research article an approach to evaluate the clothing creative design...

Research ArticleAn Approach to Evaluate the Clothing Creative Design with DualHesitant Fuzzy Information

Ya-Mei Li

Shandong Management University, Shandong, Jinan 250357, China

Correspondence should be addressed to Ya-Mei Li; yamei [email protected]

Received 28 June 2014; Accepted 4 July 2014; Published 13 July 2014

Academic Editor: Guiwu Wei

Copyright © 2014 Ya-Mei Li. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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

1. Introduction

In the context of innovation-driven reformation and devel-opment of fashion industry in China, it becomes the mostessential issue to enhance the ability of independent R&Dandcreative design level for Chinese local fashion brands. In quitea long period, fashion is considered to be determined by fash-ion designers [1, 2]. However, fashion is hereby consideredto be formed according to certain social background, insteadof being determined by certain people’s subjective minds. Sofashion could be generated by precise analysis from objectivefactors. Now in the context of fast fashion, fashion designdoes not merely rely on the designers’ creativity, but all kindsof modern information technology are applied in the processof fashion design [3–5]. According to the characteristics ofthe fashion data warehouse system, an overall structure com-posed of fashion data dictionary, fashion data sources, fash-ion datamanagement, fashion datamining, and the front-enddecision support is formed.The proposed concept of FashionData Dictionary (FDD), including Fashion Color Data Dic-tionary, FashionMaterialDataDictionary, FashionAccessoryData Dictionary, Fashion Pattern Data Dictionary, FashionTechnique Data Dictionary, Fashion Style Data Dictionary,and Fashion Look Data Dictionary, is formed, in order thatall kinds of fashion data from different sources are unifiedin 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, andart works. Fashion clothing data sources include fashionshows, fashion market, fashion brand advertisement, targetconsumer, 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 datamanagement is defined including fashion data extraction,naming method, conversion rules, and loading standard, sothat the fashion data extracted from a variety of sourcescould be loaded in the fashion warehouse with standardizeddata format. Social background has an important impact onthe formation of fashion style which is the consensus of thefashion industry, but the study of the relationship betweenthe two has always been to stay in the sociology of qualitativeresearch [9–11].

The problem of evaluating the clothing creative designwith dual hesitant fuzzy information is the multiple attributedecision making problems. In this paper, we have utilizeddual hesitant fuzzy hybrid average (DHFHA) operator todevelop the model to solve the multiple attribute decisionmaking problems for evaluating the clothing creative design.Finally, a practical example for evaluating the evaluatingthe clothing creative design is given to verify the developedapproach.

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2014, Article ID 352619, 4 pageshttp://dx.doi.org/10.1155/2014/352619

2 Journal of Control Science and Engineering

2. Preliminaries

Definition 1 (see [12]). Let𝑋 be a fixed set; then a dual hesitantfuzzy set (DHFS) on𝑋 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 nonmember-ship 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}, and𝜂+∈ 𝑔+(𝑥) = ⋃

𝜂∈𝑔(𝑥)max{𝜂} for all 𝑥 ∈ 𝑋.

In the following,Wang et al. [13] had developed somedualhesitant fuzzy arithmetic aggregation operator based on theoperations of DHFEs.

Definition 2 (see [13]). Let 𝑑𝑗(𝑗 = 1, 2, . . . , 𝑛) be a collection

of DHFEs; then their aggregated value by using the DHFWAoperator is also a DHFE, and

DHFWA𝜔(𝑑1, 𝑑2, . . . , 𝑑

𝑛)

=

𝑛

⨁

𝑗=1

(𝜔𝑗𝑑𝑗)

= ⋃

𝛾𝑗∈ℎ𝑗 ,𝜂𝑗∈𝑔𝑗

{

{

{

{

{

{

1 −

𝑛

∏

𝑗=1

(1 − 𝛾𝑗)𝜔𝑗}

}

}

,

{

{

{

𝑛

∏

𝑗=1

(𝜂𝑗)𝜔𝑗}

}

}

}

}

}

,

(3)

where 𝜔 = (𝜔1, 𝜔2, . . . , 𝜔

𝑛)𝑇 is the weight vector of ℎ

𝑗(𝑗 =

1, 2, . . . , 𝑛), and 𝜔𝑗> 0, ∑𝑛

𝑗=1𝜔𝑗= 1.

