Espacios. Vol. 37 (Nº 07) Año 2016. Pág. 21

The SMEs' internationalization: Multicriteria-Based Priorization Using Fuzzy Logic [1]

Internacionalización de las PyMes: Priorización basada en Multicriterios usando Lógica Difusa

Jorge Aníbal RESTREPO 2, Sonia MARTÍN Gómez 3, Juan Gabriel VANEGAS 4

Recibido: 01/11/15 • Aprobado: 30/11/15


1. Introduction

2. Literature review

3. Method

4. Implementation and results

5. Conclusions



Purpose. Develop a model based on a frame logic to quantify SMEs' internationalization by integrating linguistic variables such as human talent, infrastructure, innovation strategies, FTAs, marketing strategy and finance, among others.It is argued that the company management of international markets depends on internal factors, especially the capabilities and resources available, based on the premise that the profits made by a company depend on external factors (competitive environmental features) and internal factors (the integration of resources available), those latter are perhaps this research's biggest challenge, because it is required to propose a suitable battery of capabilities and define their importance and strategic relevance to building competitive advantages.
Design/ Methodology/Approach. Fuzzy inference system is proposed to model the resources, skills and competencies that determine internationalisation success. Data: 157 linguistic variables are used, arisen from entrepreneurs, experts, consultants and researchers in international trade, and through expert judgment, 18 factors explaining export capabilities are defined. The proposed model is applied by means of a case study of the textile and clothing cluster in Medellin, Colombia.
Findings. In model's implementing it got a particular global index of 28.2 for internationalisation capabilities. The result confirms the hypothesis that the capabilities and resources currently available to the sector analyzed, are not sufficient for a successful integration into the international market, and most importantly, specifies the factors and variables to intervene to improve the export's capability.
Limitations. In the particular case of textile companies, is highlighted the lack of a continuous information record and very few studies directed towards the long-term plans development. Similarly, there is little consistency in the exports criteria.
Originality/Value. Method emerges as an innovative management tool, linked to internal organizational spheres and their different abilities.
Keywords: Fuzzy Set Methods, Exports, Strategy and Business Strategy.


Propósito. Desarrollar un modelo basado en una lógica del marco de cuantificar internacionalización de las PYMES mediante la integración de variables lingüísticas tales como el talento humano, infraestructura, estrategias de innovación, los TLC, estrategia de marketing y finanzas, entre others.It se argumenta que la gestión de la empresa de los mercados internacionales depende interna factores, especialmente las capacidades y los recursos disponibles, basados ​​en la premisa de que los beneficios obtenidos por una empresa dependen de factores externos (características ambientales de la competencia) y factores internos (la integración de los recursos disponibles), los últimos son quizá el mayor reto de esta investigación, porque es necesario proponer una batería adecuada de capacidades y definir su importancia y relevancia estratégica para la construcción de ventajas competitivas.
Diseño / metodología / enfoque. Se propone sistema de inferencia borrosa para modelar los recursos, habilidades y competencias que determinan el éxito de internacionalización. Datos: se utilizan 157 variables lingüísticas, surgido de empresarios, expertos, consultores e investigadores en el comercio internacional, ya través de la opinión de expertos, se definen 18 factores que explican la capacidad de exportación. El modelo propuesto se aplica por medio de un estudio de caso del cluster textil y de la confección en Medellín, Colombia.
Recomendaciones. En el modelo de implementación que tiene un índice global de 28,2 particular, para las capacidades de internacionalización. El resultado confirma la hipótesis de que las capacidades y los recursos actualmente disponibles para el sector analizado, no son suficientes para una buena integración en el mercado internacional, y lo más importante, especifica los factores y variables que intervenir para mejorar la capacidad de la exportación.
Limitaciones. En el caso particular de empresas del sector textil, se pone de relieve la falta de un registro de información continua y muy pocos estudios dirigidos hacia el desarrollo de planes a largo plazo. Del mismo modo, hay poca coherencia en los criterios de exportación.
La originalidad / valor. Método emerge como una innovadora herramienta de gestión, vinculada a esferas internas de la organización y sus diferentes habilidades.
Palabras clave: Métodos conjunto difuso, Exportaciones, la estrategia y la estrategia empresarial.

