# PROPOSING A METHOD FOR ASSESSMENT OF BRAND IMITATION FACTORS/PROPUESTA DE UN METODO PARA EVALUAR LOS FACTORES DE IMITACION DE MARCA.

1. INTRODUCTIONBrands are being made by peoples. They are the results of relationships between Peoples who build them and the individuals who purchase them (Harris 2007). Branding affects all aspects of a company and involves customers and employees. A company that makes a brand shapes all the things related to the business (King and Grace 2008). Branding is an effort to integrate all the things pertinent to a product or service in order to make customers remember them (Walvis 2008). Brand personality is a key factor that shows condition of a brand. Successful branding results in success in making eligible brand personality (Keller and Richey 2006). After success in branding the companies may face a new problem, called brand imitation. Being similar to a leading brand can help new products to remain competitive. For example, "if you don't have access to your favorite drinking like Redbull, you'll probably prefer the drinking which name is similar to it" (van Horen and Pieters 2012).

Although imitating a brand is a technique for mimicking developed brands' success but it makes financial losses to the leading brands in long term (Zaichkowsky 2006).This prevalent technique may imitate a brand at least in color, size, and shape in addition to name and logo (Scott Morton and Zettelmeyer 2004). "Imitation in similar packaging can confuse two thirds of buyers and mislead on third of them" (Le Roux, Bobrie et al. 2016). Brand imitation can also decrease customer satisfaction of luxury brands because copycat brands cannot often please customers for their lack of quality. Therefore, it will mentally affect people who avoid buying imitated brands. This process will erode people's confidence in those brands and make financial losses to them. Copycats, first, find the specification of a leading brand. For this purpose, they focus on name, logo, color, size, or shape of a product. "They also may mimic meaning or theme of a specified brand for instance, the wild cat theme of the puma or the traditional family-produced olive oil theme of the Bertolli brand" (Van Horen and Pieters 2013).

In studying brand imitation, it is necessary to recognize the factors that affect imitation. These factors are important because we must know which factor affects imitation more in order to prevent imitation process. In this study, we try to recognize these factors and rank them. For this purpose, we need to identify these factors by conducting a literature review. Then we ask experts to judge about the selected factors. We must assign a weight coefficient to each factor and then ranking process will start. Ranking will be performed by using TOPSIS-Rough method. Also, the authors rank the effective factors by use of TOPSIS-Fuzzy method. This is useful because we can compare the findings of the employed methods and study the results. Therefore, this paper recognizes brand imitation constructs and deals with two important questions: (1) what are the provoking qualities which give rise to brand imitation? And (2) how important are these effective qualities in preventing imitation? These questions display the main ideas behind this study and answering them fills the gap in the previous works. This paper adds to the literature in several aspects. First, this is the first study in collecting and ranking imitation factors while previous studies just developed and tested the stimulating factors. Second, we employ a ranking method based on TOPSIS-Rough. This method consolidates the potencies of rough set theory in tackling vagueness and the capacity of TOPSIS in modeling multi criteria decision making to achieve robust results in existing research, but most studies do not consider this approach. Finally, we compare the results obtained by TOPSIS-Rough with those of TOPSIS-Fuzzy approach to check the strength of the applied method.

The reminder of the paper is organized as follows. In section 2 a review of imitation brand, its definition, especial aspects, and related works are presented. The proposed method based on TOPSIS-Rough is described in section 3. An empirical experiment is carried out using TOPSIS-Rough method in section 4. A TOPSIS-Fuzzy analysis is performed in section 4 to recalculate the ranking of the effective factors and evaluate the results' robustness of the proposed method by a comparison presented in section 5. Finally, section 6 concludes the paper.

2. LITERATURE REVIEW

2.1. Defining imitation

Imitation is different from counterfeit. We define imitation as "product or service, though not identical, (which) is viewed as similar in substance, name, shape, form, meaning or intent to an acknowledge and widely known product or service currently in the market place"(Lai and Zaichkowsky 1999). In other words, imitated products are those that look similar to other branded products, but are not identical (Le Roux, Bobrie et al. 2016). For defining lookalikes we refer to Balabanis and Craven (1997) to define it as "a new generation of own brand products that have similar packaging characteristics to leading brand products" (Le Roux, Bobrie et al. 2016). Imitation is similarity in shape, logo, theme, appearance to a popular or accepted product or service (Lai and Zaichkowsky 1999).

2.2. Imitation aspects

After knowing about imitation the important thing is to understand whatever can be imitated. Researchers have defined multitude aspects of imitation. They have listed the aspects of products or services that can be imitated. "Copycats imitate the name, logo, and/or package design of a leading national brand to take advantage of the latter's positive associations and marketing efforts" (Femke van Horen and Pieters 2012). Although everything that is important to success of a product can be imitated, feature is most accessible aspect of a product to imitate. Name, logo and package that are mentioned above belong to feature.

