An extension of fuzzy SWOT analysis: An application to information technology

When considering today’s uncertain atmosphere, many people and organizations believe that strategy has lost its meaning and position. When future is predictable, common approaches for strategic planning are applicable; nonetheless, vague circumstances require different methods. Accordingly, a new approach that is compatible with uncertainty and unstable conditions is necessary. Fuzzy logic is a worldview compatible with today complicated requirements. Regarding today’s uncertain and vague atmosphere, there is an absolute requirement to fuzzify the tools and strategic planning models, especially for dynamic and unclear environment. In this research, an extended version of Strengths, Weaknesses, Opportunities and Threats (SWOT) fuzzy approach has been presented for strategic planning based on fuzzy logic. It has solved the traditional strategic planning key problems like internal and external factors in imprecision and ambiguous environment. The model has been performed in an information technology corporation to demonstrate the capabilities in real world cases.


Introduction
Classic Strengths, Weaknesses, Opportunities and Threats (SWOT) analysis has been developed based on stable environment that means if the environment of an organization were steady, invariable, and predictable, the classic SWOT analysis could be performed for the organization.In today's world, environment of organizations is stormy, fast changing, unpredictable, and with uncertainties.For instance, external (or internal) factors of an organization are not always opportunity (strength) or threat (weakness); in other words, in different conditions, they have different meanings.For encountering with today's complicated and ambiguous environment, fuzzy SWOT analysis is useful and can solve some problems of classic SWOT analysis [1].The highlights of this paper are using tri-angular membership function, using three α-cut planes for defuzzifying, and a combinational method consisting of TOPSIS and the weighted average for prioritization.
SWOT (an acronym standing for Strengths, Weaknesses, Opportunities and Threats) analysis is a commonly used tool for analyzing internal and external environments in order to attain a systematic approach and support for decision making [2][3][4][5][6][7][8][9][10].The SWOT approach is based on the aggregation of the internal (strengths, weak-nesses) and external (opportunities, threats) factors for adopting strategies.In other words, the extracted strategies of SWOT matrix is comprised of four categories of factors combinations:
Helms and Nixon in 2010 presented a research in which academic researches of the last decade in the field of strategic management, and especially the SWOT method, were analyzed [12].Moreover, similar researchers analysed and reviewed the performance of SWOT analysis and illustrated its applications, performance and future possible contributions [13].The previous approaches have not considered quantitative methods to evaluate and sort the strategies under uncertain situations; however, the illustrated literature review that is presented in Section 2 overviews some possible methods for this matter.One possible approach that deals with uncertainty is fuzzy logic.
A fuzzy set is a class of objects with grades of membership.A membership function is between zero and one [14].Fuzzy logic is derived from fuzzy set theory to deal with reasoning that is approximate rather than precise.It allows for the model to easily incorporate various subject experts' opinion in developing critical parameter estimates [15].In other words, fuzzy logic enables us to handle uncertainty [16,17].There are some kinds of fuzzy numbers.Among the various shapes of fuzzy number, triangular fuzzy number (TFN) is the most popular one.It is represented with three points as follows: A = (a1, a2, a3).The membership function is illustrated in Figure 1.Let A and B are defined as A = (a1, a2, a3), B = (b1, b2, b3).Then C = (a1 + b1, a2 + b2, a3 + b3) is the addition of these two numbers.Besides, D = (a1 − b1, a2 − b2, a3 − b3) is the subtraction of them.Moreover, E = (a1 × b1, a2 × b2, a3 × b3) is the multiplication of them [15,18,19].strategies.In other words, the extracted strategies of SWOT matrix is comprised of four categories of factors combinations: • Strengths and Opportunities (S-O); • Strengths and Threats (S-T);
Helms and Nixon in 2010 presented a research in which academic researches of the last decade in the field of strategic management, and especially the SWOT method, were analyzed [12].Moreover, similar researchers analysed and reviewed the performance of SWOT analysis and illustrated its applications, performance and future possible contributions [13].The previous approaches have not considered quantitative methods to evaluate and sort the strategies under uncertain situations; however, the illustrated literature review that is presented in Section 2 overviews some possible methods for this matter.One possible approach that deals with uncertainty is fuzzy logic.
A fuzzy set is a class of objects with grades of membership.A membership function is between zero and one [14].Fuzzy logic is derived from fuzzy set theory to deal with reasoning that is approximate rather than precise.It allows for the model to easily incorporate various subject experts' opinion in developing critical parameter estimates [15].In other words, fuzzy logic enables us to handle uncertainty [16,17].There are some kinds of fuzzy numbers.Among the various shapes of fuzzy number, triangular fuzzy number (TFN) is the most popular one.It is represented with three points as follows: A = (a1, a2, a3).The membership function is illustrated in Figure 1.Let A and B are defined as A = (a1, a2, a3), B = (b1, b2, b3).Then C = (a1 + b1, a2 + b2, a3 + b3) is the addition of these two numbers.Besides, D = (a1 − b1, a2 − b2, a3 − b3) is the subtraction of them.Moreover, E = (a1 × b1, a2 × b2, a3 × b3) is the multiplication of them [15,18,19].The remainder of this research is organized as follows.Initially, the existing research on fuzzy SWOT are presented in Section 2, afterward, Section 3 represents algorithm of proposed fuzzy SWOT.Finally the proposed model is applied to a case analysis for checking the applicability of the model.