1. Introduction

For Colombia, it is argued that internationalization's pattern should be considered strengthening the business environment to address a demanding globalization's process in a gradual way and taking the export's topic as the first step to position itself in the global arena. Without being that single base, the process must emerge from a local historical context and strengthen company's development according to domestic level to face international markets and challenges with the capability that this demands. This reality requires practical tools for the international strategic development of SMEs in Colombia, be able to withstand the challenges involved in any integration process to which the country is linked.

Globally, Colombia is widely recognized for its significant advantages as a textil and clothing's producer. This industry represents around 8% industrial gross domestic product (GDP), and 3% of national GDP, and contributes 13% of manufactured exports and accounts for 24% of industrial employment. The textile and clothing industry is composed of about 10 thousand factories in seven cities. Medellín absorbs about 40% of companies in the system, which places it in the textile industry's top in Colombia, generating more than 6% of industrial GDP (Inexmoda, 2012).

Comparatively, the international trade level of the Colombian textile industry evidences a lower penetration compared with the world's total exports from this sector, which emphasizes the need to rethink the business strategy under the light of empirical evidence reflected in the strength or weakness of the export's succesful critical factors. In this sense, this paper proposes a model for creating a global export capability's evaluation index of SMEs, using linguistic nature's qualitative variables. The fuzzy inference system (FIS) is used as a flexible analysis approach, which allows a comprehensive assessment of the ability to export business in a systematic way.

This paper proposes a model to represent linguistic data both qualitative and quantitative and create a global assessing index of the firms' export capability using a Fuzzy Inference System (FIS) as a flexible analysis approach. The relations between explanatory variables are comprised using the expert's criteria. Every critical successful factor is evaluated by specific set of variables which relations are defined by entrepreneurs' perception into the assessment model. We use FIS to model the correlation between variables and adjust the data to assess export capability of small and medium-sized enterprises' (SMEs) in the textile-clothing industry, Medellín-Colombia.

This paper has 5 sections, as follows: section 2 gives a theoretical review on the companies' internationalisation and the theorical background about management issues addressed through the fuzzy logic perspective. Section 3 presents the fuzzy inference system theory. Section 4 has a case of study for the textil-clothing industry where this method was applied and section 5 presents the limitations and conclusions.

2. Literature review

2.1. Theory of the enterprises internationalization through the exporting process.

The company's internationalization, as an economic phenomenon, has aroused research interest from diverse edges. Santiso (2007), studied the spanish economy firms, and shows how in the nineties, they became global players taking Latin America as an international springboard for the Spanish companies's conversion. In Argentina, the internationalization process of a group of industrial companies is analyzed by installing plants abroad, Bisang (1992), presented the hypothesis that the process rather than a punctual and random phenomenon is the result of complex causes related to the characteristics and dynamics of domestic production structure (Bisang et al., 1992). For Colombia, Castro (2007) argues that internationalization's model should consider strengthening the Colombian business environment to address a gradual and demanding globalization process. He argues that the export's issue has been taken as the first step in internationalization, but can not be the sole basis, the process must come from a local historical context and strengthen the internal company's development to get to the international markets and their challenges with the ability that this demands. Concludes that through practical tools for international strategic development of Colombia's SMEs, the challenges of any integration process to link the country will be achieved.

Other studies indicate as a common denominator that internationalization means the set of operations to establish links with some degree of stability, between the company and international markets, through an incremental process of involvement and international projection (Root, 1994; Scepter , 1999)

However, given the different theoretical approaches that attempt to explain the firms' internationalization process, three perspectives are considered, in the first instance the economic perspective that considers company internationalization by analyzing globalization, multinational companies and their operations and more specifically, through the transnational corporations activities, where theories have detailed the internationalization's process through a figure that has focused on the costs and economical advantages of internationalization (Gomez, 2006 belong; Scepter, 1999).