2.3. Effective imitation factors

Similarity to a leading brand is the most common strategy for copycat brands (Fazio 1986). "An important precondition for efficient brand imitation strategy is similarity to the leader brand. Connection and relevance to the leader brand are pivotal keys for evaluation imitating. (Fazio 1986, Van Horen and Pieters 2013). In this paper, we aim to investigate the effective imitation factors. This seems important to know why some brands are more imitated than others. For this purpose, first, the authors seek the effective factors which reveal how leading brands can protect themselves from imitation. Name, appearance, place, and price are important factors that may affect imitation. We can use feature, as an important factor, instead of name because feature also includes name. Appearance signifies the figure of product such as packaging feature. Place represents where product is sold. Product price is also a significant quality (Le Roux, Bobrie et al. 2016).

Theme copycat is mainly varied from feature copycat. Theme is the background of brand feature (van Horen and Pieters 2012)."Brand specificand feature specific factors are hypothesized to influence speed. Brand specific factors include the brand's category market, share, and the brand's sponsorship-whether it's a national or a store brand. Feature specific factors subsume the price premium charged for the new feature and the use of new technology to introduce a new feature. Research shows that an inverted U-Shaped relationship captures the relationship between share and imitation speed. (Sinapuelas 2007). High share and low share brands tend to imitate slower than intermediate share brands. High category share brands tend to wait and see until uncertainties are resolved and consumers accept the new feature, while low share brands are slow to imitate because of the lack of resources to imitate fast.

According to Porter's five forces theory bargaining power of suppliers, bargaining power of buyers, threat of new entrants, threat of substitutes, and industry rivalry are the cardinal factors that affect attractiveness of an industry. These factors also affect brand imitation because attractiveness of an industry can affect attractiveness of a leading brand in that industry. Also, legislation is another factor that influences the attractiveness of an industry. Therefore, legislations and the level of intellectual property rights impact imitation. The threat of new entrants by spread of technology is also another effective factor. Moreover, brand value is an cardinal factor. By having category market share we don't need to write industry rivalry. In summary, Factors that affect imitation are showed in Table 1.

2.4. Rough number based on rough set theory

The process of project risk and network analysis confronts uncertainties. Therefore, adopting methods with the capability of modeling uncertainties, such as fuzzy logic, seems appropriate for initial judgments. In addition, this study uses ordered pair numbers that needs a particular model to draw a comparison between them. If conventional mathematical logic is used, it will be necessary to apply desk comparisons or stable comparison sort. This kind of sorting has a great disadvantage because it demands large amount of memory. Since data of this filed have high-volume, the above methods are not applicable for this problem and rough numbers system is employed instead. This is an appropriate tool for dealing with inaccurate data based on expert opinions. The rough set theory was first proposed by (Pawlak 1982). This is an efficient mathematical tool for dealing with subjective and inaccurate data with no need for excessive assumptions and additional revisions. In this theory, the concept of vagueness is shown by a pair of upper approximation and lower approximation, based on accurate concepts (Pawlak 1991). The lower approximation of set S is the set of all elements that are certainly included in S while the upper approximation includes elements whose attachment to S is uncertain. Fig. 1 shows the primary logic of rough set theory.

2.4.1. Rough numbers and standard mathematical operations

Let us assume U is a world encapsulating all things. The boundary region of S in U is composed of elements that are neither an element of the target set nor excluded from the set (Greco, Matarazzo et al. 2001). Zhai, et al.(2008) argued that upper approximation, lower approximation, and boundary region can be used against human inaccurate and subjective judgments. Assume a set of n groups of human judgments R = {[J.sub.1], [J.sub.2], x x x, [J.sub.n] as sorted as [J.sub.1] < [J.sub.2] < x x x < [J.sub.n] where Y is an arbitrary object of U. In this case, the upper and lower approximations of [J.sub.i] and boundary region is determined as follows:

[Lower approximation: Apr ([J.sub.i]) = U {Y [member of] U/R(Y) [less than or equal to] [J.sub.i]}] (1)

[Upper approximation: Apr ([J.sub.i]) = U {Y [member of] U/R(Y) [greater than or equal to] [J.sub.i]}] (2)

[[Boundary region: Bnd ([J.sub.i]) =U {Y [member of] U/R(Y) [not equal to] [J.sub.i]}] = {Y [member of] U/R(Y) > [J.sub.i]} [union] {Y [member of] U/R(Y) < [J.sub.i]}] (3)

Therefore, human subjective judgments and preferences, [J.sub.i], can be displayed by a rough number determined by its lower limit, Lim([J.sub.i]), and the upper limit, Lim([J.sub.i]). Interval of boundary region indicates the degree of accuracy. A rough number with the small interval of boundary region is interpreted as a more accurate number. Human judgment and the interval of boundary region are expressed by the following equations:

[Rough number: RN([J.sub.i]) = [Lim ([J.sub.i]), Lim([J.sub.i])]] (4)

