SELECTING TARGET MARKET BY SIMILAR MEASURES IN INTERVAL INTUITIONISTIC FUZZY SET

. The selection of the target market plays vital role in promoting the marketing strategies of companies. We presented is a method for target market selection. We introduce some novel similarity measures between intuitionistic fuzzy sets and the novel similarity measures between interval-valued intuitionistic fuzzy sets. They are constructed by combining exponential and other functions. Finally, we introduce a multi-criteria decision making model to select target market by using the novel similarity measure of interval intuitionistic fuzzy sets.


Introduction
The target market consists of a set of customer groups having common needs or characteristics that the organizations wish to serve. The selecting of target market helps the suppliers choosing which and how many segments to serve (Bernstein, 2014). Businesses understand that customers are diverse in demands, attitudes and preferences. There is no organization which can satisfy all customers in the markets. Instead of competing in the marketplace, trying to fight against competitors, they should identify the most attractive segment that they can provide effectively (Bernstein, 2014;Kotler &Armstrong, 2003). Marketing strategies allow organizations to find out and develop markets or tailor their services to meet the needs of potential markets. There are normally three ways to reach the market: mass marketing, target marketing and consumer marketing. Mass marketing, which assumes that all customers are treated similarly, will no longer be effective in the coming century (Kuo, Ho & Hu, 2002). Instead, it will be a targeted marketing strategy, which identifies target segments and marketing plans that fit into it (Kotler & Armstrong, 2003). Market segmentation also raises profit or effectiveness of firms (Chiu, Chen, & Kuo, 2009). Besides that, it helps businesses to recognize the position of their product on the market, explore new opportunities and gain competitive advantages through differentiation of the product (Kotler, 1980). Any segmentation scheme should have the following characteristics: exhaustiveness, reliability and operability. By analyzing the attractiveness of each segment, managers make strategic decisions about their sources and finance for each segment, deciding on quality of the product, price and finally determining the time introduce goods to the market (Bernstein, 2014).
There are a lot of methods to segment the market but not all segments are effective. Kotler and Armstrong (2003) pointed out an example of the salt market to prove this claim. It is clear that race or ethical dispositiondoes not affect the amount of salt consumption, so this segment is not effective. According to the authors, the market segment should have the following criteria: measurable, accessible, substantial and actionable. In Simkin and Dibb's view (1998), target marketing plays a key role in making a decision for firms. Although the activities of marketers are changing on the market, selecting the target market is still an important strategic issue. It is necessary to study the market attractiveness criteria. Market size, exchange rate growth, competitive forces, appropriate customers and profits are just a few of the many criteria that can be applied to assess the attractiveness of a target market of an enterprise. The study also found that many firms continue to evaluate target markets on the basis of short-term profit-taking measures. The target market is the center of the marketing decisions, which are seen as the output of evaluation and selection the market segmentation (Aghdaie, 2015). Selecting the target segment is a complex process that takes into account many factors such as the segment's expected response to marketing variables, the likelihood of success, the competitive nature of the segment management resources and the ability to deploy segmentation strategies (Winter, 1979). Thus, the target market selection can be considered as a multi-criteria decision making model.