Literature Review
Ghazinoory et al. presented a method based on fuzzy logic to solve SWOT structural problems, like lack of considering uncertain and two sided factors and the lack of prioritization [11].In this paper, the triangular membership function has been defined for all factors; the minimum of internal and external factors was calculated for aggregating.In defuzzifying, α-cut plane technique was used and prioritization has been done based on the amount of each fuzzy area in SWOT matrix quadrants.The remainder of this research is organized as follows.Initially, the existing research on fuzzy SWOT are presented in Section 2, afterward, Section 3 represents algorithm of proposed fuzzy SWOT.Finally the proposed model is applied to a case analysis for checking the applicability of the model.

Literature Review
Ghazinoory et al. presented a method based on fuzzy logic to solve SWOT structural problems, like lack of considering uncertain and two sided factors and the lack of prioritization [11].In this paper, the triangular membership function has been defined for all factors; the minimum of internal and external factors was calculated for aggregating.In defuzzifying, α-cut plane technique was used and prioritization has been done based on the amount of each fuzzy area in SWOT matrix quadrants.Kheyrkhah mentioned structural problems of classic SWOT like not to prioritize internal and external factors and disability to consider vagueness in some of internal and external factors, and they stated that fuzzy SWOT analysis could solve these problems [20].Moreover, they compared the extracted strategies from fuzzy SWOT analysis with strategies extracted from classic SWOT analysis in order to show supremacy of fuzzy SWOT analysis.Hosseini Nasab described one of classic SWOT defects and proposed a fuzzy SWOT approach to solve this problem [21,22].
In this paper, three points as a triangular area in EFE-IFE coordinate specified and according to the strategic triangular position (relative position of three points) a realistic strategy has been extracted.Ecmekcioglu proposed multi-criteria fuzzy SWOT to solve classic SWOT problems like not to prioritize strategies and vagueness of factors.The proposed model has three parts.First, using fuzzy AHP to specify the weight of internal and external vector, second, using fuzzy TOPSIS for prioritization, and third, specifying the best strategy proposal by evaluating the internal and external factors [23].Chernov indicated that there are different uncertainties and vagueness in real competitive market and real economic conditions causing classic SWOT to be ineffective [24].
Amin presented a novel method using fuzzy logic, triangular fuzzy numbers and SWOT analysis to deal with vagueness of human thought.Their quantified SWOT was applied in the context of supplier selection.Moreover, they proposed a fuzzy linear programming model to specify how much should be purchased from each supplier [18].Ghazinoory illustrated a literature review of SWOT analysis of about 577 papers that have been published up to the end of 2009.Historical development of SWOT, methodological development of SWOT, suggestions and challenges are explained.Furthermore, they stated some problems of SWOT analysis and suggested a proposed model to solve the problems [25].
Kazaz as a first part analysed 50 large construction firms in Turkey by SWOT analysis.They identified each firm primary goal.The results of the first part were used to develop a fuzzy model for determining the main objectives of the firms.Finally extracted strategies related to the firm's main goal were introduced [26].Dimic used a SWOT analysis and fuzzy Delphi method as the basis to evaluate impact factors.Fuzzy SWOT analysis is applied to formulate strategic options and the selection of the optimal option is realized through DEMATEL (Decision-making and Trial and Evaluation Laboratory)-based ANP (Analytic Network Process) [27].Beheshti presented a hybrid COPRAS G with MODM model to optimize the strategy portfolio optimization based on strategies emanated from SWOT Matrix under uncertain circumstances.They applied their proposed model in Iranian mercantile exchange to validate their model [28].
In this paper, a solution that has used fuzzy logic and fuzzy sets theory in SWOT analysis is pro-posed and a mathematical method for different phase of the solution is presented.The strategy selection process, especially the closeness coefficient for the fuzzy area has been extended by adding a step based on TOPSIS method.