[Interval of boundary region: IBR([J.sub.i]) = Lim([J.sub.i]) - Lim([J.sub.i])] (5)

Interval analysis operations for rough numbers are applied as Equations (6) to (8):

[R[N.sub.1] [direct sum] R[N.sub.2] = ([L.sub.1], [U.sub.1] + ([L.sub.2], [U.sub.2]) = ([L.sub.1] + [L.sub.2], [U.sub.1] + [U.sub.2])] (6)

[R[N.sub.1] [cross product] K = ([L.sub.1], [U.sub.1]) x K = (K[L.sub.1], K[U.sub.1])] (7)

[R[N.sub.1] [cross product] R[N.sub.3] = ([L.sub.1], [U.sub.1]) x ([L.sub.2], [U.sub.2]) = ([L.sub.1] x [L.sub.2], [U.sub.1] x [U.sub.2])] (8)

Where, R[N.sub.1] = ([L.sub.1], [U.sub.1]) and R[N.sub.2] = ([L.sub.3], [U.sub.2]) are two rough numbers and K is a non-zero constant.

2.4.2. Comparison of rough numbers and converting into crisp values

Rough set-based rating, pursued by this study, follows its own rules. In summary, there are three general rating rules (Zhai, Khoo et al. 2008). Let us assume [U.sub.A] and [U.sub.B] are the upper limit of numbers A and B, and [L.sub.A] and [L.sub.B] are the lower limit of rough numbers A and B, respectively. There are three possible alternatives:

[if [U.sub.A] > [U.sub.B] and [L.sub.A] [greater than or equal to] [L.sub.B] or [U.sub.A] [greater than or equal to] [U.sub.B] and [L.sub.A] > [L.sub.B] then A> B] (9)

[if [U.sub.A] = [U.sub.B] and [L.sub.A] = [L.sub.B] then A = B] (10)

[if [U.sub.A] > [U.sub.B] and [L.sub.A] < [L.sub.B] or [U.sub.A] > [U.sub.B] and [L.sub.A] < [L.sub.B] then calculate [M = [U + L/2]]] (11)

In Equation (11), rough numbers are compared via the following rules after the calculation of M:

[if [U.sub.A] > [U.sub.B] and [L.sub.A] < [L.sub.B] and [M.sub.A] [less than or equal to] [M.sub.B] then A < B] (12)

[if [U.sub.A] > [U.sub.B] and [L.sub.A] < [L.sub.B] and [M.sub.A] > [M.sub.B] then A > B] (13)

[if [U.sub.A] < [U.sub.B] and [L.sub.A] > [L.sub.B] and [M.sub.A] [less than or equal to] [M.sub.B] then A<B] (14)

[if [U.sub.A] < [U.sub.B] and [L.sub.A] > [L.sub.B] and [M.sub.A] > [M.sub.B] then A>B] (15)

Following the calculation of rough numbers, a set of rough numbers should be converted to crisp values in order to sort their rank. Let [L.sub.A] and [U.sub.A] be the upper approximation and the lower approximation of rough number A and [lambda](0 [less than or equal to] [lambda] [less than or equal to] 1) be the optimism index. Therefore, the equation for converting the rough number to a crisp value (Song, Ming et al. 2013) will be as follows:

[A = (1 - [lambda]) [L.sub.A] + [lambda][U.sub.A]] (16)

3. PROPOSED METHOD

The proposed method is accompanied by two assumptions. First, assume that there are k DMs and their opinions contributing to the final decision with the same importance (k = 1,... k). Second, assume that there are m selection alternatives (i = 1,..., m). The proposed method consists of eight steps as follows.

[mathematical expression not reproducible] (17)

Where [f.sup.k.sub.ij] is the value of the ith alternative in the jth criterion of expert's opinion according to the kth expert. Then, group decision matrix is formed as matrix (18).

[mathematical expression not reproducible] (18)

So that:

[f.sub.ij] ~ {[f.sup.1.sub.ij], [f.sup.2.sub.ij],..., [f.sup.k.sub.ij],... [f.sup.m.sub.ij]}

Step 2: converting [f.sub.ij] array of matrix F to a rough number in order to constitute the rough group assessment matrix F using equations (19) and (20).

