Selection of Business Process Modeling Tool with the Application of Fuzzy DEMATEL and TOPSIS Method

Business Process Modeling (BPM) is an effective activity of representing business processes for a company and is typically performed by business analysts who provide expertise in the modeling domain [1,2]. For enterprises, BPM is an essential proportion of the quality improvement of Information Systems (IS) [3]. BPM and management are becoming an essential part of today’s enterprises [4]. Meanwhile, Business Process Modeling (BPM) tools are considered a great way to connect BPM languages and modeling stakeholders. BPM tools can display the corresponding model to stakeholders, and stakeholders can also operate and control the model through BPM tools. For example, automobile manufacturing modelers can use BPM tools to build automobile manufacturing business process models.

Choosing a proper BPM tool can be seen as an essential problem for a company because poorly chosen BPM tools can have a serious and negative impact on a company’s BPM modeling process, which will directly affect the development of enterprise IS. Choosing an effective BPM tool for the company is a complicated process, and different criteria that affect BPM need to be considered [5]. Therefore, the process can be a difficult task for managers in the enterprise to carry out. Meanwhile, the selection of the BPM tool process can be seen as the Multi-Criteria Decision Making (MCDM) issue. The TOPSIS technique is a mainstream MCDM method that can approach the BPM tool selection problem. Additionally, to obtain the optimal BPM tool, the experts must analyze various information and factors in the company that affects BPM tool selection [6,7]. To select the optimal BPM tool, we have to consider different parameters, such as technical parameters (expressiveness, readability, usability, formability, etc.), economical parameters (application cost, operating cost, etc.), and so on. Meanwhile, there are direct and indirect affecting relationships between these parameters. Additionally, experts will have uncertainty when determining the influence between these parameters, which can be seen as a hybrid fuzzy problem. A fuzzy DEMATEL technique can approach hybrid fuzzy problems and the direct and indirect affecting relationships between the technical parameters.

Although BPM tool choice has a great impact on enterprise IS, there are very few related studies and references on this topic. Therefore, depending on the issues discussed above, the key target of the study is to propose a fuzzy DEMATEL and TOPSIS combination method to support companies in dealing with the BPM tool selection problem.

The main constitutions of this study are shown below:

The rest structure of the paper is shown below. The “Literature Review” section introduces business flow modeling tools and related methods for multicriteria decision-making. The section “Business Process Modeling Tool Selection Methodology” describes the proposed BPM tool selection methodology that integrates fuzzy DEMATEL and TOPSIS. Section “Results” depicts the simulation and experimental results of an example. A detailed discussion and future work will be presented in the “Discussion and Conclusion” section.

A business process is a continuous, gradual, and uncontrollable result that a series of intrinsically linked business activities or events produce [2]. It is very important for a company to effectively manage the business process. Apart from that, BPM [8] is one of the essential components of business process management, and BPM can describe the integration and relation of different enterprise activities [3]. The BPM is inseparable from a large number of BPM languages, and there are currently many BPM languages being advocated or practiced [9,10].

In the 1980s, since the first Framework Program of Research and Development (Esprit program), a large number of languages of BPM have appeared in North America and Europe [11]. These include MERISE [12], GRAI [13,14,15], NIAM [16], CIMOSA [17], IEM [18,19,20], UML [21], BPMN [22], EPC [23], Petri net [19], IDEFx [24], ARIS [25], 4EM [26], DEMO [27] and so on.

Here, all the business process modeling languages can be divided into the following three categories according to different modeling characterizations [20]:

In addition, various kinds of BPM tools can support all the BPM languages mentioned above. For example, GDToolkit [28], TimeNet [29], GreatSPN [30], JFern, JPetriNet and PIPE2 can support Petri nets [31]; ADONIS:CE, Bizagi Modeler, Cardanit, BPMN.io & family, Sparx Enterprise Architect, MagicDraw can support BPMN [32,33]; MO2GO can support IEM [20].