Second, the theory of resources and capabilities (Wernerfelt, 1984), which consider the internationalization as an incremental learning comminment on the knowledge accumulation and the incorporation of resources and skills to address foreign markets, It is presented the Uppsala model particular case and its derivations and particular adaptations (Johanson and Vahlne, 1990, Ignatius Press, 1999; Alonso, 1994; Gutierrez and Heras, 2000).

Third, the network's theory, communities clusters and the internationalization process arise (Thorelli and Cavusgil, 1990 Thomas, 1985). Because of its importance the new concepts of internationalization process must be considered as a logical development of interorganizational  and social networks of the companies, category in which the concept  of the particular case of cluster is located (Blankenburg, 1995, Johanson and Mattson, 1988 ).

As argued above, there is an extensive theoretical body on the subject. However, this work takes over the theory of resources and capacities as a support model, this theory dates from 1984 and its porpuse has been to analyze the resources and capabilities to identify the firm's potential to establish competitive advantage by identifying and assess the resources and skills available, wether it owns them or it has the potential to access them, it is emphasized the importance of this analysis to explain the evolution of their results (Wernerfelt, 1984).

In the 80's, the strategic vision that internal company factors facilitate or hinder the way towards internationalization is emphasized. The resource-based theory exposes  circumstances that explain how similar companies operating in competitive environments and common success factors for the industry, generate an average of higher and differentials returns  (Huerta et al., 2004).

In this vein, the company management of international markets depends on internal factors, especially the capabilities and resources available, based on the premise that the profits made by a company depend on external factors (competitive environmental features) and internal factors (the integration of resources available), those latter are perhaps this research's biggest challenge, because it is required to propose a suitable battery of capabilities and define their importance and strategic relevance to building competitive advantages.

In general, the supportting theory considers the capabilities, skills and organizational procedures, such as processes, assets, information systems and knowledge that enable a company to formulate appropriate strategies to compete internationally (Barney, 1986 strategies 1991; Claver and Quer, 2001).

In this context, business leadership's biggest challenge will be to identify, develop, protect and deploy resources and capabilities in such a way that the company creates a sustainable competitive advantage that gives a higher profit (Amit and Schoemaker, 1993). In short, the company's competitive position is a directly proportional function on how to combine their resources and capabilities

2.2. Fuzzy Inference System

The Fuzzy Inference System –FIS- is used widely to modeling problems where the analyst have qualitative information and besides linguistic, vague and subjective, as the decision analysis, operative risk evaluation, medical diagnostic, pattern recognitions and so on. The possible use of FIS has extend to entire social sciences' field (Kaufman, 1990; Kulkarni, 2001; Glykas et al., 2004; Medina, 2007; Xirogiannis et al., 2008), it no mean that Fuzzy Logic may be able to replace the analysis statistical, but it can get a rigorous theoretical scheme for treating many socio-economics problems and support decisions making. FIS could be an administrative tool that allows measuring the state of different fuzzy issues and helps us to make a better management.

Actually, the fuzzy or fuzzy logic attracts a large number of followers , because it uses expressions that are neither fully true nor completely false , ie , is the adaptive logic to concepts that can take any value of truthfulness in set of values ​​that fluctuate between two extremes , absolute truth and complete falsity . It is important to clarify what is diffuse , complex or imprecise is not the logic itself, but the object you intend to study : expresses the lack of concept's definition to which it applies. Fuzzy logic is inaccurate information, example the company's contribution margin is low or the exchange rate's volatility is high, in 0terms of fuzzy sets it combine rules to define actions : if proposition 1, then Proposition 2 . Example: If the currency's Volatility is high, then the exporting firms' profit margin is low. So, the fuzzy control systems adjust input variables, defined in terms of fuzzy sets , using rule groups that cause one or more output values.