[Lower approximation: Apr ([f.sup.k.sub.ij]) = [union] {Y [member of] U/R(Y) [less than or equal to] [f.sup.k.sub.ij]}] (19)

[Upper approximation: Apr ([f.sup.k.sub.ij]) = [union] {Y [member of] U/R(Y) [greater than or equal to] [f.sup.k.sub.ij]}] (20)

Thus, [f.sup.k.sub.ij] can be displayed as a rough number determined by its lower limit, Lim ([f.sup.k.sub.ij]) and upper limit, Lim([f.sup.k.sub.ij]), in which:

[mathematical expression not reproducible] (21)

[mathematical expression not reproducible] (22)

[x.sub.ij] and [y.sub.ij] are the lower approximation and the upper approximation components of [f.sup.k.sub.ij], respectively. [N.sub.ijL] and [N.sub.ijU] are the number of components placed in the lower approximation and upper approximation of ([f.sup.k.sub.ij]), respectively. Now, rough number RN([f.sup.k.sub.ij]) can be displayed as Equation (23):

[mathematical expression not reproducible] (23)

where [f.sup.kL.sub.ij] and [f.sup.kU.sub.ij] are the lower limit and the upper limit of rough number RN([f.sup.k.sub.ij]) in the kth pairwise comparison matrix, respectively. Then, it is possible to formulate the sequence of rough numbers as Equation (24):

[mathematical expression not reproducible] (24)

In addition, mean rough intervals are defined as Equations (25), (26) and (27):

[mathematical expression not reproducible] (25)

[mathematical expression not reproducible] (26)

[mathematical expression not reproducible] (27)

where [f.sup.L.sub.ij] and [f.sup.U.sub.ij] are the lower limit and the upper limit of rough number [[f.sup.L.sub.ij], [f.sup.U.sub.ij], respectively. m is the number of experts. At this point, it is possible to form the rough group decision matrix, F, as matrix (28):

[mathematical expression not reproducible] (28)

Step 3: Generating the positive ideal solution (PIS) and negative ideal solution (NIS) based on the characteristic of each criterion. Obviously, for the benefit criterion, its PIS value and the NIS are the largest and the lowest values that it may take, respectively. The PIS and NIS are formulated in Equation (29).

[mathematical expression not reproducible] (29)

Where [f.sup.+] (j) and [f.sup.-] (j) are PIS and NIS values with respect to criterion j. B and C represent benefit criterion and cost criterion, respectively.

Step 4: calculating the deviation coefficient. The deviation coefficient (in the form of rough numbers) is calculated using the distance between the rough number and its PIS and NIS values as follows:

[mathematical expression not reproducible] (30)

[mathematical expression not reproducible] (31)

[[d.sup.+L.sub.ij], [d.sup.+U.sub.ij]] represents the distance between a rough number and its PIS. [d.sup.+L.sub.ij] and [d.sup.+U.sub.ij] denote the lower and upper limits, respectively. Now, we can establish the deviation coefficient matrix [D.sup.+] as follows:

[mathematical expression not reproducible] (32)

[mathematical expression not reproducible] (33)

[mathematical expression not reproducible] (34)

[[d.sup.-L.sub.ij], [d.sup.-U.sub.ij] represents the distance between a rough number and its NIS. [d.sup.-L.sub.ij] and [d.sup.-U.sub.ij] denote the lower and upper limits, respectively. Now we can establish the deviation coefficient matrix, [D.sup.-], as follows:

[mathematical expression not reproducible] (35)

Step 5: Normalizing the deviation coefficients of alternatives and obtaining the normalized deviation coefficient matrices, [D.sup.+] and [D.sup.-], as follows:

[mathematical expression not reproducible] (36)

[mathematical expression not reproducible] (37)

[??] and [??] represent the lower and the upper limits of normalized deviation coefficients between a rough number and the PIS.

[mathematical expression not reproducible] (38)

[mathematical expression not reproducible] (39)

[??] and [??] represent the lower and upper limits of normalized deviation coefficients between a rough number and the NIS.

Step 6: Calculating the separation measure [S.sub.i.sup.+] and [S.sub.i.sup.-] (weighted normalized deviation) of each alternative as follows:

[mathematical expression not reproducible] (40)

[mathematical expression not reproducible] (41)

Separation measures [S.sup.+.sub.i] and [S.sup.-.sub.i] represent weighted normalized deviation of alternative i from its PIS and NIS values, respectively. [w.sub.j] is the weight of the jth criterion obtained from expert's opinion.

Step 7: Transforming the separation measures [S.sup.+.sub.i] and [S.sup.-.sub.i] into a crisp value with the optimistic indicator [alpha](0 [less than or equal to] [alpha] [less than or equal to] 1). If decision makers are more pessimistic, they select a smaller value for [alpha]([alpha] < 0.5). If decision makers are more optimistic, they can select [alpha] with a bigger value [alpha]([alpha] < 0.5). If decision makers keep a realistic and moderate attitude, in other words, neither very optimistic nor very pessimistic, they give [alpha] value of 0.5. The transformation calculation is as follows:

[mathematical expression not reproducible] (42)

[mathematical expression not reproducible] (43)

[S.sup.+*.sub.i] and [S.sup.-*.sub.i] represent the crisp value of rough number [S.sup.+.sub.i] and [S.sup.-.sub.i], respectively.

Step 8: Calculating the distance closeness coefficient ([CC.sub.i]) of all alternatives for their priority rankings.