Algorithm
Algorithm of the proposed fuzzy SWOT analysis consists of six stages as follows: The first two stages are based on paper of Ghazinoory et al. [11].The general scheme of the algorithm is shown in Figure 2. The last two stages encompassing extracting strategies and final prioritization are the extension and changes added by the authors to the FSWOT based approach.

Membership Function
Membership function is triangular and specified by tree parameters, as follows: where a, b, and c are pessimistic, probable, and optimistic values, respectively.This membership function is defined for each external and internal factor in the range −10 to 10.An example of the triangular membership function is shown in Figure 3 [29,30].

Membership Function
Membership function is triangular and specified by tree parameters, as follows: where a, b, and c are pessimistic, probable, and optimistic values, respectively.This membership function is defined for each external and internal factor in the range −10 to 10.An example of the triangular membership function is shown in Figure 3 [29,30].

Aggregation
Membership functions aggregation is based on following equation: µ I (x) and µ E (y) are membership functions of internal and external factors respectively and µ s (x, y) is the result of aggregation that forms a three-dimensional (3D) surface.Figure 4 shows how this surface is made.
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Aggregation
Membership functions aggregation is based on following equation: I () and  E () are membership functions of internal and external factors respectively and  s (, ) is the result of aggregation that forms a three-dimensional (3D) surface.Figure 4 shows how this surface is made.

Defuzzification
In this stage, three α-cut surfaces parallel to SWOT matrix plane are defined for cutting the aggregated surface resulted in previous stage.The value of each of the three surfaces is between 0 and 1 and depends on experience of strategist.If the company is in turbulent and unpredictable market, α value can be close to 0 and if the market is stable and predictable, the values can be close to 1.A rectangular area is generated by crossing the aggregated surface and α-cut plane.In this paper, Picture of the rectangular area in SWOT matrix plane is named "fuzzy area".Figure 5 shows defuzzification with one α plane.

Defuzzification
In this stage, three α-cut surfaces parallel to SWOT matrix plane are defined for cutting the aggregated surface resulted in previous stage.The value of each of the three surfaces is between 0 and 1 and depends on experience of strategist.If the company is in turbulent and unpredictable market, α value can be close to 0 and if the market is stable and predictable, the values can be close to 1.A rectangular area is generated by crossing the aggregated surface and α-cut plane.In this paper, Picture of the rectangular area in SWOT matrix plane is named "fuzzy area".Figure 5 shows defuzzification with one α plane.

Prioritization
There is   ×   for each α value where   and   are the numbers of internal and external factors, respectively.Prioritization is done for every three α value, as Figure 6.