Fuzzy logic models are acutely flexible, tolerant to data's inaccuracy and enable to manipulate  non-linear functions of diferent complexity, most importantly, do not rely on statistical assumptions about the data's characteristics and their probability distributions. When it manipulated imprecise and insufficient information and statistical tools are used can not guarantee and neither is it enought to generate significant results. A combination of a fuzzy logic system with the experience incorporated from an expert group, in the process of knowledge decision making,  is an extraordinary way to gain positive results (Kosko, 1994a).

However, the fuzzy sets application have been widely disseminated to the design and decision making's  support in differents knowledge's areas: project evaluation, operational risk's assessment, fraud or fault detection, diagnostic systems for medical applications, diagnostic systems in psychology and sociology, marketing applications, industrial's drivers, socio-political evaluation and quality control, among others ( Medina , 2006). In the business' decisions there are applications on measuring business perception (Mendoza, 2009) (Rush, et al, 2007 ; Aguirre , 2010); audit's technological capabilities, measuring intellectual capital of companies and institutions ( Medina , 2010; Serrano, 2012 ), innovativeness measurement   ( Capaldo , 2003) , development of diagnostics in the business sector ( Medina, 2006 ), investment decisions' evaluation ( Aluja Gil , 2002 ), problems' analysis and classical theory's inconsistencies of investment and new approaches to fuzzy logic ( Magni , 2002; Hwang , 1992), raised technical analysis research of investment incorporating the human cognitive process in the automatic patterns detection, serving as a complement to fundamental analysis ( Dourra and Siy , 2002); credit evaluation process in a more objective perspective in order to minimize operational risk and credit risk in the granting's counterparty  (Medina and Paniagua, 2008), production planning and determination of production levels , inventory and capability over a given planning horizon in order to reduce the total costs resulting from the production plan ( Narasimhan et . al, 1996 ) . applications relating to the supply chain to control material flow between suppliers, factories, warehouses and users efficiently and at the lowest cost (Thomas , 1996), aggregate production planning (Shi and Haase , 1996), planning enterprise resource ( Miranda , 2005), determination and demand forecasting combining market projections and delivery ( Wanga and Chang, 2010 ), competitiveness' analysis of SMEs in the textile-clothing Aburrá Valley ( Vanegas and Restrepo, 2013).

A system based on fuzzy logic, due to the required calculations' simplicity (basically sums and comparisons), can leverage the experts' knowledge in a subject, as the basis for achieving an automatic optimization to formalize the ambiguous knowledge that emerges of common sense, in an operable form (Del Brio and Sanz, 2002).

3. Method

3.1. Hypothesis

The normal transformation's process of a local company in international is gradual, where the level of company's engagement grows parallel with his external market's knowledge and the variables inherent to their own process. As a result, international company expansion involves a set of incremental steps, where initially, is installed outside its borders those closest to the customer value chain activities, as in the exports' case, framed as a foreign trade activity, for starting from there, begin to make progress in its internationalization assuming greater challenges and commitments, as it is the investments direct case. Starting from the premise that the benefits got by a company have a causal relationship between external factors (competitive features of the environment) and internal factors (the integration of available resources). As has been established that the firms behavior in international markets depends on internal factors to it, in the case of SMEs in the textile / clothing of Medellin sector states that the capabilities and resources currently available are not sufficient for a successful integration into the international market, thus adopt strategies required to improve internal areas where weaknesses occur and enhance those where there are strengths and facilitate the competitive advantages' incorporation required for international positioning; the biggest challenge of this research is to quantify by an numerical index global the internal resources to propose a suitable set of resources and capabilities in order to define improvement plans for the competitive advantages' construction in the internationalisation process.

3.2. Design of Research

The researhc's objectives are limited to Medellín's city as the leading textil's producer as well as an international fashion center in Colombia. This is an analytical research with a qualitative-quantitative mix orientation, intended to measure the export capabilities and resources, from a set of internal variables, chosen through the Delphi method by a experts's group from textile-clothing SME's.