Definition 3 (see [13]). Let 𝑑𝑗(𝑗 = 1, 2, . . . , 𝑛) be a col-

lection of DHFEs; then their aggregated value by using theDHFOWA operator is also a DHFE, and

DHFOWA𝑤(𝑑1, 𝑑2, . . . , 𝑑

𝑛)

=

𝑛

⨁

𝑗=1

(𝑤𝑗𝑑𝜎(𝑗))

= ⋃

𝛾𝜎(𝑗)∈ℎ𝜎(𝑗) ,𝜂𝜎(𝑗)∈𝑔𝜎(𝑗)

{

{

{

{

{

{

1 −

𝑛

∏

𝑗=1

(1 − 𝛾𝜎(𝑗))𝑤𝑗}

}

}

,

{

{

{

𝑛

∏

𝑗=1

(𝜂𝜎(𝑗))𝑤𝑗}

}

}

}

}

}

,

(4)

where (𝜎(1), 𝜎(2), . . . , 𝜎(𝑛)) is a permutation of (1, 2, . . . , 𝑛),such that 𝑑

𝜎(𝑗−1)≥ 𝑑𝜎(𝑗)

for all 𝑗 = 2, . . . , 𝑛, and 𝑤 =

(𝑤1, 𝑤2, . . . , 𝑤

𝑛)𝑇 is the aggregation-associated weight vector

such that 𝑤𝑗∈ [0, 1] and ∑𝑛

𝑗=1𝑤𝑗= 1.

Definition 4 (see [13]). Let 𝑑𝑗(𝑗 = 1, 2, . . . , 𝑛) be a collection

of DHFEs; then their aggregated value by using the DHFHAoperator is also a DHFE, and

DHFHA𝑤,𝜔(𝑑1, 𝑑2, . . . , 𝑑

𝑛)

=

𝑛

⨁

𝑗=1

(𝑤𝑗

𝑑𝜎(𝑗))

= ⋃

𝛾𝜎(𝑗)∈ℎ𝜎(𝑗) , 𝜂𝜎(𝑗)∈ 𝑔𝜎(𝑗)

{

{

{

{

{

{

1 −

𝑛

∏

𝑗=1

(1 − 𝛾𝜎(𝑗))𝑤𝑗}

}

}

,

{

{

{

𝑛

∏

𝑗=1

( 𝜂𝜎(𝑗))𝑤𝑗}

}

}

}

}

}

,

(5)

where𝑤 = (𝑤1, 𝑤2, . . . , 𝑤

𝑛) is the associatedweighting vector,

with 𝑤𝑗∈ [0, 1], ∑𝑛

𝑗=1𝑤𝑗= 1, ℎ

𝜎(𝑗)is the 𝑗th largest

element of the dual hesitant fuzzy arguments 𝑑𝜎(𝑗)

(𝑑𝜎(𝑗)

=

𝑛𝜔𝑗𝑑𝑗, 𝑗 = 1, 2, . . . , 𝑛), 𝜔 = (𝜔

1, 𝜔2, . . . , 𝜔

𝑛) is the weighting

vector of dual hesitant fuzzy arguments 𝑑𝑗(𝑗 = 1, 2, . . . , 𝑛),

with 𝜔𝑖∈ [0, 1], ∑𝑛

𝑖=1𝜔𝑖= 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 weightedaverage (DHFWA) operator; if 𝜔 = (1/𝑛, 1/𝑛, . . . , 1/𝑛),then DHFHA is reduced to the dual hesitant fuzzy orderedweighted average (DHFOWA) operator.

Definition 5 (see [12]). Let 𝑑𝑖= (ℎ𝑑𝑖, 𝑔𝑑𝑖) (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 ofthe elements in ℎ and 𝑔, respectively.

3. An Approach to Evaluate the ClothingCreative Design withDual Hesitant Fuzzy Information

Let𝐴 = {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 = (𝑑𝑖𝑗)𝑚×𝑛

is the dual hesitant fuzzydecision 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 designwith dual hesitant fuzzy information.

Step 1. Weutilize the decision information given inmatrix𝐷,and the DHFHA operator

𝑑𝑖= DHFHA

𝑤,𝜔(𝑑𝑖1, 𝑑𝑖2, . . . , 𝑑

𝑖𝑛)

=

𝑛

⨁

𝑗=1

(𝑤𝑗

𝑑𝜎(𝑖𝑗))

Journal of Control Science and Engineering 3

Table 1: Dual hesitant fuzzy decision matrix.