•
According to Figure 4, the center of gravity for every fuzzy area is calculated as [31]:

Prioritization
There is n i × n e for each α value where n i and n e are the numbers of internal and external factors, respectively.Prioritization is done for every three α value, as Figure 6.

Prioritization
There is   ×   for each α value where   and   are the numbers of internal and external factors, respectively.Prioritization is done for every three α value, as Figure 6.

•
According to Figure 4, the center of gravity for every fuzzy area is calculated as [31]: • According to Figure 4, the center of gravity for every fuzzy area is calculated as [31]:

•
In the second step, according to Figure 3, the closeness coefficient for the fuzzy area is calculated as [14,32]: where d + j is the distance between center of gravity and positive ideal point (+10, +10) and d − j is the distance between center of gravity and negative ideal point (−10, −10).d + j and d − j are calculated, as follows [33]: Prioritization is done based on cc j value, each fuzzy area with greater cc j has higher priority.Location of fuzzy areas in SWOT matrix plane has three states as follows: State 1: one quadrant fuzzy area as shown in Figure 7.
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•
In the second step, according to Figure 3, the closeness coefficient for the fuzzy area is calculated as [14,32]: where   + is the distance between center of gravity and positive ideal point (+10, +10) and   − is the distance between center of gravity and negative ideal point (−10, −10).  + and   − are calculated, as follows [33]: Prioritization is done based on   value, each fuzzy area with greater   has higher priority.Location of fuzzy areas in SWOT matrix plane has three states as follows: State 1: one quadrant fuzzy area as shown in Figure 7. State 2: two quadrant fuzzy area, as shown in Figure 8.

Extracting Strategies
Every fuzzy area is the aggregation result of two internal and external factors and can result in strategy if the two factors are related together.Being related or not depends on the strategist's experience.Extracted strategy should be based on SWOT matrix quadrant.If the fuzzy area is two/four quadrant, the extracted strategy should be based on quadrant including greater part of the

•
In the second step, according to Figure 3, the closeness coefficient for the fuzzy area is calculated as [14,32]: where   + is the distance between center of gravity and positive ideal point (+10, +10) and   − is the distance between center of gravity and negative ideal point (−10, −10).  + and   − are calculated, as follows [33]: Prioritization is done based on   value, each fuzzy area with greater   has higher priority.Location of fuzzy areas in SWOT matrix plane has three states as follows: State 1: one quadrant fuzzy area as shown in Figure 7. State 2: two quadrant fuzzy area, as shown in Figure 8.

Extracting Strategies
Every fuzzy area is the aggregation result of two internal and external factors and can result in strategy if the two factors are related together.Being related or not depends on the strategist's experience.Extracted strategy should be based on SWOT matrix quadrant.If the fuzzy area is two/four quadrant, the extracted strategy should be based on quadrant including greater part of the

•
In the second step, according to Figure 3, the closeness coefficient for the fuzzy area is calculated as [14,32]: where   + is the distance between center of gravity and positive ideal point (+10, +10) and   − is the distance between center of gravity and negative ideal point (−10, −10).  + and   − are calculated, as follows [33]: Prioritization is done based on   value, each fuzzy area with greater   has higher priority.Location of fuzzy areas in SWOT matrix plane has three states as follows: State 1: one quadrant fuzzy area as shown in Figure 7. State 2: two quadrant fuzzy area, as shown in Figure 8.

Extracting Strategies
Every fuzzy area is the aggregation result of two internal and external factors and can result in strategy if the two factors are related together.Being related or not depends on the strategist's experience.Extracted strategy should be based on SWOT matrix quadrant.If the fuzzy area is two/four quadrant, the extracted strategy should be based on quadrant including greater part of the

Extracting Strategies
Every fuzzy area is the aggregation result of two internal and external factors and can result in strategy if the two factors are related together.Being related or not depends on the strategist's experience.Extracted strategy should be based on SWOT matrix quadrant.If the fuzzy area is two/four quadrant, the extracted strategy should be based on quadrant including greater part of the fuzzy area, if extracting strategy is not possible, strategy should be based on the smaller part of fuzzy area.If all parts of the fuzzy area are equal, then strategies are extracted from related quadrant.