Here, some of the BPM tools are free of charge. For example, for the Petri net supporting tools, JFern, JPetriNet, and PIPE2 are free of charge, and GreatSPN, GDToolkit, and TimeNet are charged; for BPMN supporting tools, ADONIS: CE, Bizagi Modeler, Cardanit and BPMN.io & family are free of charge, and Sparx Enterprise Architect and MagicDraw are charged; for the IEM supporting tool, MO2GO is charged. Although some experts believe that more expensive BPMN tools have more comprehensive features and can handle more difficult business process modeling problems, they can also be more difficult to operate and control, and therefore, employee training can also be more difficult [33]. Meanwhile, some of the BPM languages and corresponding support tools are very easy to learn. For example, the IEM modeling language or MO2GO tool is very simple and straightforward to use, and beginners do not need much training when building a model [34]. Meanwhile, although some of the BPM tools are free of charge or cheap, the learning and expressive efficiency of these tools are not poor.

Therefore, it is very difficult for companies to select an optimal BPM tool, and when project managers select the BPM tools for their company, they must evaluate all candidate BPM tools depending on the different evaluation criteria, such as efficiency criteria, economic criteria, safety criteria, and so on.

Although it is very important for the company to select optimal BPM tools, which will directly affect the development of enterprise IS, there is very limited research and publications in this area. Many researchers and institutions are more focused on the analysis of BPM languages. Khouloud and Sonia proposed an approach for selecting a BPM language based on the requirements of the modeler and considered the different criteria for comparing modeling languages [3]. Vernadat reviewed and summarized important research works and contributions made to BPM over the last four decades, outlining major BPM constructs and their extensions as well as prominent modeling tools and methods [20]. Alotaibi analyzed BPM criteria, methods, and linguistics and divided them into different groups depending on their features [35]. Kožíšek and Vrana summarize the current knowledge of BPM languages, especially for UML, BPMN, and EPC, which are increasingly important in the agri-food industry, and they describe the history of BPM, currently mostly used alternatives [36]. Geiger et al., present an analysis of the current state and evolution of BPM Notation support and implementation [22].

However, these reference studies are related to the selection of BPM language or the review and introduction of different BPM languages, tools, or methods, and there is no specific method for BPM tool selection. Therefore, in this study, we will mainly focus on this issue.

The capability estimation and best choice of BPM tools are related to different levels and various criteria; therefore, the problem of BPM tool selection is the multiple criteria decision-making (MCDM) issue [37,38]. MCDM is a well-known branch of decision-making [39]. It is related to proposing and dealing with multistandard decision-making issues [40]. MCDM supports company BPM experts in quantifying special standards depending on their essentialness in different decision targets [41]. There are many different MCDM methodologies, and several mainstream MCDM methodologies are the Analytic Hierarchy Process (AHP) [42,43], Analytic Network Process (ANP) [44], Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) [45,46,47,48], classic MAUT [49], ELECTRE [50] and so on. Here, some methods are more adaptable than others in special decision issues.

The main objective of this research is to select the best BPM tool for companies where many parameters should be considered in decision-making.

These parameters are multidisciplinary (technical parameters, economical parameters, and time parameters), and we apply the TOPSIS method to obtain the final optimal BPM tool. The reasons for choosing the TOPSIS method are as follows [7]:

Meanwhile, the parameters that we considered in this paper are symmetry parameters. We have to consider not only benefit parameters (efficient parameters) but also cost parameters (economical parameters, time parameters). Therefore, we need to find a decision-making method that can handle positive and negative symmetrical parameters. TOPSIS is a well-known methodology as a symmetrical method used for solving MCMD problems [51,52]. To obtain the best options from all competitors, the TOPSIS methodology uses the key formula of the calculation result of the maximum distance from the Negative-Ideal (N-I) solution and the minimum distance from the Positive-Ideal (P-I) solution [51,52,53,54]. Therefore, it can be seen as a symmetric issue approaching the process in mathematical equations.