Methodologically, the work was split in two stages:

  1. Building an affinity diagram, focused on the capacities of technological innovation exposed by  Yam et al (2004), Cheng et al (2006), besides we use the value chain exposed by Porter (1985). 
  2. Designing a Mamdani Fuzzy Inference System, based on works by Medina (2006) and proposed by Kosko (1994), Jang et al (1997) and Kasavov (1998).

3.3. Sample

The main mechanisms for collecting information used were: surveys, semi-structured interviews, direct observations, participatory activities and document review. To determine the sample firms, we turn to ACOPI (Asociacion colombiana de las micro, pequeñas y medianas empresas) and their databases. We determine 13 companies for the pilot study. Surveys are conducted to the company legal representatives or, alternatively, whom run the strategic business planning function.

After several meetings was built a matrix with the critical success factors, subfactors and variables that capture and to assess the export capability of SMEs, and a survey was run employers in ACOPI in which, by using a Likert scale collected the factors, subfactors and variables more important to the assessment, up to 18 definitive subfactors (see Figure 2).

3.4. Fuzzy sets and Fuzzy Inference Systems

A fuzzy logic system, unlike what its name suggests, is a reasoning alternative to the classical logic seeking to describe fuzzy variables, is formalized by Zadeh in 1965 and it is the base on Fuzzy Set theory. Allow describe facts that are not total true or total false, allows us use relative ideas of reality, defining the grades of membership and following the pattern's reasoning similar to the human brain (Kosko, 1995).

In the managerial environment, there is a broad knowledge dissonant with reality, that means, imprecise and vague knowledge, ambiguous and of uncertain or probabilistic nature.  Thus, the poor capability of expression by bipolar classical logic is one of the main drawbacks to deal with this kind of knowledge and information and classify the membership function to certain analysis categories. 

Fuzzy expression refers to an event in which there are both ambiguity and vagueness (Bellman & Zadeh, 1970).  The mathematical representation goes from a universal set of objects x, U = {x1 … xn}, where a fuzzy set A defined by equation ordered pairs (equation 1):

A = {x, μA(x)}, ∀ x∈ U             (1)

Where μA(x) is x's membership degree to fuzzy set A, and μA: U → M is a membership function from U to space M, which is associate to a real number in the interval [0, 1].  Thus, a value close to the upper limit marks the x's highest degree of membership to A (Zadeh, 1965).

The Mamdani Fuzzy Inference Systems FIS, (Mamdani, 1977, 1981) was the first system proven in a practical way as universal approximation of functions. Later Kosko & Wang  (1992) formally settled that any relation among input and output variables can estimated by FIS, built in linguistic terms with a high-grade of accuracy (universal approximator).

The steps to build a FIS are suggest in Figure 1, a details of all development can find in Jang (1997), Kosko (1995) and Medina (2010):

  1. Fuzzyfication. Define the inputs and outputs of system (linguistic variables), their linguistic terms (fuzzy sets) and their membership functions μA(x).
  2. Knowledge base. Define the fuzzy rules If-then which specify the relation among input and output of  system.
  3. Composition operations. Define operations of union, Intersection, Complementation, the Cartesian product and the Cartesian Co-products between fuzzy sets.
  4. Inference Mechanisms (Estimated Reasoning). Define the procedure to gather conclusions from fuzzy rules type IF-THEN and values that take the inputs Xi of systems applying composition relations.
  5. Aggregation.Define the output fuzzy set as the aggregations of activation strength of each rule defined for the system.
  6. Defuzzyfication: in the last step you get a crisp value from the output fuzzy set. Provides the solution,  allow evaluate the system performance and decisions  making.

Figure 1 - Steps to building a FIS.

Source: Jang et al (1997)

3.5. Fuzzy Sets Limitations

Rajendra et al (2009), describe as limitations of fuzzy logic system the following:

  1. The fuzzy logic systems lack the skills of machine learning, as well as a neural network-type memory and pattern recognition.  Therefore, hybrid systems (e.  g.  , neurofuzzy systems) are becoming more popular for specific applications. 
  2. Finding out exactly membership functions and fuzzy rules is a difficult task.  Most cases is impossible to predict how many membership functions it needed even after wide testing.
  3. Confirmation and proof of a fuzzy knowledge-based system usually needs extensive testing with hardware in the loop, it is an expensive affair.
  4. System stability is an important concern for fuzzy control.