A well-known and useful method for selecting the most suitable alternative from a set of alternatives is the multi-criteria decision making (MCDM). It has been applied widely to the complexity of economic decision problems as well as many other fields. In these cases, it is difficult for the makers to show their opinions by crisp numbers, so the linguistic variables is used efficiently. The linguistic variables have been recognized as a useful approach in decision making problems. In 1986, Atanassov generalized Zadeh's fuzzy set (Xu, 2010) by introducing the intuitionistic fuzzy set (IFS) (Atanassov, 1986), which considers the information for both the membership function and non-membership function. From its inception to the present day, IFS proved to be very effective in dealing with the uncertainty in the real-world problems such as the pattern recognition, the decision making, etc. After that, the intervalvalued intuitionistic fuzzy set (IVIFS) was introduced by Atanassov and Gargov (1989), in which the membership function and non-membership function are subintervals of [0, 1]. As opposed to fuzzy sets, intuitionistic fuzzy (IF) set also has broad applications for uncertain data processing such as decision making, medical diagnosis, agriculture, image segmentation (Buhaesku, 1988;Hung & Wu, 2002;Mitchell, 2004;Szmidt &Kacprzyk, 2004;Ye, 2011;Park, Hwang, Park, Wei & Lee, 2013;Shi & Ye, 2013;Shidpour, Bernard & Shahrokhi, 2013;Bharati & Singh, 2014;Li & Zeng, 2015;Liu, Shen, Mu, Chen & Chen, 2016;Zhou, Zhao, Yu & Tian, 2016). Along with distance measurements, correlation measurements, similar measurement of IF sets and interval IF sets is also studied and widely used in many areas and now it still is a hot topic (Chiang & Lin, 1999;Gerstenkorn & Mańko, 1991;Ye, 2016). Similarity measures are tools to show the similarity of two objects. It is useful to handle the problems such as decision making, machine learning, pattern recognition (Szmidt & Kacprzyk, 1996;Liang & Shi, 2003;Hwang, Yang, Hung & Lee, 2012;Li & Cheng, 2002;Xu, 2007b;Zeng & Wang, 2011;Ye, 2011;Park, Hwang, Park, Wei & Lee, 2013). The similarity measure (SM) between IF sets were introduced by Liang and Shi (2003) and applied in the pattern recognition problem. Xu (2006) developed the similarity measure which constructed by the distance measure in multi-criteria decision making. This problem was proposed and applied in the multi-criteria decision making by Zhou (2016). The proposed methods used polynomial functions or fractional functions. Ye (2016) generalized new version of weighted cosine similarity measures between two IF sets through the degrees of membership, nonmembership and hesitancy in IF sets and applied to mechanical decision schemes using intuitionistic fuzzy numbers. Phong and Son (2017) resolved linguistic classification problem by the linguistic SM, the linguistic vector, and the linguistic vector similarity.
The existing models which evaluate and select market segment or target market, usually use the triangular or trapezoidal fuzzy numbers to express the assessment of decision makers (DMs) (see for example Aghdaie, Zolfani & Zavadskas, 2013). The interval-valued intuitionistic fuzzy set is a stronger tool in reflecting the vague features of the subjective judgments of the DMs. The proposed similarity measures of Shi and Ye (2013), Ye (2016) have been successfully applied in classification or pattern recognition, however, they were not effective in some cases. These inspire us to introduce a new similarity measure of intuitionistic fuzzy sets which can overcome some drawbacks and apply the new measure for selecting target market. The rest of this paper is as follows. In Section 1, we recall the concept of intuitionistic fuzzy set, interval-valued intuitionistic fuzzy set and the similarity measure of them. The new similarity measure between the IFSs were built by combining exponential and other functions in Section 2 and we will compare the results computed by our method to other ones. The similarity measure of the interval-valued intuitionistic fuzzy sets is proposed in Section 3. In Section 4, we use the similarity measure of interval-valued intuitionistic fuzzy sets in multi-criteria decision making model. Section 5, a case study will cary out to apply the new measure for target market selection. Finally, we compare the proposed method with some existing models.

