (a_{1}, a_{2}, \dots, a_{n}) \\ = {(\frac{1}{n (n - 1) (n - 2)} \sum_{\begin{array}{l} i, j, k = 1 \\ i \neq j \neq k \end{array}}^{n} a_{i}^{p} a_{j}^{q} a_{k}^{r})}^{\frac{1}{p + q + r}} \end{array}$ (6)

then GBM^p,q,r is called the generalized Bonferroni mean (GBM) operator.

In particular, if r = 0, then the GBM operator reduces to the BM operator. However, it is noted that both BM operator and the GBM operator do not consider the situation that i = j or j = k or i = k, and the weight vector of the aggregated arguments is not also considered. To overcome this drawback, Xia et al. [34] defined the weighted version of the GBM operator.

Definition 6. Let p, q, r ≥ 0 and a_i (i = 1, 2, ⋯ , n) be a collection of nonnegative numbers with the weight vector w = (w₁, w₂, ⋯ , w_n) ^T and w_j > 0, $\sum_{j = 1}^{n} w_{j} = 1$ . If $G W B M^{p, q, r} (a_{1}, a_{2}, \dots, a_{n}) = {(\frac{1}{n (n - 1) (n - 2)} \sum_{\begin{array}{l} i, j, k = 1 \\ i \neq j \neq k \end{array}}^{n} w_{i} w_{j} w_{k} a_{i}^{p} a_{j}^{q} a_{k}^{r})}^{\frac{1}{p + q + r}}$ (7) then GWBM^p,q,r is called the generalized weighted Bonferroni mean (GWBM) operator.

In the following, we shall develop 2-tuple linguistic generalized Bonferroni mean (2TLGBM) operator and 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator.

Definition 7. Let p, q, r ≥ 0 and {(r₁, a₁) , (r₂, a₂) , …, (r_n, a_n)} be a set of 2-tuple linguistic variables, If $\begin{array}{l} 2 T L G B M^{p, q, r} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = Δ {(\frac{1}{n (n - 1) (n - 2)} \sum_{\begin{array}{l} i, j, k = 1 \\ i \neq j \neq k \end{array}}^{n} {(Δ^{- 1} (r_{i}, a_{i}))}^{p} {(Δ^{- 1} (r_{j}, a_{j}))}^{q} {(Δ^{- 1} (r_{k}, a_{k}))}^{r})}^{\frac{1}{p + q + r}} \end{array}$ (8) then 2TLGBM^p,q,r is called the 2-tuple linguistic generalized Bonferroni mean (2TLGBM) operator.

If r = 0, then the 2TLGBM operator reduces to the 2TLBM operator. $\begin{array}{l} 2 T L G B M^{p, q, 0} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = 2 T L B M^{p, q} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = Δ {(\frac{1}{n (n - 1)} \sum_{\begin{array}{l} i, j \\ i \neq j \end{array}}^{n} {(Δ^{- 1} (r_{i}, a_{i}))}^{p} {(Δ^{- 1} (r_{j}, a_{j}))}^{q})}^{\frac{1}{p + q}} \end{array}$ (9)

However, it is noted that both 2TLBM operator and the 2TLGBM operator do not consider the situation that i = j or j = k or i = k, and the weight vector of the aggregated arguments is not also considered. To overcome this drawback, we shall propos the weighted version of the 2TLGBM operator.

Definition 8. Let { (r₁, a₁) , (r₂, a₂) , … , (r_n, a_n) } be a set of 2-tuple linguistic variables, and let p, q, r ≥ 0. w = (w₁, w₂, ⋯ , w_n) ^T is the weight vector of { (r₁, a₁) , (r₂, a₂) , …, (r_n, a_n) } (i = 1, 2, ⋯ , n),where w_i indicates the importance degree of (r_i, a_i), satisfying w_i > 0 (i = 1, 2, ⋯ , n), and $\sum_{i = 1}^{n} w_{i} = 1$ . If

$\begin{matrix} 2 TLG W {BM}_{w}^{p, q, r} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = Δ {(\sum_{i, j, k = 1}^{n} {(w_{i} w_{j} w_{k} Δ^{- 1} (r_{i}, a_{i}))}^{p} {(Δ^{- 1} (r_{j}, a_{j}))}^{q} {(Δ^{- 1} (r_{k}, a_{k}))}^{r})}^{\frac{1}{p + q + r}} \end{matrix}$ (10) then $2 TLG W {BM}_{w}^{p, q, r}$ is called the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator.

