An Approach to Evaluate the Clothing Creative Design with Dual Hesitant Fuzzy Information

Abstract

The problem of evaluating the clothing creative design with dual hesitant fuzzy information is the multiple attribute decision making problem. In this paper, we have utilized dual hesitant fuzzy hybrid average (DHFHA) operator to develop the model to solve the multiple attribute decision making problems for evaluating the clothing creative design. Finally, a practical example for evaluating the clothing creative design is given to verify the developed approach.

1. Introduction

In the context of innovation-driven reformation and development of fashion industry in China, it becomes the most essential issue to enhance the ability of independent R&D and creative design level for Chinese local fashion brands. In quite a long period, fashion is considered to be determined by fashion designers [1, 2]. However, fashion is hereby considered to be formed according to certain social background, instead of being determined by certain people’s subjective minds. So fashion could be generated by precise analysis from objective factors. Now in the context of fast fashion, fashion design does not merely rely on the designers’ creativity, but all kinds of modern information technology are applied in the process of fashion design [3–5]. According to the characteristics of the fashion data warehouse system, an overall structure composed of fashion data dictionary, fashion data sources, fashion data management, fashion data mining, and the front-end decision support is formed. The proposed concept of Fashion Data Dictionary (FDD), including Fashion Color Data Dictionary, Fashion Material Data Dictionary, Fashion Accessory Data Dictionary, Fashion Pattern Data Dictionary, Fashion Technique Data Dictionary, Fashion Style Data Dictionary, and Fashion Look Data Dictionary, is formed, in order that all kinds of fashion data from different sources are unified in format. Each data dictionary regulates its data type, level, content, and standard presentation [6, 7]. Sources of fashion data extraction are fashion clothing, social background, and art works. Fashion clothing data sources include fashion shows, fashion market, fashion brand advertisement, target consumer, fashion e-shop, and fashion and fabric exhibition. Social background data sources include politics, economy, environment, science and technology, sports, and lifestyle. Art works data sources include TV drama, art, design, music, performance art, and literature [8]. The fashion data management is defined including fashion data extraction, naming method, conversion rules, and loading standard, so that the fashion data extracted from a variety of sources could be loaded in the fashion warehouse with standardized data format. Social background has an important impact on the formation of fashion style which is the consensus of the fashion industry, but the study of the relationship between the two has always been to stay in the sociology of qualitative research [9–11].

The problem of evaluating the clothing creative design with dual hesitant fuzzy information is the multiple attribute decision making problems. In this paper, we have utilized dual hesitant fuzzy hybrid average (DHFHA) operator to develop the model to solve the multiple attribute decision making problems for evaluating the clothing creative design. Finally, a practical example for evaluating the evaluating the clothing creative design is given to verify the developed approach.

2. Preliminaries

Definition 1 (see [12]). Let 𝑋 be a fixed set; then a dual hesitant fuzzy set (DHFS) on 𝑋 is described as 𝐷=𝑥,ℎ(𝑥),𝑔(𝑥)∣𝑥∈𝑋, (1) in which ℎ(𝑥) and 𝑔(𝑥) are two sets of some values in [0,1], denoting the possible membership degrees and nonmembership degrees of the element 𝑥∈𝑋 to the set 𝐷, respectively, with the conditions 0≤𝛾,𝜂≤1,0≤𝛾⁺,𝜂⁺≤1, (2) where 𝛾∈ℎ(𝑥), 𝜂∈𝑔(𝑥), 𝛾⁺∈ℎ⁺(𝑥)=⋃_{𝛾∈ℎ(𝑥)}max{𝛾}, and 𝜂⁺∈𝑔⁺(𝑥)=⋃_{𝜂∈𝑔(𝑥)}max{𝜂} for all 𝑥∈𝑋.

In the following, Wang et al. [13] had developed some dual hesitant fuzzy arithmetic aggregation operator based on the operations of DHFEs.

Definition 2 (see [13]). Let 𝑑_𝑗  (𝑗=1,2,…,𝑛) be a collection of DHFEs; then their aggregated value by using the DHFWA operator is also a DHFE, and DHFWA_𝜔𝑑₁,𝑑₂,…,𝑑_𝑛=^𝑛_𝑗=1𝜔_𝑗𝑑_𝑗=_{𝛾𝑗∈ℎ𝑗,𝜂𝑗∈𝑔𝑗}1−^𝑛_𝑗=11−𝛾_𝑗^𝜔𝑗,^𝑛_𝑗=1𝜂_𝑗^𝜔𝑗, (3) where 𝜔=(𝜔₁,𝜔₂,…,𝜔_𝑛)^𝑇 is the weight vector of ℎ_𝑗  (𝑗=1,2,…,𝑛), and 𝜔_𝑗>0, ∑^𝑛_𝑗=1𝜔_𝑗=1.