[mathematical expression not reproducible] (44)

Then, the author prioritize the data sequences based on the [CC.sub.i]. An alternative with a larger [CC.sub.i] is a better choice because it is probably closer to the PIS and farther from the NIS.

4. CASE STUDY

In this study, three groups of brand experts were asked to rank the brand imitation factors through questionnaires. One group included brand experts with academic career. The second group consisted of experts with practical experiments, and the third group was formed with peoples who were expert in academic and practical aspects of brand studies, simultaneously. Each group included 5 experts. The weight factor for advices of group 1 and 2 was 0.4 and it was 0.7 for group 3. Factors are shown in Table (1). Ranking Steps are classified as follows:

Step 1: Forming individual decision-making matrix, as shown in Table (2), using the opinion of three groups of brand experts derived from questionnaire. The rows of this matrix stand for alternatives i.e. the factors that affect brand imitation whereas the columns stand for criteria i.e. Expert's opinion.

Then, group decision matrix is formed(F), as presented in Fig. 2.

Fig.2. Group decision matrix based on experts' opinion 9,4,8,2,7 7,2,8,6,5 5,3,4,5,7 4,9,7,5,8 1,3,5,4,3 3,5,5,1,3 3,5,5,7,4 7,2,2,5,7 5,1,5,1,5 5,9,9,7,6 5,2,3,7,5 7,2,7,5,2 4,6,7,9,7 5,2,2,3,8 7,1,7,3,6 F 8,5,6,7,7 7,2,6,6,7 7,4,8,9,8 5,4,9,3,3 3,1,5,4,5 1,1,2,1,8 3,5,8,5,5 5,3,6,5,5 1,3,2,1,8 7,9,5,7,8 7,3,8,7,6 5,2,9,5,8 7,9,6,7,2 7,5,5,2,4 6,6,8,1,9 7,9,8,9,6 1,3,8,7,9 7,5,7,3,6 9,7,9,7,8 7,5,8,1,6 8,7,8,9,4

Step 2: Transforming the group decision matrix to rough numbers for forming rough group decision matrix as presented in Table (3).

Step 3: Positive and negative ideal solutions are defined as presented in Table (4).

Step 4: Calculating the deviation coefficients (distance of each criterion from the PIS in table (5) and from the NIS in table (6)).

Step 5: Normalizing the deviation coefficients of alternatives in tables (7) and (8).

Step 6: Computing the separation measure [S.sup.+.sub.i] and [S.sup.-.sub.i], as shown in table (9).

Step 7: Transforming the separation measures [S.sup.+.sub.i] and [S.sup.-.sub.i] into crisp values with the optimistic indicator as presented in table (9).

Step 8: Calculating the relative closeness to the ideal solution and ranking the alternatives. The rank results can be seen in table (9). The rank of criteria is as follows:

F12>F9>F11>F6>F4>F1>F5>F10>F2>F8>F3>F7.

5. COMPARISON AND DISCUSSION

For comparison, TOPSIS method was implemented with fuzzy numbers. According to the resulted, shown in Table (10), the ranking is as follows:

F12>F11>F6>F9>F4>F5>F1>F10>F2>F7>F3>F8.

In both methods F12 (Legislation) is the most important factor. Both Rough and Fuzzy numbers describe similar mathematical concepts. Both applied methods describe vague information and recognized the range of ambiguity through fuzzy and rough limit measures. Mathematical operations of both rough and fuzzy groups are based on ranges. Rough theory is similar to fuzzy, evidence, and grey theory but this approach is independent.

TOPSIS rough method shows priorities in experts' judgments. Although TOPSIS fuzzy operates like a logical method for ranking in a fuzzy condition, there are several limitations. One limitation is individual membership function that needs more information and investigation. Furthrmore, fuzzy range, indicating individuality and ambiguity, is a constant dependent to the membership function. For instance, in decision matrix the related scores for expert's advice are 7, 7, 6, 5, and 8 that are in the constant distance range of triangular numbers of (8,6), (8,6), (5,7), (6,4), and (9,7), respectively. Geometric mean of collective advices of experts is (5.501, 7.529) but the fuzzy mean range is not suitable for a real experiments because the distance that shows approximation range in ranking differs when we have experts with different sciences and experiments. In TOPSIS Rough collective ranking approach, the mentioned numbers are converted to more flexible and smaller ranges as (8, 6.517), (6.517, 5), (6.964, 5.477), (7.174, 6.192), and (7.174, 6.192). The fuzzy collective mean range is (5.846, 7.207) that is smaller than fuzzy range. Similar results are derived from other arrays of matrix. Large distances show more ambiguities that are not acceptable in risk rankings. Therefore, rough numbers provide higher level of significance than fuzzy numbers.