It can be easily proved that the 2TLGWBM operator has the following properties.

Theorem 1. (Idempotency) Let x = {(r₁, a₁) , (r₂, a₂) , …, (r_n, a_n)} be a set of 2-tuple linguistic variables. If all (r_j, a_j) (j = 1, 2, ⋯ , n) are equal, i.e. (r_j, a_j) = (r, a) for all j, then

$\begin{matrix} 2 TLG W {BM}_{w}^{p, q, r} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = (r, a) \end{matrix}$ (11)

Theorem 2. (Boundedness) Let x = {(r₁, a₁) , (r₂, a₂) , …, (r_n, a_n)} be a set of 2-tuple linguistic variables, and let $(r^{-}, a^{-}) = min_{j} (r_{j}, a_{j}), (r^{+}, a^{+}) = max_{j} (r_{j}, a_{j})$

Then

$\begin{matrix} (r^{-}, a^{-}) & \leq & 2 TLG W {BM}_{w}^{p, q, r} {(r_{1}, a_{1}), (r_{2}, a_{2}), \\ \dots, (r_{n}, a_{n})} \leq (r^{+}, a^{+}) \end{matrix}$ (12)

Theorem 3. (Monotonicity) Let x = {(r₁, a₁) , (r₂, a₂) , …, (r_n, a_n)} and $x^{'} = ((r_{1}^{'}, a_{1}^{'}), (r_{2}^{'}, a_{2}^{'}), \dots, (r_{n}^{'}, a_{n}^{'}))$ be two set of 2-tuple linguistic variables, if $(r_{j}, a_{j}) \leq (r_{j}^{'}, a_{j}^{'})$ , for all j, then

$\begin{matrix} 2 TLG W {BM}_{w}^{p, q, r} ((r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})) \\ \leq 2 TLG W {BM}_{w}^{p, q, r} ((r_{1}^{'}, a_{1}^{'}), (r_{2}^{'}, a_{2}^{'}), \\ \dots, (r_{n}^{'}, a_{n}^{'})) \end{matrix}$ (13)

Theorem 4. (Commutativity) Let x = {(r₁, a₁) , (r₂, a₂) , …, (r_n, a_n)} and $x^{'} = ((r_{1}^{'}, a_{1}^{'}), (r_{2}^{'}, a_{2}^{'}), \dots, (r_{n}^{'}, a_{n}^{'}))$ be two set of 2-tuple, where $((r_{1}^{'}, a_{1}^{'}), (r_{2}^{'}, a_{2}^{'}), \dots, (r_{n}^{'}, a_{n}^{'}))$ is any permutation of { (r₁, a₁) , (r₂, a₂) , … , (r_n, a_n) }, then

$\begin{matrix} 2 TLG W {BM}_{w}^{p, q, r} ((r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})) \\ = 2 TLG W {BM}_{w}^{p, q, r} ((r_{1}^{'}, a_{1}^{'}), (r_{2}^{'}, a_{2}^{'}), \\ \dots, (r_{n}^{'}, a_{n}^{'})) \end{matrix}$ (14)

Some special cases can be obtained as the change of the parameters as follows.

If r = 0, then the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator reduces to the 2-tuple linguistic weighted Bonferroni mean (2TLGWBM) operator. $\begin{matrix} {2 TLGWBM}_{w}^{p, q, 0} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = {2 TLWBM}_{w}^{p, q, 0} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = Δ {(\sum_{i, j = 1}^{n} {(w_{i} w_{j} Δ^{- 1} (r_{i}, a_{i}))}^{p} {(Δ^{- 1} (r_{j}, a_{j}))}^{q})}^{\frac{1}{p + q}} \end{matrix}$ (15)

If r = 0, q = 0, the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator reduces to the following: $\begin{matrix} 2 TLG W {BM}_{w}^{p, 0, 0} {(r_{1}, a_{1}), (r_{2}, a_{2}), \dots, (r_{n}, a_{n})} \\ = Δ (\sum_{i, j, k = 1}^{n} {(w_{i} w_{j} w_{k} Δ^{- 1} (r_{i}, a_{i}))}^{p} {(Δ^{- 1} (r_{j}, a_{j}))}^{0} \\ {{(Δ^{- 1} (r_{k}, a_{k}))}^{0})}^{\frac{1}{p}} \\ = Δ {(\sum_{i = 1}^{n} {(w_{i} Δ^{- 1} (r_{i}, a_{i}))}^{p})}^{\frac{1}{p}} \end{matrix}$ (16)

which is the 2-tuple linguistic generalized weighted averaging (2TLGWA) operator. Furthermore, in this case, let us look at the 2TLGWBM operator for some special cases of p.