Apart from that, in the BPM tool selection process for a company, there will also be direct and indirect interdependence between all the criteria, such as the low readability of the BPM tool, which will directly affect and increase the difficulty of tool learning. Therefore, when we define the weight for the BPM tool selection criteria, we must consider direct and indirect interdependence. DEMATEL is an effective methodology to analyze the direct and indirect influence between criteria. There is an algorithm behind the DEMATEL analysis, which is always used to analyze and create the connections of causation between the assessment standards [55,56] or to derive interrelationships among factors [57]. Therefore, we can use DEMATEL analysis to fix the direct and indirect influence problem between criteria.

Additionally, in the DEMATEL analysis, when experts define the affecting rank between BPM tool selection criteria, there is uncertainty here because, in many cases, experts cannot clearly determine the impact of a specific scale value. This uncertain decision issue is the hybrid fuzzy decision-making issue. Many studies have dealt with hybrid fuzzy problems in decision-making. Mardani et al. [58] proposed a hybrid fuzzy AHP decision-making methodology to evaluate healthcare and medical problems. Akram et al. [59] proposed a fuzzy ELECTRE-II method for multicriteria decision-making problems. Celik et al. [60] used interval type-2 fuzzy AHP methods to approach decision-making problems in maritime transportation engineering. A Fuzzy ARAS method is also proposed for recycling facility location problems [61].

Although there are many methods of fuzzy application, there is no application for BPM tool selection. The above fuzzy methods do not consider the direct and indirect relationships between coefficients such as AHP and ELECTRE.

Hence, in this paper, the key objective of this study is to combine the hybrid fuzzy DEMATEL and TOPSIS methods to propose a BPM tool selection method considering the BPM process affecting parameters. This method can help company managers find the optimal BPM tools for their company.

The BPM tool choice process for this research is shown in Figure 1.

First, it is necessary to define the benefit and cost standards that will be applied for the assessment of BPM tool alternatives. Here, we will also determine the corresponding rank value for all the criteria. Afterward, we can use the Fuzzy DEMATEL technique to define the weight for the standards. Then, it is possible to decide the candidate options assessment result according to the TOPSIS method. Finally, we can define the final BPM tool for the company.

As stated earlier, choosing an effective BPM tool for the company is a complicated process, and different criteria that affect BPM need to be considered. Therefore, choosing an optimal BPM tool will be very difficult for enterprise managers to carry out. Therefore, selecting an optimal BPM tool is very important for the development of the company’s IS.

In this example, we consider 8 candidate BPM tools (JFern, JPetriNet, GreatSPN, GDToolkit, TimeNet, ADONIS: CE, Bizagi Modeler and Cardanit). Based on Table 1 and Table 2, we can create the rank table (Table 4) for all the sub-parameters to influence BPM tool selection. Here, the project manager can determine the ranking of all sub-parameters through expert surveys.

From Table 4, we can find that there are 8 candidate BPM tools with the different corresponding sub-criteria ranks. After we define all the rank values, we have to define the fuzzy weights of all the four main types of parameters (C₁, C₂, C₃ and C₄) and corresponding sub-parameters (C₁₁, C₁₂, C₁₃, C₁₄, C₁₅, C₂₁, C₂₂, C₂₃, C₃₁, C₃₂, C₃₃, C₄₁ and C₄₂) in Table 1.

Therefore, to obtain fuzzy weights for all the criteria, 10 company experts are requested to define the rank of direct fuzzy impact between criteria according to pairwise comparison depending on the direct fuzzy influence level in Table 3. The direct fuzzy influence degrees for 10 company experts can be seen in Table A1, Table A2, Table A3, Table A4 and Table A5 (Appendix A). Depending on Equation (1), we can release the TFN for the degrees, as shown in Table A6, Table A7, Table A8, Table A9 and Table A10 (Appendix A). Then, we use Equations (2)–(8) to release the defuzzy crisp values as Table A11, Table A12, Table A13, Table A14 and Table A15 (Appendix A) for the triangle fuzzy triples.

Then, we can use the crisp values to create the average direct fuzzy influence matrix T (Equation (10)) for the BPM tool selection main criteria and corresponding sub-criterions like Table 5, Table 6, Table 7, Table 8 and Table 9.