Final Prioritization
The aforementioned stages are performed and analyzed for three α value.Consequently, the score of strategies with three α values is resulted.The priority of any strategy varies according to α value.In this stage, the weighted average for all strategies is calculated as: where α i is specified by strategist and p is priority of each strategy depending on α values.Final prioritization is based on r a value.Strategy with smaller r a value has higher priority.

Case Study
To examine the applicability of the described algorithm, the proposed method was conducted for an IT company.As described before the stages of the proposed model are illustrated in Figure 10.
fuzzy area, if extracting strategy is not possible, strategy should be based on the smaller part of fuzzy area.If all parts of the fuzzy area are equal, then strategies are extracted from related quadrant.

Final Prioritization
The aforementioned stages are performed and analyzed for three α value.Consequently, the score of strategies with three α values is resulted.The priority of any strategy varies according to α value.In this stage, the weighted average for all strategies is calculated as: where   is specified by strategist and  is priority of each strategy depending on  values.Final prioritization is based on   value.Strategy with smaller   value has higher priority.

Case Study
To examine the applicability of the described algorithm, the proposed method was conducted for an IT company.As described before the stages of the proposed model are illustrated in Figure 10.  1 and 2. The values are indicating fuzzy triangular numbers (FTN) for analyzing strength, weakness, opportunity, and threats of the considered organization.These amounts were first gathered by linguistic terms from the expert's opinion and subsequently transferred to FTN quantitative values.   1 and 2. The values are indicating fuzzy triangular numbers (FTN) for analyzing strength, weakness, opportunity, and threats of the considered organization.These amounts were first gathered by linguistic terms from the expert's opinion and subsequently transferred to FTN quantitative values.Based upon the factors mentioned above, the SWOT matrix is denoted as Table 3.

ID
According to the proposed method, membership functions for all of the internal and external factors were generated.In the next stage, aggregation was performed.Aggregation result of I 11 and E 1 factors is shown in Figure 11.As described before, in this stage, three α-cut planes cut the resulted surface achieved from aggregation, as shown in Figure 12.In this paper, α values are: 0.1, 0.5, and 0.9.0.1 is represented for almost indefinite condition, 0.5 is represented for semi-definite condition, and 0.9 is for the almost definite one.This process was done for all (14 × 9) pyramids.126 (14 × 9) pyramids were generated from aggregation that means there are 126 fuzzy areas for each α value.Figure 13 shows the fuzzy areas that resulted from three α-cut planes.As α increases from 0.1 to 0.9, the fuzzy areas decrease.For α = 0.1, the fuzzy area is four quadrant that has more flexibility in extracting strategies.For α = 0.9, fuzzy area is one quadrant and does not have flexibility for strategy.As described before, in this stage, three α-cut planes cut the resulted surface achieved from aggregation, as shown in Figure 12.In this paper, α values are: 0.1, 0.5, and 0.9.0.1 is represented for almost indefinite condition, 0.5 is represented for semi-definite condition, and 0.9 is for the almost definite one.This process was done for all (14 × 9) pyramids.As described before, in this stage, three α-cut planes cut the resulted surface achieved from aggregation, as shown in Figure 12.In this paper, α values are: 0.1, 0.5, and 0.9.0.1 is represented for almost indefinite condition, 0.5 is represented for semi-definite condition, and 0.9 is for the almost definite one.This process was done for all (14 × 9) pyramids.126 (14 × 9) pyramids were generated from aggregation that means there are 126 fuzzy areas for each α value.Figure 13 shows the fuzzy areas that resulted from three α-cut planes.As α increases from 0.1 to 0.9, the fuzzy areas decrease.For α = 0.1, the fuzzy area is four quadrant that has more flexibility in extracting strategies.For α = 0.9, fuzzy area is one quadrant and does not have flexibility for strategy.126 (14 × 9) pyramids were generated from aggregation that means there are 126 fuzzy areas for each α value.Figure 13 shows the fuzzy areas that resulted from three α-cut planes.As α increases from 0.1 to 0.9, the fuzzy areas decrease.For α = 0.1, the fuzzy area is four quadrant that has more flexibility in extracting strategies.For α = 0.9, fuzzy area is one quadrant and does not have flexibility for strategy.Prioritization was fulfilled for each bunch of fuzzy areas.As described before, prioritization is based on closeness of coefficient value.Table 3 shows the result of  = 0.1 prioritization.Percent of each fuzzy area in SWOT matrix quadrants was calculated as shown in Table 4 that is useful for extracting strategies.Not all of these 126 fuzzy areas result in strategy.The factors should be related and it depends on strategist.After considering and studying these 126 fuzzy areas, 16 strategies were extracted.Table 5 shows the extracted strategies, their priority, α value, and their quadrants.It should be noted that priority of each strategy varies as α value changes.Prioritization was fulfilled for each bunch of fuzzy areas.As described before, prioritization is based on closeness of coefficient value.Table 3 shows the result of α = 0.1 prioritization.Percent of each fuzzy area in SWOT matrix quadrants was calculated as shown in Table 4 is useful for extracting strategies.Not all of these 126 fuzzy areas result in strategy.The factors should be related and it depends on strategist.After considering and studying these 126 fuzzy areas, 16 strategies were extracted.Table 5 shows the extracted strategies, their priority, α value, and their quadrants.It should be noted that priority of each strategy varies as α value changes.For final prioritization, the weighted average for each strategy was calculated.According to the Equation ( 8), r a values were calculated.The strategy with smaller r a has higher priority.Table 6 shows the final priorities.

