A Hybrid Fuzzy Model To The Ranking Problem of Companies operating R&D Activities in Technology Innovation Centers

Technology innovation centers where universities share information with industry collaborations and institutions and have a wide range of companies in its field. Developing technology and competition have forced to make innovations, the companies in technology innovation centers operating Research and Development (R&D) activities have tried to prove themselves by proposing different projects to industrial organizations and making innovations and they are still working since they may get some promotions from the government. A decision for ranking companies has a number of criteria, which range from financial incentives and infrastructure to R&D activities. Most of the criteria are based on linguistic terms that decision makers can express with fuzzy statements. For this reason, in this study, the problem for ranking the companies operating R&D activities is solved by using a hybrid model, combining the Fuzzy Analytic Hierarchy Process and Fuzzy TOPSIS methods. Four different main decision criteria, 16 sub-criteria and three random companies were considered for this study. A network was formed, and surveys were carried out with the opinions of the experts on R&D activities and including experts from some technology development zones of Turkey. The proposed hybrid model was applied successfully to a case study for the ranking the companies operating R&D activities in Çukurova University Technology Development Zone in Turkey. Using actual data, it is showed the applicability of the proposed approach and compare the best alternative obtained by the proposed method for three companies in Çukurova University Technology Development Zone in Turkey.


Introduction
The basis of the infrastructure of the national innovation system is a technology innovation centers, business incubators, technology parks. These centers are called in different names in the countries. They are designed for the rapid transmission of developments in production, development of high-tech and competitive products [1].
Technology innovation centers where universities share information with industry collaborations and institutions and have a wide range of companies in its field. These centers foster university-industry collaboration which targets combining academic and industrial resources to conduct research and development focused on industry-oriented problems and innovation and, additionally, educating a workforce capable of advancing national technological and economic goals [2]. These companies are operating within the technology innovation centers or by providing benefit to the outside institutions and organizations to commercialize their projects. Developing technology and competition have forced to make innovations and it has triggered the collaboration of companies in the technology innovation centers with the industry. When we look at the World, Saaty and Ozdemir [3] conclude "to serve both consistency and redundancy, it is best to keep the number of elements seven or less. It appears that Miller's seven plus or minus two is indeed a limit, a channel capacity on our ability to process information." This explains why multi-criteria decision-making models are widely used, as they provide an effective method for acquiring solutions to complex decision-making problems.
There exists a geometric system that consists of m-points in a n-dimensional space for a decision-making problem where multi-attributes (n) are considered for alternatives (m) [4]. Analytic Hierarchical Model (AHP), fuzzy AHP and fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) methods are examples of multi-criteria decision-making models. These methods have been used in different areas including alternative selections, marketing decisions, performance assessments, resource allocations, quality management etc., and we refer readers to the study of Mardani et al. [5] for a comprehensive two-decade review (1994 to 2014) on fuzzy multiple criteria decision-making techniques and applications.
In particular, one application area for multi-criteria decision-making models is to find solutions to ranking problems. Ozkan et al. [6] have evaluated the R&D performance of cities in Turkey. They have used the DEMATEL and ANP methods together while determining the performance criteria of cites. They have made a suggestion using the VIKOR method to list the cities. Yu et al. [7] have proposed an integrated supplier selection approach that includes the risk attitude of the decision maker using ANN, AHP and TOPSIS methods. Mashal and Alsaryrah [8] have proposed a fuzzy analytical hierarchy process model for determining suitable internet of things applications for each user. Dincer, [9] has applied integrated multi-criteria decision-making methods to measure the market competition and concentration in the European Banking Sector. Luna et al. [10] have proposed a new solution to the problem in the sector with fuzzy TOPSIS by determining appropriate criteria to solve the excess consumption and management confusion in aquaculture.
According to the researchers and the opinion of the experts, it is understood worldwide that there are no certain criteria for companies' innovative success ranking. The aim of this study is to make an objective and quantitative evaluation of the companies operating R&D activities. A decision for ranking companies has a number of criteria, which range from financial infrastructure to R&D activities. Most of the criteria are based on linguistic terms that decision makers can express with fuzzy statements. For this reason, in this study the problem for ranking the companies is solved by using a hybrid model, combining the Fuzzy Analytic Hierarchy Process and Fuzzy TOPSIS methods. To the best knowledge of the authors, the study has the distinction of being the first in this field. Four different main decision criteria, sixteen sub criteria and three random companies were considered for this study. A network was formed, and surveys were carried out with the opinions of the experts on R&D activities and from different technology innovation centers of Turkey. The fuzzy AHP technique, which is one of the MCDM methods, was used to determine the weights and fuzzy TOPSIS method was used for the ranking stage of the companies. After the integration of these methods, several companies operating R&D activities in Çukurova University Technology Development Zone were applied for ranking problems and the results of the method were discussed.