With TOPSIS Rough collective method change in expert's priorities can be recognized because of rough number's capability for determining limitations based on total expert's priorities. If experts in previous example alter their judgments to 4, 7, 6, 4, and 7, then Fuzzy ranges will change as these: (3, 5), (6, 8), (5, 7), (3, 5), and (8, 6). Also, rough ranges will change to these: (4, 5.426171), (5.426171, 7), (4.578857, 6.66494), (4, 5.426171), and (5.426171, 7). It is clear that fuzzy modified ranges also have the constant distance that is equal to 2. This constant distance is not real because change in advices cannot be recognized in this method. This will affect decision and ranking in affair.

This study is an effort to rank imitation using rough numbers' specifications. Comparing the results of this method with Topsis-Fuzzy, according to brand imitation literature, reveals that which method can be more useful for this purpose. The result derived from Topsis-Fuzzy method is similar to TOPSIS-Rough method but not the same. The important thing is that legislation is the most important factor that affects imitation in both methods. In rough method, technology is more important. This finding seems to be true because high technology can prevent imitation while the appearance attracts imitators. In Topsis-Fuzzy method, in addition, value is more important than technology that is not really true because if a company decides to imitate a product with high brand value and it will not be able to copy technology and manufacture the product it can't imitate it. This means the TOPSIS-Rough method has gave us more logical answers.

6. CONCLUSION

Brand imitation can result in deep failures for businesses. To prevent this, we must first know what brand imitation is and recognize brand imitation factors. These factors are collected from literature. The second step is to rank these factors. In this paper, we employed TOPSIS-Rough method to rank the factors and compared the results with TOPSIS-Fuzzy. By comparison of two mentioned methods, it is clear that the most important factor that affects imitation is legislation. Thus, the act of laws for preventing imitation can be emphasized. The second effective factor is technology. Technology is influential in two ways. It can be effective by preventing new entrants according to Porter's theory. It also can avoid imitation by making it difficult for rivals. It means that if we want to stop brand imitation, we must codify law to stop them. Also imitation occurs usually in cases that lack of high technology is observed. Laws and technology are two cardinal factors that can prevent brand imitation and counterfeit. According to the findings, appearance is the third factor. Attractiveness of appearance and also easiness of appearance imitating can be effective. Brand value is the fourth factor which shows prosperity of a brand. Imitators are eager to select brands with high value to imitate. Following the effective factors are adduced with their significance priority:

TOPSIS FUZZY:

Legislations > Appearance > Value > Technology > Market share > Finance > Feature > Substitutes > Place > Suppliers > Price > Buyers

TOPSIS ROUGH :

Legislations > Technology > Appearance > Value > Market share > Feature > Finance > Substitutes > Place > Buyers > Price > Suppliers

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SEYED BABAK EBRAHIMI (1)

ESMAEIL GHADERIFAR (2)

FATEME JAMALI MOGHADAM (3)

KAMBIZ MANUCHEHRIAN (4)

ABBASALI ARFA (5)

JEL: M00, M10, O10

RECEIVED: 10/01/2019

MODIFIED: 02/04/2019

ACCEPTED: 19/05/2019

(1) Assistant Professor in Financial Engineering Department of Faculty of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran. He earned his MSc from Sharif University of Technology as a top student in the field of economics. During his undergraduate period, he was awarded as the best student in research in Industrial Engineering Department of Iran University of Science and Technology for three consecutive years. He was also the top young Iranian researcher in Science and Technology and was elected as the best Ph.D. graduate. His research interests include econometrics, microeconomics, time series analysis and pricing. ORCID: https://orcid.org/0000-0002-2678-4240. Email: b_ebrahimi@kntu.ac.ir

(2) PhD of Technology Management Allameh Tabataba'i Universtity, Tehran, Iran. He also has M.B.A degree. He is Director of Strategic Technologies Center of Vice-Presidency for Science and Technology. He are leading lots of innovation and technology projects in Iran. Esmaeil has authored couple of articles in national and international journals and conferences. ORCID: https://orcid.org/0000-0003-4409-2085. Email: ghaderifar@atu.ac.ir

(3) Expert in marketing, entrepreneurship and decision science. She has studied Master of industrial engineering focusing on fuzzy and rough MCDM methods in risk evaluation as her dissertation in 2015. She is also working on data mining and analysis as her main area of interest. Fateme has authored couple of articles in Iranian journals and conferences. ORCID: https://orcid.org/0000-0002-6722-9809. Email: fatemejamalimoghadam@yahoo.com

(4) MS.C student of industrial engineering at Karaj Azad University. He also has M.B.A degree. Focused on Project Management also branding is his favorite field of investigation. He is interested in fields that are not studied completely by researchers. Brand Imitation is such a topic in brand studies that is not clearly studied by all of its aspects. So he is interested in it. ORCID: https://orcid.org/0000-0003-1992-2083. Email: kmanuchehrian@gmail.com