𝐺1

𝐺2

𝐺3

𝐺4

𝐴1

{{0.6, 0.8}, {0.4}} {{0.3, 0.5}, {0.3}} {{0.3}, {0.6, 0.7}} {{0.6}, {0.4}}

𝐴2

{{0.3, 0.4}, {0.5}} {{0.3, 0.5}, {0.6}} {{0.3, 0.4}, {0.5}} {{0.4, 0.6}, {0.4}}

𝐴3

{{0.5, 0.7}, {0.2)} {{0.4, 0.6}, {0.6} {{0.3, 0.6}, {0.2}} {{0.3, 0.4}, {0.5}}

𝐴4

{{0.4, 0.5}, {0.2}} {{0.3}, {0.4, 0.5}} {{0.3}, {0.5, 0.6}} {{0.2}, {0.3}}

𝐴5

{{0.4}, {0.4, 0.5}} {{0.2, 0.3}, {0.5}} {{0.3, 0.6}, {0.4}} {{0.4, 0.6}, {0.3}}

= ⋃

𝛾𝜎(𝑖𝑗)∈ℎ𝜎(𝑖𝑗) , 𝜂𝜎(𝑖𝑗)∈ 𝑔𝜎(𝑖𝑗)

{

{

{

{

{

{

1 −

𝑛

∏

𝑗=1

(1 − 𝛾𝜎(𝑖𝑗))𝑤𝑗}

}

}

,

{

{

{

𝑛

∏

𝑗=1

( 𝜂𝜎(𝑖𝑗))𝑤𝑗}

}

}

}

}

}

(6)

to derive the overall preference values 𝑑𝑖(𝑖 = 1, 2, . . . , 𝑚) of

the alternative 𝐴𝑖.

Step 2. Calculate the scores 𝑆(𝑑𝑖) (𝑖 = 1, 2, . . . , 𝑚) of

the overall dual hesitant fuzzy preference values 𝑑𝑖(𝑖 =

1, 2, . . . , 𝑚).

Step 3. Rank all the alternatives 𝐴𝑖(𝑖 = 1, 2, . . . , 𝑚) and

select the best one(s) in accordance with the scores 𝑆(𝑑𝑖) (𝑖 =

1, 2, . . . , 𝑚).

Step 4. End.

4. Numerical Example

Thus, in this section we will present a numerical examplefor evaluating the clothing creative design with dual hesitantfuzzy information in order to illustrate the method proposedin this paper. There are five possible clothing creative designalternatives 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 (𝐺

2), the fabrics of clothing

design (𝐺3), and the design of comfort (𝐺

4), respectively. In

order to avoid influencing each other, the decision makersare required to evaluate five possible clothing creative designalternatives 𝐴

𝑖(𝑖 = 1, 2, 3, 4, 5) under the above four

attributes in anonymity and the decision matrix 𝐷 = (𝑑𝑖𝑗)5×4

is presented in Table 1.In the following, we utilize the approach developed for

evaluating the clothing creative design with dual hesitantfuzzy information.

We utilize the decision information given in matrix 𝐷and the DHFHA operator to obtain the overall preferencevalues 𝑑

𝑖of the clothing creative design alternatives 𝐴

𝑖(𝑖 =

1, 2, 3, 4, 5) and calculate the scores 𝑠(𝑑𝑖) (𝑖 = 1, 2, 3, 4, 5) of

the overall dual hesitant fuzzy values 𝑑𝑖(𝑖 = 1, 2, 3, 4, 5) of

the clothing creative design alternatives 𝐴𝑖:

𝑠 (𝑑1) = 0.1324, 𝑠 (𝑑

2) = 0.1878, 𝑠 (𝑑

3) = −0.1022

𝑠 (𝑑4) = 0.3768, 𝑠 (𝑑

5) = 0.0256.

(7)

Then, we rank all the clothing creative design alternativesin accordance with the scores 𝑠(𝑑

𝑖) (𝑖 = 1, 2, 3, 4, 5) of the

𝑑𝑖(𝑖 = 1, 2, . . . , 5): 𝐴

4≻ 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 hybridaverage (DHFHA) operator to develop the model to solve themultiple attribute decision making problems for evaluatingthe clothing creative design. Finally, a practical example forevaluating the clothing creative design is given to verify thedeveloped approach.

Conflict of Interests

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

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4 Journal of Control Science and Engineering

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