If p = 1, the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator reduces to 2-tuple linguistic weighted averaging (2TLWA) operator.

If p → 0, the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator reduces to 2-tuple linguistic weighted geometric (2TLWG) operator.

If p→ ∞, the 2-tuple linguistic generalized weighted Bonferroni mean (2TLGWBM) operator reduces to 2-tuple linguistic max operator.

4 An approach to multiple attribute decision making with linguistic information

In this section, we shall utilize the developed operators to multiple attribute decision making.

For a multiple attribute decision making problems with linguistic information, let A = {A₁, A₂, ⋯ , A_m} be a discrete set of alternatives, G ={ G₁, G₂, ⋯ , G_n } be the set of attributes, whose weight vector is ω = (ω₁, ω₂, ⋯ , ω_n), with ω_j ≥ 0, j = 1, 2, ⋯ , n, $\sum_{j = 1}^{n} ω_{j} = 1$ . Suppose that R = (r_ij) _m×n is the multiple attribute decision making matrix, where r_ij ∈ S is an attribute values, which take the form of linguistic variable, given by the decision maker for the alternative A_i ∈ A with respect to the attribute G_j ∈ G.

In what follows, we shall apply the 2TLGWBM operator to solve the MADM problems with linguistic variables.

Step 1. Transforming linguistic decision matrix R = (r_ij) _m×n into 2-tuple linguistic decision matrix $\tilde{R} = {(r_{ij}, 0)}_{m \times n}$ .

Step 2. We utilize the decision information given in matrix $\tilde{R}$ , and the 2TLGWBM operator $\begin{matrix} {\tilde{r}}_{i} & = & 2 {TLGWBM}_{w}^{p, q, r} {(r_{i 1}, 0), (r_{i 2}, 0), \dots, (r_{in}, 0)} \\ = & Δ {(\sum_{m, s, t = 1}^{n} {(w_{m} w_{s} w_{t} Δ^{- 1} (r_{im}, 0))}^{p} {(Δ^{- 1} (r_{is}, 0))}^{q} {(Δ^{- 1} (r_{it}, 0))}^{r})}^{\frac{1}{p + q + r}} \end{matrix}$ to derive the overall preference values ${\tilde{r}}_{i} (i = 1, 2, \dots, m)$ of the alternative A_i.

Step 3. Rank all the alternatives A_i (i = 1, 2, ⋯ , m) and select the best one(s) in accordance with ${\tilde{r}}_{i} (i = 1, 2, \dots, m)$ . If any alternative has the highest ${\tilde{r}}_{i}$ value, then, it is the most important alternative.

Step 4. End.

5 Numerical example

We are now at an age that images become the dominant factor of culture, the so-called visual culture age, surrounded by increasingly rich visual images. The rise of visual culture is an inevitable result of modernization. And it has become the core bond of contemporary culture fission under the wave of globalization. From the perspective of visual culture, the industrial design, which put the functional modeling as its main task, build the world of spectacles of products in people’s daily life. Because of its attractive look and special ways of visual construction, product becomes a visual text filled with formalism, functionalism, meanings and particular ways of seeing. Visuality is the core character of visual culture. When we doing researches on industrial design from the perspective of visual culture, “visuality of products” becomes the most basic concept. The surface structure of products’ visuality refers to products’ visualized exterior, reflecting the integration of function and form, and the integration of art and tech. The deep structure refers to the inner mechanism in the seeing of product, mainly including the social dimension constructed by modern-postmodern, economic dimension by production-consuming and the subject dimension by designers-public. As the overall penetration of visualization to our everyday life, there is a trend of aestheticization of it. The industrial design is just the practical art about aestheticization of everyday life. So, it is our everyday life that build the scenes and environment of products’ seeing. As the object being observed in everyday life, the products’ exterior is something that can be observed, concerning taste, style, beauty, usefulness, the feature of symbol and so