Definition 3 (see [13]). Let 𝑑_𝑗  (𝑗=1,2,…,𝑛) be a collection of DHFEs; then their aggregated value by using the DHFOWA operator is also a DHFE, and DHFOWA_𝑤𝑑₁,𝑑₂,…,𝑑_𝑛=^𝑛_𝑗=1𝑤_𝑗𝑑_𝜎(𝑗)=_{𝛾𝜎(𝑗)∈ℎ𝜎(𝑗),𝜂𝜎(𝑗)∈𝑔𝜎(𝑗)}1−^𝑛_𝑗=11−𝛾_𝜎(𝑗)^𝑤𝑗,_𝑛𝑗=1𝜂_𝜎(𝑗)^𝑤𝑗, (4) where (𝜎(1),𝜎(2),…,𝜎(𝑛)) is a permutation of (1,2,…,𝑛), such that 𝑑_{𝜎(𝑗−1)}≥𝑑_𝜎(𝑗) for all 𝑗=2,…,𝑛, and 𝑤=(𝑤₁,𝑤₂,…,𝑤_𝑛)^𝑇 is the aggregation-associated weight vector such that 𝑤_𝑗∈[0,1] and ∑^𝑛_𝑗=1𝑤_𝑗=1.

Definition 4 (see [13]). Let 𝑑_𝑗  (𝑗=1,2,…,𝑛) be a collection of DHFEs; then their aggregated value by using the DHFHA operator is also a DHFE, and DHFHA_𝑤,𝜔𝑑₁,𝑑₂,…,𝑑_𝑛=^𝑛_𝑗=1𝑤_𝑗𝑑̇_𝜎(𝑗)=_{̇𝛾𝜎(𝑗)∈̇ℎ𝜎(𝑗),̇𝜂𝜎(𝑗)∈̇𝑔𝜎(𝑗)}1−^𝑛_𝑗=11−𝛾̇_𝜎(𝑗)^𝑤𝑗,_𝑛𝑗=1𝜂̇_𝜎(𝑗)^𝑤𝑗, (5) where 𝑤=(𝑤₁,𝑤₂,…,𝑤_𝑛) is the associated weighting vector, with 𝑤_𝑗∈[0,1], ∑^𝑛_𝑗=1𝑤_𝑗=1, ℎ̇_𝜎(𝑗) is the 𝑗th largest element of the dual hesitant fuzzy arguments 𝑑̇_𝜎(𝑗)  (𝑑̇_𝜎(𝑗)=𝑛𝜔_𝑗𝑑_𝑗,𝑗=1,2,…,𝑛), 𝜔=(𝜔₁,𝜔₂,…,𝜔_𝑛) is the weighting vector of dual hesitant fuzzy arguments 𝑑_𝑗 (𝑗=1,2,…,𝑛), with 𝜔_𝑖∈[0,1], ∑^𝑛_𝑖=1𝜔_𝑖=1, and 𝑛 is the balancing coefficient. In particular, if 𝑤=(1/𝑛,1/𝑛,…,1/𝑛)^𝑇, then DHFHA is reduced to the dual hesitant fuzzy weighted average (DHFWA) operator; if 𝜔=(1/𝑛,1/𝑛,…,1/𝑛), then DHFHA is reduced to the dual hesitant fuzzy ordered weighted average (DHFOWA) operator.

Definition 5 (see [12]). Let 𝑑_𝑖=(ℎ_𝑑𝑖,𝑔_𝑑𝑖)  (𝑖=1,2) be any two DHFEs, 𝑠(𝑑)=(1/#ℎ)∑_𝛾∈ℎ𝛾−(1/#𝑔)∑_𝜂∈𝑔𝜂 the score function of 𝑑, and 𝑝(𝑑)=(1/#ℎ)∑_𝛾∈ℎ𝛾+(1/#𝑔)∑_𝜂∈𝑔𝜂 the accuracy function of 𝑑, where #ℎ and #𝑔 are the numbers of the elements in ℎ and 𝑔, respectively.