Conclusions
Regarding to problems of classic SWOT for analyzing today's environment, a different method of SWOT analysis that was based on fuzzy logic for enriching SWOT analysis for analyzing today's environment was proposed.This method has specifications, like considering two sided factors, more flexibility in extracting strategies, and optimized prioritization.In the contrary to classic SWOT, this method is useful for analyzing unstable and turbulent environment.It is more applicable and reliable than classic SWOT.The highlights of this paper are using triangular membership function, using three α-cut planes for defuzzifying, and a combinational method consisting of TOPSIS and the weighted average for prioritization.The fuzzy logic type one has been implemented in this paper.
When considering the vagueness of environment, velocity of changes in IT industry in Iran, while considering the time frame and the low accuracy of forecasting SWOT factors in future, the SWOT analysis was considered and analyzed under uncertain circumstances by applying fuzzy logic in this research.
The proposed approach for evaluating and selecting the appropriate strategies are completely useful considering vague circumstances.As a case in point in this research, the scheduled approach was performed in an information technology enterprise to solve the complexity and undesirable approaches that were previously employed within their organizations.For increasing applicability and reliability, other fuzzy types are proposed for future researches encompassing hesitant fuzzy linguistic term set, interval valued intuitionistic fuzzy, intuitionistic fuzzy preferences relations, etc.Furthermore, on the basis of strategies ranking, budget limitations, and other structural or organizational policies, a novel stochastic or fuzzy strategy portfolio optimization model could be designed and presented for future researches.

3. 1 .
Membership FunctionMembership function is triangular and specified by tree parameters, as follows: (: , , ) a, b, and c are pessimistic, probable, and optimistic values, respectively.This membership function is defined for each external and internal factor in the range −10 to 10.An example of the triangular membership function is shown in Figure3[29,30].

Figure 6 .
Figure 6.Center of gravity and coefficient of closeness.

Figure 6 .
Figure 6.Center of gravity and coefficient of closeness.

Figure 6 .
Figure 6.Center of gravity and coefficient of closeness.

Figure 10 .
Figure 10.The stages of the proposed model.

8 Figure 10 .
Figure 10.The stages of the proposed model.

Table 3 .
Strengths, Weaknesses, Opportunities and Threats (SWOT) Matrix of Considered IT Organization.