In Table 5, Table 6, Table 7, Table 8 and Table 9, all the values are obtained from the average of the direct fuzzy influences, and all these direct influence values are defined by the 10 experts. For example, in Table 5, average direct fuzzy influence rank from C₁ to C₃ is 0.545 which is obtained from the average fuzzy influence value of 10 experts ($\frac{0.73+0.5+0.27+0.27+0.25+0.73+0.5+0.5+0.73+0.97}{10}$ = 0.545) (Equation (10)). After that, depending on the Equations (11) and (12), we can calculate the normalized direct influence matrix T (Table 10, Table 11, Table 12, Table 13 and Table 14) for all the criterion and sub-criterions.

In Table 10, for instance, the normalized direct influence value for C₁ to C₃ is 0.262, which is obtained from the multiplication between the direct influence rank from C₁ to C₃ (0.545 in Table 5) and the $\lambda$ value ($\frac{1}{\max 1\le \mathrm{n}\le 4 {{\displaystyle \sum }}_{\mathrm{j}=1}^4{\mathrm{t}}_{\mathrm{nj}}}= \frac{1}{\max \left({{\displaystyle \sum }}_{\mathrm{j}=1}^4{\mathrm{t}}_{1\mathrm{j}}, {{\displaystyle \sum }}_{\mathrm{j}=1}^4{\mathrm{t}}_{2\mathrm{j}}, {{\displaystyle \sum }}_{\mathrm{j}=1}^4{\mathrm{t}}_{3\mathrm{j}}, {{\displaystyle \sum }}_{\mathrm{j}=1}^4{\mathrm{t}}_{4\mathrm{j}}\right)}=\frac{1}{\max \left(1.819,1.656,1.679,2.081\right)}=0.481$) for the average direct influence matrix (Table 5). After that, depending on the Equations (13)–(16), we can obtain the total direct and indirect influence matrix E (Table 15, Table 16, Table 17, Table 18 and Table 19) and the corresponding sum of rows (or in Equation (15)) and columns (co in Equation (16)) of the E.

From the Table 15, Table 16, Table 17, Table 18 and Table 19, we can find the direct and indirect relationships between criteria or sub-criteria. The ro_n (highlighted in yellow) means the total given both direct and indirect effects from criteria n to the other criteria (for example, in Table 15, ro₁ = 1.484 + 1.852 + 1.614 + 1.696 = 6.646), and co_j (highlighted in pink) means the total received both direct and indirect effects from other criteria to criterion j (for example, in Table 15, co1 = 1.484 + 1.592 + 1.585 + 1.874 = 6.535). After, we obtain the overall direct and indirect impact matrix E with corresponding ro_n and co_j values, when n equals j, we can release the (ro_j + co_j) (highlighted in lime green) value, which means the centrality of criterion j, for all the criteria (Table 15, Table 16, Table 17, Table 18 and Table 19).

After that, we can calculate the normalized (ro + co) value for all the criterions and sub-criterions like Table 20.

In Table 20, for example, the NRC value for Efficiency parameters (C₁) is 0.251, which is obtained by dividing ro₁ + co₁ (Efficiency parameters (C₁) in Table 15 by the sum of column ro_n + co_j in Table 15 ($\frac{13.181}{6.646+6.172+6.153+7.317}=0.251$). After that, the final weight of sub-parameter is the multiplication of the weights of the four main and corresponding sub-criteria.

After we define the weight for all the criteria and sub-criteria, we can use these weights (Table 20) and Equations (19) and (20), and Table 4 to obtain the weighted normalized values such as Table 21.

In Table 21, the abbreviation max denotes the benefit standard, and abbreviation min denotes the cost standard. The final weighted normalized value for alternative 1 (T1) corresponding to sub-criteria C₁₁ is 0.009. The number is obtained by multiplying the final weight of sub-criteria C₁₁ (0.251 × 0.194 = 0.049) and the normalized decision matrix value for C₁₁ ($0.190=\frac{2}{\sqrt{{{\displaystyle \sum }}_{\mathrm{i}=1}^{24}{\mathrm{y}}_{\mathrm{i}1}{}^2}}$).