3. An Approach to Evaluate the Clothing Creative Design with Dual Hesitant Fuzzy Information

Let 𝐴={𝐴₁,𝐴₂,…,𝐴_𝑚} be a discrete set of alternatives, and let 𝐺={𝐺₁,𝐺₂,…,𝐺_𝑛} be the state of nature. Suppose that the decision matrix 𝐷=(𝑑_𝑖𝑗)_𝑚×𝑛 is the dual hesitant fuzzy decision matrix, where 𝑑_𝑖𝑗  (𝑖=1,2,…,𝑚,𝑗=1,2,…,𝑛) are in the form of DHFEs.

In the following, we apply the DHFHA operator to the MADM problems for evaluating the clothing creative design with dual hesitant fuzzy information.

Step 1. We utilize the decision information given in matrix 𝐷, and the DHFHA operator 𝑑_𝑖=DHFHA_𝑤,𝜔𝑑_𝑖1,𝑑_𝑖2,…,𝑑_𝑖𝑛=^𝑛_𝑗=1𝑤_𝑗𝑑̇_{𝜎(𝑖𝑗)}=_{̇𝛾𝜎(𝑖𝑗)∈̇ℎ𝜎(𝑖𝑗),̇𝜂𝜎(𝑖𝑗)∈̇𝑔𝜎(𝑖𝑗)}1−^𝑛_𝑗=11−𝛾̇_{𝜎(𝑖𝑗)}^𝑤𝑗,_𝑛𝑗=1𝜂̇_{𝜎(𝑖𝑗)}^𝑤𝑗 (6) to derive the overall preference values 𝑑_𝑖  (𝑖=1,2,…,𝑚) of the alternative 𝐴_𝑖.

Step 2. Calculate the scores 𝑆(𝑑_𝑖)  (𝑖=1,2,…,𝑚) of the overall dual hesitant fuzzy preference values 𝑑_𝑖  (𝑖=1,2,…,𝑚).

Step 3. Rank all the alternatives 𝐴_𝑖  (𝑖=1,2,…,𝑚) and select the best one(s) in accordance with the scores 𝑆(𝑑_𝑖)  (𝑖=1,2,…,𝑚).

Step 4. End.

4. Numerical Example

Thus, in this section we will present a numerical example for evaluating the clothing creative design with dual hesitant fuzzy information in order to illustrate the method proposed in this paper. There are five possible clothing creative design alternatives 𝐴_𝑖  (𝑖=1,2,3,4,5) for four attributes 𝐺_𝑗  (𝑗=1,2,3,4). The four attributes include the fashion design style (𝐺₁), the color of dress design (𝐺₂), the fabrics of clothing design (𝐺₃), and the design of comfort (𝐺₄), respectively. In order to avoid influencing each other, the decision makers are required to evaluate five possible clothing creative design alternatives 𝐴_𝑖  (𝑖=1,2,3,4,5) under the above four attributes in anonymity and the decision matrix 𝐷=(𝑑_𝑖𝑗)_5×4 is presented in Table 1.

Table 1 

Dual hesitant fuzzy decision matrix.

In the following, we utilize the approach developed for evaluating the clothing creative design with dual hesitant fuzzy information.

We utilize the decision information given in matrix 𝐷 and the DHFHA operator to obtain the overall preference values 𝑑_𝑖 of the clothing creative design alternatives 𝐴_𝑖  (𝑖=1,2,3,4,5) and calculate the scores 𝑠(𝑑_𝑖)  (𝑖=1,2,3,4,5) of the overall dual hesitant fuzzy values 𝑑_𝑖  (𝑖=1,2,3,4,5) of the clothing creative design alternatives 𝐴_𝑖: 𝑠𝑑₁=0.1324,𝑠𝑑₂=0.1878,𝑠𝑑₃𝑠𝑑=−0.1022₄=0.3768,𝑠𝑑₅=0.0256. (7)

Then, we rank all the clothing creative design alternatives in accordance with the scores 𝑠(𝑑_𝑖)  (𝑖=1,2,3,4,5) of the 𝑑_𝑖  (𝑖=1,2,…,5): 𝐴₄≻𝐴₂≻𝐴₁≻𝐴₅≻𝐴₃, and thus the most desirable clothing creative design alternative is 𝐴₄.

5. Conclusion

In this paper, we have utilized dual hesitant fuzzy hybrid average (DHFHA) operator to develop the model to solve the multiple attribute decision making problems for evaluating the clothing creative design. Finally, a practical example for evaluating the clothing creative design is given to verify the developed approach.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.