4. Implementation and results

4.1. Defining the knowledge base or fuzzy rules

The exercise of the affinity diagram allowed to get five keys critical factors to measure export capability: 1) marketing, 2) logistics, 3) planning, 4) human talent, and 5) finance. Then in brainstorming sessions with international trade experts, 18 subfactors finding (Figure 2) which act as a proxy to explain SMEs' export capability.  The figure shows how each critical success factor (FCEi) with i = 1 ... 5, will explain by subfactors Fji with j = 1 ... 18.

Afterwards, following the same rule of formation, each sub factor Fji, j = 1 ... 18 can explain by the set of variables Vkji, k = 1 … 157, which are divide into each of the 18 items to assessment the export capability.  Please note that those 157 explanatory variables arose from a comprehensive analysis and discussion by an expert team. They after evaluating first proposal of 250 variables got an end range of 157 variables.  Such a large set of data has an imprecise ingredient, so we should seek a solution through fuzzy sets.

Figure 2 - Subfactors explaining export capability: 18 subfactors which explain 5 reasons settling export capability.

The analysis is makes through two steps:

  1. The first one we weighting these 157 early explanatory variables (Vkji)  through assigned scores to each depending their level according to the experts assessment. This procedure get qualify the grade of each subfactors Fji (j = 1 ... 18).
  2. The second step used the previous qualification to develop an FIS to assessment the export capability.

The 18 inputs will use to qualify each of five critical success factor: marketing, logistic infrastructure, planning manage, human and financial issues. Every item represents a FIS, these are the first grade of system. We must develop five FIS and the outputs of these level are the inputs of the level following. Then these variables are collect into bigger level variables, we called a second level: Marketing and Logistic, Planning and Human Talent, Finance). Last, the third level collect all information gathered of previos systems. The total number of fuzzy systems developed is represent by eight FIS connected between them. Figure 2, represent them by the main variables (squares in Blue), to get an integral evaluation the Capability of SMEs (ECS).

The following four fuzzy sets are assign to each inputs-outputs: greater fortress (FMy), minor fortress (FMn), minor weakness (DMn) and greatest weakness (DMy), we selected a range for each variable between [0-40], as it represent in Figure 3.

Figure 3 - Fuzzy sets for input and output variables

To build the knowledge base or FIS's fuzzy rules, we apply the heuristic procedure marked in Medina (2010), used in cases where we considering large number of input variables. A summary is present to following:

The first step is pondering each input Xi, according to effect that each Xi has on output Yj. Let  Pi weights assign to each input (relative importance of the input variable). Piϵ[0,1,. i = 1,.,n. and n = FIS input variables. J = 1,…,m    m is fuzzy sets defined for input i.

Weighting the importance of each fuzzy set (linguistic label) assigned to each input "Xi". Then "Cij" is the weight assigned to each fuzzy set of the input Xi, and indicates the effect on the output Yj.

 The experts must qualify any scenarios of the knowledge matrix, that is, the experts should define a set of "reference rules", that allows to later, validate the FIS output. In general extreme and middle escenarios are evaluate easier for qualifying when the system is big. Rules type Mamdani are express by:

If X1 is A1 and X2 is A2 and...... and Xk is Ak Then Y is B

The score for each cell of matrix knowledge calculated by the relation following:

The next step is correlating all scores in each cell of the score matrix with the fuzzy sets assign to output variable Yj. This procedure is carry out by getting the maximum and minimum value of the scores matrix, Kmax and Kmin respectively. Kmax - Kmin decide the scores range that can take the output Yj, therefore, the fuzzy sets must assign to this range. The score on the intersection of fuzzy sets (L1 and L2) decide the score from which is assign a fuzzy set (low, middle, high) to each cells into the matrix.