After that, depending on Table 21, Equations (21) and (22), the P-I and N-I solutions are determined. The P-I solution and N-I solution can be seen as Table 22.

Depending on the data from Table 21 and Table 22, Equations (23) and (24), the relative distances of each candidate option from the P-I and N-I solutions can be released. Finally, the relative distance of each candidate option to the P-I solution is released depending on Equation (25). The relative distances of each alternative from the P-I and N-I solutions and the result of the relative distance of each alternative from the P-I solution can be seen as Table 23.

Table 23 shows the evaluation result of the considered alternatives obtained by using TOPSIS technology. In Table 23, the C_i* value is obtained by the relative closeness to the ideal solution (Equation (25)). For example, the value for the C_i* value for T1 is 0.405 (${\mathrm{H}}_{\mathrm{i}}{}^{*}=\frac{{\mathrm{d}}_{\mathrm{i}}{}^0}{\left({\mathrm{d}}_{\mathrm{i}}{}^0+{\mathrm{d}}_{\mathrm{i}}{}^{*}\right)}=\frac{0.06}{\left(0.06+0.088\right)}=0.405$). Meanwhile, in Table 23, di* is the n-dimensional Euclidean distance from each solution in Table 21 to the P-I solution (T⁺ Table 22), and d_i⁰ is the n-dimensional Euclidean distance from each solution in Table 21 to the N-I solution (T⁻ Table 22). For example, the d_i^* value for T1 is 0.88 ($\sqrt{{\displaystyle \sum }_{\mathrm{j}=1}^{13}{\left({\mathrm{x}}_{\mathrm{ij}}-{\mathrm{x}}_{\mathrm{j}}{}^{*}\right)}^2}=$ $\sqrt{\begin{array}{c}{\left(0.009-0.023\right)}^2+{\left(0.015-0.025\right)}^2+{\left(0.011-0.027\right)}^2+{\left(0.019-0.025\right)}^2+{\left(0.025-0.025\right)}^2+{\left(0.012-0.012\right)}^2+\\ {\left(0.022-0.011\right)}^2+{\left(0.021-0.011\right)}^2+{\left(0.003-0.001\right)}^2+{\left(0.027-0.009\right)}^2+{\left(0.029-0.001\right)}^2+{\left(0.014-0.071\right)}^2+\\ +{\left(0.013-0.063\right)}^2\end{array}}$= 0.88). Meanwhile, the d_i⁰ value for T1 is 0.06 ($\sqrt{{\displaystyle \sum }_{\mathrm{j}=1}^{13}{\left({\mathrm{x}}_{\mathrm{ij}}-{\mathrm{x}}_{\mathrm{j}}{}^0\right)}^2}=$ $\sqrt{\begin{array}{c}{\left(0.009-0.009\right)}^2+{\left(0.015-0.01\right)}^2+{\left(0.011-0.05\right)}^2+{\left(0.019-0.012\right)}^2+{\left(0.025-0.001\right)}^2+{\left(0.012-0.047\right)}^2+\\ {\left(0.022-0.045\right)}^2+{\left(0.021-0.042\right)}^2+{\left(0.003-0.05\right)}^2+{\left(0.027-0.046\right)}^2+{\left(0.029-0.048\right)}^2+{\left(0.014-0.014\right)}^2+\\ +{\left(0.013-0.013\right)}^2\end{array}}$ = 0.06). From the C_i* value in Table 23, it is possible to find that the alternative T4 obtains the highest value (0.642) (highlighted in green). Here, when considering the four types of criteria (BPM efficiency (C₁), various expenses incurred when using the BPM tool (C₂), application, installment, operating and training time (C₃), and security issues affected by BPM tools (C₄)), alternative T4 is the best overall performing BPM tool. Therefore, managers can select BPM tool T4 for the company.