(5) Expert in innovation and technology area. He is working on this area since 2001. Nowadays, He is acting deputy of Strategic Technologies Center of Vice-Presidency for Science and Technology. He also participated in scientific conferences and workshop as a board Abbasali has written reports and articles in innovation national meeting and conferences. ORCID: https://orcid.org/0000-0002-6130-4871. Email: a.arfa@isti.ir

DOI: 10.17230/ad-minister.34.9

Table 1. Factors that affect imitation Shown in Factors Description calculation as F1 Feature Affection of brand feature and theme F2 Place Place where products are sold F3 Price Product's Price F4 Market Category Market Share Share F5 Finance Brand's sponsorship F6 Value Brand value F7 Suppliers Bargaining power of suppliers F8 Buyers Bargaining power of buyers F9 Technology Spread of technology F10 Substitutes Threat of substitutes F11 Appearance Affection of appearance F12 Legislations Legislations and the level of intellectual property rights Shown in Reference calculation as (Le Roux, Bobrie et al. 2016), F1 (Femke van Horen and Pieters 2012) (Le Roux, Bobrie et al. 2016), F2 (Femke van Horen and Pieters 2012) (Le Roux, Bobrie et al. 2016), F3 (Femke van Horen and Pieters 2012) F4 (Sinapuelas 2007), (Wilbur and Farris 2014) (Sinapuelas 2007), (Harris F5 2007) (Sinapuelas 2007), (Chehab, F6 Liu et al. 2016), (de Oliveira, Silveira et al. 2015) Porter's five forces theory, F7 (Dessain and Fishman 2017), (Wu, Tseng et al. 2012) Porter's five forces theory, F8 (Dessain and Fishman 2017), (Wu, Tseng et al. 2012) Porter's five forces theory, F9 (Dessain and Fishman 2017), (Wu, Tseng et al. 2012) Porter's five forces theory, F10 (Dessain and Fishman 2017), (Wu, Tseng et al. 2012) F11 (Le Roux, Bobrie et al. 2016), (Zaichkowsky 2006) Porter's five forces theory, F12 (Dessain and Fishman 2017), (Wu, Tseng et al. 2012) Table 2. individual decision-making matrix Group 1 DM 1 DM 2 DM 3 DM 4 DM 5 F1 9 4 8 2 7 F2 4 9 7 5 8 F3 3 5 5 7 4 F4 5 9 9 7 6 F5 4 6 7 9 7 F6 8 5 6 7 7 F7 5 4 9 3 3 F8 3 5 8 5 5 F9 7 9 5 7 8 F10 7 9 6 7 2 F11 7 9 8 9 6 F12 9 7 9 7 8 Table 3. Rough group decision matrix Factors Group 1 Group 2 Group 3 F1 [3.498, 7.348] [3.556, 6.702] [3.837, 5.536] F2 [5.084, 7.708] [1.974, 3.852] [2.067, 4.063] F3 [3.837, 5.536] [2.795, 5.453] [1.785, 3.865] F4 [6.036, 8.149] [2.996, 5.308] [2.795, 5.453] F5 [5.327, 7.509] [2.446, 4.942] [2.328, 5.857] F6 [5.849, 7.207] [3.905, 6.377] [5.738, 8.081] F7 [3.434, 5.798] [2.079, 4.324] [1.157, 2.789] F8 [4.174, 5.884] [4.127, 5.260] [1.320, 2.371] F9 [6.206, 7.965] [4.671, 7.062] [3.623, 6.988] F10 [3.927, 7.303] [3.210, 5.447] [2.931, 7.153] F11 [6.937, 8.499] [2.368, 6.965] [4.313, 6.408] F12 [7.431, 8.497] [2.591, 6.518] [5.738, 8.081] Table 4. Positive and negative ideal solutions Group 1 Group 2 Group 3 Positive ideal solutions 8.498885 7.061609 8.081353 Negative ideal solutions 3.433573 1.973596 1.156688 Table 5. deviation coefficients from PIS ([D.sup.