Preliminary
Let X be a universal set. We recall the concepts of IFS and interval-valued intuitionistic fuzzy set (IVIFSs) on X.
Definition 1. (Atanassov, 1986) An IFS X is defined by form ∈    is the membership degree and ( ) 0,1 A x ν ∈    is the non-membership of the element x in X to A, respectively such as Definition 2. (Atanassov, 1989) An interval -value IFS on X is a defined by form are the membership degree and the non-membership of the element x in X to A, respectively, and we have some following characteristics (Xu, 2007a): ν + µ ≤ to show the value in IVIFs, and call it the interval intuitionistic fuzzy value.
Definition 3. (Xu, 2007a). Let x and y be two interval intuitionistic fuzzy values. We have the following basic operations: Now, we recall the similarity measure of the intuitionistic fuzzy sets. Given is a SM of the intuitionistic fuzzy sets if the following conditions are satisfied:

New similarity measure of the IFSs
We recall the concept of Hausdorff distance which is important and effective in pattern recognition and classifying problem. For any two intervals Nadler, 1978;Hung & Yang, 2004).
The distance and the similarity measure are dual couple. The similarity measure can define via the distance function (Hung & Yang, 2004). The exponential function has been acknowledged as a useful tool to measure the similarity (Zadeh, 1971; N. R. Pal & S. K. Pal, 1992). Therefore, motivate by the exponential function and the Hausdorff distance, in this section, we will propose a new similarity which combines them. We also compare our measure with some other ones. Let ).
Definition 5. We define a mapping 0 : (1) Now, we can define the similarity measure of the IF sets that assigned with the weight of each element in the universal set.
We assume that each element x i in the universal We recall some existing similarity measures as follows: + The similarity measure of Ye (2011) + The similarity measure of Shi and Ye (2013) + The similarity measure of Ye (2016) ( ) However, one can find some drawbacks of the cosine similarity measure as follows:

( , ) ( , ) S A B S A B
< then we put B belongs to pattern A 2 . We consider the following example:

The similarity measure of the IVIFSs
We will extend our method to the IVIFSs in this section. Let A and B be two arbitrary IVIFSs in X as follows: for all 1,2,..., . i n = Definition 7. We define the similarity measure of two intervals IF A and B as follows Theorem 3. Let A and B be two arbitrary IVIFSs on X. We have .
Remark. It is easy to show that the SM of A and B in the Definition 8 satisfies all the conditions of the Theorem 3.
Example 4. We consider a pattern recognition problem about the classification of minerals; the data was quoted from Liu et al. (2016). There are three classes of given minerals, which are expressed by the IVIFSs A 1 , A 2 , A 3 in the feature space { } 1 2 3 4 5 6 , , , , , Assume there is a new mineral A along with its known attribute values. Our aim is to determine which class that A belongs to. The descriptive data information is given in Table 1. According to the Table 2, we can comment that the similarity measure between A i (i = 1, 2, 3) and A with 1 1 1 1 1 1 6 6 6 6 6 6 ( , , , , , ) w = is 3 1 2

( , ) ( , ) ( , ) S A A S A A S A A
> > , so A belongs to class A 3 .  We also compare the result of our method to the results obtained by other methods in Li and Cheng (2002), Bustince and Burillo (1995), Shidpour, Bernard, and Shahrokhi (2013), Hung (2001) and Buhaesku (1988) (see Table 3). Our result is identical with the results using these methods.

Multi-criteria decision making model
In the MCDM problem, the decision makers are responsible for choosing the best suitable option from the set of alternatives. They must assess alternatives under criteria. The criterion outcomes are a basis to rank the options (Kelemenis &Askounis, 2010). The fundamental process of MCDM model includes the following steps (Kelemenis & Askounis, 2010;Shen, Olfat, Govindan, Khodaverdi & Diabat, 2013): Step 1. Construct the decision matrix.
Step 2. Determine the matrix of the criteria weight.
Step 3. Construct the weighted decision matrix.
Step 4. Rank the alternatives. The object of this section is applying the similarity measure for the interval-valued intuitionistic fuzzy sets to construct a novel MCDM model. Let { ( 1,2,..., )} i P i m = be a set of alternatives for evaluation, j C ( 1,2,..., ) j n = be n criteria to select the optimal option. There are h decision makers (DMs) ( 1,2,..., ) to identify the importance of criteria and the meeting criteria of alternatives through the linguistic terms given in the Table 4 and Table 5. The SM of the interval-valued IF sets is used to rank the alternatives. The model has the following steps:  Step 1. Determine the weight vector w j of the criterion ( 1,2,..., ) j C j n = . Each of criterion has a different importance, which is made by the DMs. Assume that the aggregated weight of the criterion C j is represented by The criteria are divided into two types, benefit or cost, therefore the cost criteria need to be transformed into benefit type. The P ij is converted to the standardized value r ij by ij ij r P = if C j is benefit type, ij c ij r P = if C j is cost type (According to Xu & Hu, 2010).
Step 3. Determine the overall values of alternatives The overall value of each alternative with respect to each criterion is multiple of the value r ij with the aggregated weight w j , 1,2,..., ; 1,2,..., .
ij ij j V r i m j n = ⊗ w = = (According to Shen et al., 2013).
Step 4. Rank the alternatives In order to identify the optimal alternative, all alternatives need to be compared with the ideal solution