Fuzzy sets and fuzzy numbers
Zadeh [11] was the first researcher who had the idea of fuzzy set theory: he proposed such a theory to handle vagueness in human thought and expression. Membership grades constitute the basics of objects found within a fuzzy set class definition. In this definition, each object is given a membership attribute and a membership function sets this attribute between 0 and 1.

Fig. 1. A triangular fuzzy member
The tilde symbol, '~', is placed above to show that the number represents a fuzzy set. As seen in Fig.1,

Proposed model
The proposed model was designed to be used in single level multi-attribute decision making (MADM) problems.  In the second stage, Chang's extent analysis model [12] is used in order to calculate criteria weights.
Ranking of the alternatives are obtained in the third stage of the model by using fuzzy TOPSIS method. In order to solve MADM, our hybrid model combines theoretical fundamentals from Chang's extent analysis with fuzzy TOPSIS. Fig. 3 shows the activity diagram for the proposed hybrid model.

Fuzzy analytic hierarchy process for criteria weights
The root of FAHP is extended to fuzzy set theory, which was proposed by Zadeh [11]. Instead of using crisp values, Buckley [13] utilized fuzzy ratios. By doing so, Buckley [13] introduced hierarchical structures analysis environment.
In the second stage of the proposed model, the weights of criteria are calculated by using Chang's extent analysis. Initially, we define as an object set, and as a goal set, respectively. According to the principles of Chang's extent analysis [12], each object is taken correspondingly, and extent analysis for each of the goal, i g is implemented in order to obtain the values of m extent analyses with the following signs: 12 ,..., are triangular fuzzy numbers. After these assumptions are defined, Chang's extent analysis includes four main steps: Step 1: The value of fuzzy synthetic extent with respect to the i th object is defined as, where  sign represents the multiplication operation on fuzzy numbers. Fuzzy addition operation of m extent analysis values is performed for particular matrixes such that: Step 2: The degree of possibility of it can be denoted as: Step 3: The degree possibility for a convex fuzzy number to be greater than k convex fuzzy numbers Then, the weight vector is given by where are n elements.
Step 4: Normalized weight vectors are obtained after normalization. W is a nonfuzzy number that represents priority weights of attributes [12].

Fuzzy TOPSIS for alternative ranking
In the third stage of the proposed model, the alternatives are ranked using fuzzy TOPSIS method. There are numerous techniques in order to sort the alternatives based on a criterion set such as fuzzy ELECTRE, fuzzy TOPSIS, fuzzy AHP, fuzzy PROMETHEE and fuzzy MCDM approaches [4,14,15]. TOPSIS method was first proposed by Hwang and Yoon [16]. TOPSIS method is built on the shortest distance and longest distance mechanism. A preferable solution should have a short distance to the positive-ideal solution and long distance to negative ideal solution. Therefore, in order to be ranked first an alternative must have both shortest distance to positive ideal solution and farthest distance to negative ideal solution at the same time. The term Ideal solution is used to show the best criteria value, which is attainable from the alternatives in consideration. Negative ideal solution is used to indicate the opposite: worst criteria value which is attainable from the alternatives in consideration [17]. However, it is not generally feasible to get direct value from a decision maker about any criteria in a typical decision problem.
When decision maker evaluations are vague, fuzzy logic substitutes as a good method to be used in solving MADM problems. When fuzzy theory is used along with TOPSIS method then it is called fuzzy TOPSIS. Fuzzy TOPSIS is developed as an extension of TOPSIS in order to encapsulate linguistic evaluations of alternatives and criteria. A great number of applications for fuzzy TOPSIS could be found in the literature [4,5,[18][19][20][21][22].

Alternative set definition and obtaining decision maker linguistic assessment
At the beginning of the Fuzzy TOPSIS method, the alternatives are assessed with respect to each criterion using linguistic values given in Table 1, accordingly. The fuzzy assessment values are held in Ỹ matrix. ỹ ij holds the specific assessment of the decision maker for alternative i according to criteria j where ( = 1,2, … , ), ( = 1,2, … , ) and k is the number of alternatives and l is the number of criteria at the lowest level of the decision hierarchy.

Determining the positive ideal solutions and negative ideal solutions
The set of positive ideal solutions and negative ideal solutions are given as follows; A + = {̃1 + ,̃2 + , … ,̃+ = {(̃| ∈ ), (̃| ∈ ′)} (12) where J is associated with the positive criteria while ′ is associated with the negative criteria.