+]) Group 1 Group 2 Group 3 F1 [1.151, 5.001] [0.360, 3.506] [2.545, 4.245] F2 [0.791, 3.415] [3.210, 5.088] [4.018, 6.014] F3 [2.962, 4.662] [1.609, 4.266] [4.216, 6.296] F4 [0.350, 2.462] [1.753, 4.066] [2.629, 5.286] F5 [0.990, 3.172] [2.119, 4.615] [2.224, 5.753] F6 [1.292, 2.650] [0.685, 3.156] [0, 2.343] F7 [2.701, 5.065] [2.738, 4.983] [5.292, 6.925] F8 [2.614, 4.324] [1.802, 2.935] [5.710, 6.762] F9 [0.534, 2.293] [0, 2.390] [1.093, 4.458] F10 [1.196, 4.572] [1.614, 3.852] [0.928, 5.150] F11 [0, 1.562] [0.097, 4.694] [1.673, 3.767] F12 [0.002, 1.068] [0.543, 4.470] [0, 2.343] Table 6. deviation coefficients from NIS ([D.sup.-]) Group 1 Group 2 Group 3 F1 [0.065, 3.915] [1.582, 4.728] [2.680, 4.380] F2 [1.650, 4.275] [0, 1.878] [0.911, 2.907] F3 [0.403, 2.103] [0.8[\22, 3.479] [0.628, 2.708] F4 [2.603, 4.715] [1.022, 3.335] [1.639, 4.296] F5 [1.893, 4.075] [0.473, 2.969] [1.172, 4.700] F6 [2.415, 3.774] [1.932, 4.403] [4.581, 6.925] F7 [0, 2.364] [0.105, 2.350] [0, 1.633] F8 [0.741, 2.451] [2.153, 3.286] [0.163, 1.214] F9 [2.773, 4.532] [2.698, 5.088] [2.466, 5.831] F10 [0.493, 3.870] [1.236, 3.473] [1.774, 5.996] F11 [3.503, 5.065] [0.394, 4.991] [3.157, 5.252] F12 [3.998, 5.064] [0.618, 4.545] [4.581, 6.924] Table 7. Normalized deviation coefficients from PIS ([D.sup.+']) Group 1 Group 2 Group 3 F1 [0.227, 0.987] [0.071, 0.689] [0.368, 0.613] F2 [0.156, 0.674] [0.631, 1] [0.580, 0.868] F3 [0.585, 0.920] [0.316, 0.838] [0.609, 0.909] F4 [0.069, 0.486] [0.345, 0.799] [0.380, 0.763] F5 [0.196, 0.626] [0.417, 0.907] [0.321, 0.831] F6 [0.255, 0.523] [0.135, 0.620] [0, 0.338] F7 [0.533, 1] [0.538, 0.979] [0.764, 1] F8 [0.516, 0.854] [0.354, 0.577] [0.825, 0.976] F9 [0.105, 0.452] [0, 0.470] [0.158, 0.644] F10 [0.236, 0.903] [0.317, 0.757] [0.134, 0.744] F11 [0, 0.308] [0.019, 0.923] [0.242, 0.544] F12 [0.0003, 0.211] [0.107, 0.879] [0, 0.338] Table 8. Normalized deviation coefficients from NIS ([D.sup.-']) Group 1 Group 2 Group 3 F1 [0.013, 0.773] [0.311, 0.929] [0.387, 0.632] F2 [0.326, 0.844] [0, 0.369] [0.132, 0.420] F3 [0.080, 0.415] [0.162, 0.684] [0.091, 0.391] F4 [0.514, 0.903] [0.201, 0.655] [0.237, 0.620] F5 [0.374, 0.804] [0.093, 0.583] [0.169, 0.679] F6 [0.477, 0.745] [0.380, 0.865] [0.662, 1] F7 [0, 0.467] [0.021, 0.462] [0, 0.236] F8 [0.146, 0.484] [0.423, 0.646] [0.024, 0.175] F9 [0.547, 0.895] [0.530, 1] [0.356, 0.842] F10 [0.097, 0.764] [0.243, 0.683] [0.256, 0.866] F11 [0.692, 1] [0.077, 0.981] [0.456, 0.758] F12 [0.789, 0.9997] [0.121, 0.893] [0.662, 1] Table 9. Separation measure, their crisp form and final rough ranking NO S+ S- S+ crisp S- crisp CCi Rank Rough F1 [0.334, 1.212] [0.866, 1.166] 0.773 0.727 0.485 6 F2 [0.594, 1.219] [0.730, 0.906] 0.907 0.593 0.395 9 F3 [0.779, 1.343] [0.705, 0.721] 1.061 0.439 0.292 11 F4 [0.338, 0.965] [0.876, 1.161] 0.652 0.848 0.566 5 F5 [0.432, 1.134] [0.871, 1.068] 0.783 0.717 0.478 7 F6 [0.232, 0.750] [0.938, 1.268] 0.491 1.009 0.672 4 F7 [0.894, 1.492] [0.754, 0.606] 1.193 0.307 0.205 12 F8 [0.833, 1.219] [0.673, 0.667] 1.026 0.474 0.316 10 F9 [0.137, 0.762] [0.960, 1.363] 0.450 1.050 0.700 2 F10 [0.346, 1.232] [0.873, 1.154] 0.789 0.711 0.474 8 F11 [0.104, 0.803] [0.958, 1.396] 0.453 1.047 0.698 3 F12 [0.043, 0.634] [1.027, 1.457] 0.339 1.161 0.774 1 Table 10. Fuzzy ranking Criteria F1 F2 F3 F4 F5 F6 F7 F8 CCi 0.514 0.472 0.448 0.5 51 0.532 0.597 0.459 0.435 Fuzzy Rank 7 9 11 5 6 3 10 12 Criteria F9 F10 F11 F12 CCi 0.595 0. 511 0.610 0.660 Fuzzy Rank 4 8 2 1