Case study
In this section, a case study was performed in a well-known company in Vietnam, which is a joint venture company between Japan, Thailand and Vietnam covertures. This company has grown rapidly and become one of the leading companies in the automobile and motorcycles sector. The company put an acute focus into providing customers with high quality products at reasonable prices. The managers of this company involve how to select the target market to gain outstanding profit. In order to determine the most suitable market, we conducted a survey on target market research. The four market segments defined as alternatives were denoted by SE 1 , SE 2 , SE 3 , and SE 4 . The data used as input for evaluated process was collected by interview the experts. This group includedthe marketing manager, the sales manager, the experts in business and the expert in university. Simkin and Dibb (1998) carried out a survey of the criteria for selecting target markets. They referredfrom literature and interviewed with experts. As a result, Identify profitability (C1), The growth of the market (C2), Size of market (C3), likely customer satisfaction (C4), sales volume (C5), Likelihood of sustainable differential advantage (C6), Development opportunities (C7) and The differentiation of product (C8) were most heavily-used criteria. The experts recognized that these criteria were suitable in Vietnam's market. In this section, we will use these criteria to select the target market. The procedure is represented as follow: Step 1. Determining the weight of criterion.
After defining the criteria, the experts were asked to determine the important degree of each criterion using the scale for importance. Based on the opinion of experts for each criterion, we calculated their averaged values. The weight of each criterion is shown in the Table 6.
Step 2. Evaluating the performance of the market segment with respect to the criterion.
Four experts are responsible for evaluating the degree of satisfying of alternatives respect to the criteria. Their opinions were expressed through the interval intuitionistic fuzzy numbers, which is shown in the Table 5. The averaged values are assigned by the decision makers for markets under the criteria is shown in the Table 7. In this case, all the criteria used for evaluation are the criteria of benefit. Therefore, it is not necessary to convert to the standardized values.
Step 3. Determining the overall values of market segments.
The overall value of each market segment with respect to each criterion is calculated by the Equation (5), it is shown in the last column of the Table 7.
Step 4. Calculating the similarity measure S i of each market by Eq. (6) with s = t =1.
Ranking of markets based on the similarity measure. The result is shown in the Table 8 and Figure 1.  The ranking between markets is SE 3 , SE 1 , SE 4 , SE 2 , the target market is SE 3 .
In the model of Shen et al. (2013), the TOPSIS method was used to rank the options, the evaluated values were expressed by the triangular fuzzy numbers and the distance function was ( ) ( ) ( )  The similarity measures of Ye (2011Ye ( , 2016, Shi and Ye (2013) were used to arrange the order of alternatives. The results of ranking are shown in the Table 9.  The result of our method is as same as with the methods of Xu (2007b), Shen et al. (2013), Ye (2011Ye ( , 2016 and Shi and Ye (2013) There is a little difference between the ranking in the method of Wei et al. (2011)and the rest of methods. On the other hand, based on the evaluation of the decision makers in the third column of the Table 7, the SE 3 is better than the SE 1 in the almost of criteria. Thus, the ranking SE 3 , SE 1 , SE 4 , SE 2 is reliable.

Conclusions
In current markets, the businesses have to face a lot of challenges due to the development of new technologies, competitors and customers evolving trends. The target market is the center of the marketing decisions. It helps the firms provide suitable marketing strategies. In this article, we have introduced some formulas that define the similarity measures between intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. A multi-criteria decision making method is proposed under intuitionistic fuzzy environment to select the best alternatives. Finally, a case study for selecting the target market was performed. The similarity measures are new and convenient for applications. Our model can be used to rank alternatives in other fields.