on, meeting the need of people’s self-representation and the pursue of aesthetic life. Obviously, this kind of product seeing during everyday life is in the range of understanding of design language, and accomplished through the holistic cognitive of products’exterior. Aim to attract people to see the products, the stores provide the exhibition spaces for products. Varies design exhibitions become the way to show the aestheticization of products. And the advertisements become the most important display media to recommend and rebuild the products. Along with the digital technology development which progresses by leaps and bounds, a large number of digital products, which were made by the digital technology, formed the new landscape of products in our daily life. As the digital information carrier, what digital products should do is to transmit, store, organize and decode information. And there are obvious differences between digital products and traditional products. So, on the surface layer, habit layer, as well as the significance layer, digital products connect the software and hardware with interfaces, and create real visual experience in virtual space, which is different from traditional product. This not only shows the digital products’ images, but also represents the culture characteristics such as the new electronic expressionism, the informationize lifestyle, the consumerization of technology. Thus, we can find out that, from industrial society to the information-based society, industrial design turned from visibility to invisibility. Specifically, this deep shift mainly reflects in the following: in the aspect of product attributes, a transformation happened across from real to the virtual; in the aspect of design contents, occurred from the tangible to the intangible expansion. And accordingly, the cultural practice of products is also showing swerve from form to meaning, materiality to non-material and products to service. The visual turn of industrial design indicate that in the future development, the products need to inject some new things beyond vision, and the new sensibility will become the new standard. In this section, we present an empirical case study of evaluating the visual design quality. The project’s aim is to evaluate the best visual design alternative from the different visual design alternatives, which provide alternatives of visual design alternatives. The visual design quality of five possible visual design alternatives A_i (i = 1, 2, 3, 4, 5) is evaluated. The visual design quality can be calculated as a multiple attribute decision making problem. The expert group must take a decision according to the following four attributes: ① G₁ is the costs of visual design; ② G₂ is the color to visual design; ③ G₃ is the powerful functions to visual design; ④ G₄ is the outsourcing software developer reliability of visual design. The visual design quality of five possible visual design alternatives A_i (i = 1, 2, ⋯ , 5) are to be evaluated using the linguistic variables by the decision maker under the above four attributes, as listed in the following Table 1.

Table 1
Decision matrix R

G₁ G₂ G₃ G₄

A₁ P M VP EP

A₂ VP EP M G

A₃ VG G VG EG

A₄ EG P G M

A₅ P G M VP

	G₁	G₂	G₃	G₄
A₁	P	M	VP	EP
A₂	VP	EP	M	G
A₃	VG	G	VG	EG
A₄	EG	P	G	M
A₅	P	G	M	VP

Then, we utilize the proposed approach to get the most desirable visual design alternative(s).

Step 1. Transforming linguistic decision matrix R = (r_ij) _5×4 into 2-tuple linguistic decision matrix $\tilde{R} = {(r_{ij}, 0)}_{m \times n}$ . The results are shown in Table 2.

Table 2

Decision matrix $\tilde{R}$

	G₁	G₂	G₃	G₄
A₁	(P,0)	(M,0)	(VP,0)	(EP,0)
A₂	(VP,0)	(EP,0)	(M,0)	(G,0)
A₃	(VG,0)	(G,0)	(VG,0)	(EG,0)
A₄	(EG,0)	(P,0)	(G,0)	(M,0)
A₅	(P,0)	(G,0)	(M,0)	(VP,0)

Step 2. Utilizing the information given in the matrix ${\tilde{R}}_{k} = {({\tilde{r}}_{ij} (t_{k}))}_{5 \times 4} (k = 1, 2, 3)$ , and 2TLGWBM operator, we get the values ${\tilde{z}}_{i} = (r_{i}, a_{i})$ of the visual design alternative(s) A_i (i = 1, 2, 3, 4, 5).

Step 3. According to the aggregating results shown in Table 3, the ordering of the visual design alternative(s) are shown in Table 4. Note that > means “preferred to”. Thus, the best visual design alternative is A₃.

Table 3

The overall preference values of the visual design alternative(s)

	A₁	A₂	A₃	A₄	A₅
2TLGWBM	(P, 0.13)	(M, –0.45)	(VG, –0.18)	(M, 0.25)	(P, –0.21)

Table 4

Ordering of the visual design alternative(s)

	Ordering
2TLGWBM	A₃>A₄>A₂>A₁>A₅

6 Conclusion

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Model for evaluating the visual design quality with 2-tuple linguistic information

Abstract

Keywords

1 Introduction

2 Preliminaries

5 Numerical example

Table 1 Decision matrix R G1 G2 G3 G4 A1 P M VP EP A2 VP EP M G A3 VG G VG EG A4 EG P G M A5 P G M VP

References

Table 1
Decision matrix R

G₁ G₂ G₃ G₄

A₁ P M VP EP

A₂ VP EP M G

A₃ VG G VG EG

A₄ EG P G M

A₅ P G M VP