Positive and negative distance calculations of alternatives
Each distance is calculated according to following equations;

Calculating the relative distances and alternative ranking
Relative distances are computed according to following equations; As mentioned before, in classical TOPSIS method, the most preferred alternative should simultaneously have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution, which also certainly reflects the rational of human choice. Finally, the best alternative could be determined by using + and − parameters.

Application of the proposed hybrid model to the ranking problem of the companies operating R&D activities
The aim of this study is to determine the success rankings of companies R&D activities by using hybrid method using fuzzy AHP and fuzzy TOPSIS methods. First of all, 4 steps of fuzzy AHP method were applied to this problem and weights were obtained for performance criteria. In the second stage of the study, the fuzzy TOPSIS method was applied with these weights.

Stage 1: Goal, criteria and hierarchy determination
In this stage, the criteria and their hierarchy were determined. The goal definition for the proposed selection

Stage 2: Finding criteria weights
After determining criteria, the evaluation table was created after a series of meetings with the experts where they outlined their opinions about criteria based on the scale given in Table 2. During these meetings, a consensus shown in Table 3 is reached about criteria.
. Therefore, the minimum values of rows were used for calculating WG. Then, WG values were normalized between 0 and 1.

Finding sub criteria weights
After determining sub-criteria for all main criteria, calculations were created based on applying procedures of Chang's methodology. Table 5 shows the weights of the main criteria and the weights obtained by integrating the weights of the sub criteria in accordance with the hierarchical structure formed after the weights of each subcriterion have been found. If the first three rankings of the sub-criteria are to be made; Institutionalization Regarding the main criterion of Sustainability and Ecosystem Development Activity, stating the ratio of R&D revenue to total domestic income C 33 takes first place. In the second place, C 41 , stating the ratio of the number of registered domestic patents of the intellectual property main criterion to the total number of patents, and C 42 stating the ratio of the number of registered patents of the intellectual property main criterion to the total number of patent applications. Other criteria are from small to large respectively; C 27 , C 24 , C 26 , C 25 , C 23 , C 22 , C 21 , C 31 , C 12 , C 13 , C 11 , C 31 , C 43 , C 33 . The lowest criterion is C 27 , which is the ratio of the budget of the projects supported abroad to the total budget of all projects.

Stage 3: Applying Fuzzy TOPSIS
At this stage of the study, a case study was performed on three random companies operating R&D activities in Çukurova University Technology Development Zone using fuzzy TOPSIS method. The experts evaluated these three alternative companies with regards to the evaluation criteria using linguistic terms. The linguistic terms were converted to fuzzy values using Table 1. After getting fuzzy values for the port site selection problem, the normalized fuzzy assessment table was derived. Weights obtained were used in order to find weighted normalized decision matrix, given in Table 6.   Table 7 presents the positive and negative distances to the ideal solution based on the fuzzy TOPSIS method. Based on the positive and negative distances to the ideal solution, relative distances were calculated by using the equations (16). Table 8 shows the relative distances (Equations 17) to the ideal solution for given three alternative determination of performance index of companies and the best choice. After we examined the results, we could conclude that A2 is the best determination of performance index of companies a cl + value of 0.60 and a clvalue of 0.39. A3 takes second determination of performance index of companies in the preferred order and A1 is the last choice.

Conclusion
In recent years, the performance rankings have been among the important issues for almost all areas of our daily life and different industries such as universities and accordingly, the companies operating R&D activities have been affected from this. At the same time, it is thought that the performance rankings of companies can increase the competition and the encouragement between them. For this reason, it is necessary to list the performance ranks of the companies operating R&D activities especially in the Technology Innovation Centers and to reveal the growth-contraction states within themselves. In this study, first of all, criteria for evaluating companies have been established. Then, objective and quantitively results were obtained by applying fuzzy AHP and fuzzy TOPSIS methods. As a result, the most important main criteria on for evaluating companies is found as intellectual property with 0.38.
In this study, it has been tried to increase the objectivity of the survey results by applying quantitative method. The aim is to determine the criteria using the opinions of experts, improve the survey and develop a method that can reach more accurate results by using scaling method. With this study companies will be able to see the competition with other companies about their current situation and at the same time they will be able to encourage themselves for further studies. The proposed approach can be applied to all companies operating R&D activities that cover the criteria. However, the first limitation of the study is considered to be the number and content of the criteria included. Some criteria may not apply to companies located in some countries. These criteria should be updated according to the conditions and needs of each country. In the following studies, the results can be compared by using the fuzzy MCDM having different methods.

Compliance with ethical standards
Conflicts of interest The authors declare no conflict of interest. No conflict of interest exits in the submission of this manuscript, and manuscript is approved by all authors for publication.
Founding No funding was received for conducting this study.
Ethical approval This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent N/A.