The business process modeling tool selection problem has a significant influence on the total performance of enterprise business process modeling, which will directly affect the development of the enterprise information system. Some candidate options have to be considered and assessed depending on the affecting parameters (efficiency parameters (C₁), economical parameters (C₂), time parameters (C₃) and safety parameters (C₄)) and corresponding sub-parameters (expressiveness (C₁₁), readability (C₁₂) usability (C₁₃), formality (C₁₄), ease of learning (C₁₅), application and installation cost (C₂₁), operating cost (C₂₂), training cost (C₂₃), application and installation time (C₃₁), operating time (C₃₂), training time (C₃₃), internal safety (C₄₁), and external safety (C₄₂)) in a BPM tool choosing issue, causing various ambiguous information. Thus, an optimal assessment method is needed to make effective decisions. Therefore, the BPM tool selection methodology is proposed in this study with the consideration of different BPM tool selection influencing factors.

Apart from that, the process to select the BPM tool from all alternatives is a fuzzy multi-criteria decision-making (MCDM) issue. Thus, we use TOPSIS to obtain the priority of BPM tool alternatives. Here, TOPSIS is applied to determine the priorities of the BPM candidate tools. The proposed method has dramatically improved the usefulness and accuracy of decision-making in the BPM tool choice process. In addition, in the method, we find that the weights of the criteria and sub-criteria in the TOPSIS technique are determined by company expert options through the fuzzy DEMATEL method. After that, the final weight for sub-criteria is the multiplication of the defined two weights, and it is important and may change the ranking of the alternatives. This method can provide a reference for companies purchasing or applying BPM tools when selecting BPM tools so that the BPM tool can be used more efficiently, economically, quickly, and safely. Rather than providing assistance to the business process modeling tool manufacturer (Bonita [65], Camunda [66], etc. Of course, it is also possible for business process modeling tool manufacturers to use this method to evaluate the goodness of their own tools. However, the evaluation should involve the experts from the company interested in purchasing the tool.

Some scholars, such as Zhang and Su, 2019 [67], also proposed the fuzzy DEMATEL and TOPSIS combination method. However, the fuzzy part of this approach is based on a 2-tuple linguistic method and approaches the relationships between the attributes of the proof participants and determines their weights. The 2-tuple linguistic model is used to aggregate linguistic evaluation information and requires the interpretation of linguistic labels. Even though the model can increase the accuracy in the process of aggregation, it is mainly concerned with semantic ambiguity. However, the fuzzy part studied in this paper is the uncertainty of the decision data (not semantically ambiguous). The Triangular Fuzzy Number not only can be used not only to express the vagueness and uncertainty of decision data but also to represent fuzzy terms in decision data processing. Therefore, the application of triangular fuzzy numbers is more adaptable in our study.

Although the proposed method is developed for the BPM tool selection problem, it is also adaptable for other software tool selections with slight modifications. Such as ERP or office tool selection problems in manufacturing or trading companies. The main part that needs to be modified here is the criteria part. Companies can change the main criteria and sub-criteria (Table 1) according to the characteristics of the software tool they need to choose. For example, the ERP tool selection problem is more about data evaluation and control rather than graphical presentation, so the expressiveness (C₁₁) and formality (C₁₄) criteria can be removed and replaced by the data control or evaluation criteria. Meanwhile, although some criteria do not need to be changed, the contents inside the criteria need to be redefined.

Even though the method is proposed and applied for the BPM tool selection problem, and we can obtain the final BPM tool (T4 in Table 23), there are many study areas for expansion. Studies could help extend the approach by first determining the sub-criteria more rationally and precisely. Second, we find and establish a method of criteria and sub-criteria weight definition in a reasonable way. Meanwhile, as Zhang and Su, 2019 [67] consider the 2-tuple linguistic model in the fuzzy DEMATEL method, it is also very important for our research to consider semantic ambiguity. Therefore, further studies will focus on these study areas.

This study first describes the significance of BPM tool selection for information systems (IS) in companies. After that, the key target is expressed to approach the issue in BPM tool selection. Then, the method is proposed with the application of DEMATEL and the TOPSIS method to approach BPM tool selection with the consideration of different BPM tool evaluation criteria. Finally, depending on the method proposed in this paper, the company can choose the optimal and most suitable BPM tool. This method allows the BPM process in the company to be more economical, efficient, time-saving, and safe.