Figure 4 - Triangular fuzzy set to output Yj

The system response can adjust by changing limits position L1 and L2 such the system response is adjust to the reference fuzzy matrix, Figure 4 (Compared the score of each cell with the score on the intersection) rules qualified by the experts previously. This procedure lets us to get the fuzzy rules matrix.

Finally the approval should begin with the fuzzy rules matrix suggested on previous step to adjust the system. All cells are evaluate by experts, first it needs verified the "reference rules" are getting. After, needs to verify all other rules propose are consistent, if not, the limits L1 and L2 must move to adjust the system response.

After applied the procedure we got the fuzzy rules matrices of each fuzzy systems (eight FIS, eight rules matrices). The Table 1 shown the fuzzy rules matrix of third level which qualify the export capability of SMEs and use as input variables: Marketing and Logistic, Planning and Human Talent and Finances with 64 rules (4x4x4). Rules express as:

If "Marketing and Logistic" is "DMn" and "Planning and Human Resource" is "FMn" and "Finance" is "DMn" THEN "Export Capability" is "DMn".

Table 1 - Fuzzy rules matrix for qualify the export capability of SMEs

4.2. Approval model

This section presents the approval and consistency the model, it is run through experts work sessions. It contrasts the expert judgment versus  the simulating model, verifying their functionality and comparing with projected results. Three focal groups were taken account, sorted as optimistic, normal and pessimistic scenarios, then we check that the index global from system output was suitable in each case.

The FIS arrangement, adjust both IF-THEN rules and the change fuzzy sets position in the defined ranges. Then it looks a consistent output with the expert judgment about SMEs export capability. The entrepreneurs and expert group consultants are members of Colombian Association of Small Industries (ACOPI) with expertise in international markets. They were interviewed and they helped us in all standardization. 

Another confirmation use the fuzzy surfaces, which shown the relations and consistency between input and output. If the behaviors are not consistent we must review the rules and suggest the use of another fuzzy sets to the input or output variables or move the fuzzy sets in the range of each variable. The application was developed in Matlab. An example of a fuzzy surface is show in the Figure 5.

Figure 5 - Surface charts for variables at level I (Matlab toolbox)

Figure 6  shows the rules editor and fuzzy surfaces to evaluate the export capability  of the SMEs company, the surfaces mark a no lineal relations between variables, when the inputs increase their qualification (planning and HHRR, Marketing and Logistic and finances), then improves the company export capability.   The evaluation allows identify which issues should improve, where administrative action must take to  carry out a better export capability. The qualifications for Planning and HHRR=27.6, Marketing and Logistic=28.7, and finances=28.1. Qualifications for export capability in 28.2 which equal to "Minor Fortress" (FMn). We have this qualification after of evaluate the previous fuzzy systems (first and second system level).

Figure 6 - Rules Viewer and Fuzzy surface of  export capability.

After verifying the algorithm's consistency, an experimental application and adjustment is carry out with the method propose.  Respondents identified several benefits to this tool for the ECS's diagnosis, and the impact of its implementation in any company in the manufacturing sector. Therefore, the model approach was accepted by respondents, and the learning process was highlighted.  It concluded as textile and clothing companies need to design and participe in the programs, projects and strategies to strengthen their innovation ability to compete for success in the region. This test is performed at 13 pilot enterprises ACOPI members .

Aggregation exercise's results are reported in Table 2 . Evaluations were weighted according to the weight given to each item, then the export capability's average value is calculated. From columns 3 to 15 presents the expert evaluation, column 16 shows the average value and column 17 contains the weight for each input. For example, the value obtained by the marketing factor is 27.2 , and is the weighted result sum of each secondary factor as follows : 30.4*.30 +26.4*.35 +25.2*35 = 28.2, matching the fuzzy set " Low strength ( FMn ) ," according to expert opinion. The procedure is repeated for each factor and a 28.2 value is obtained as a final export capability  grade , which match a "minor Fortaleza" ( FMn .) This result is consistent with the results of the FIS model (Figure 6).

Table 2.  Export capability results of level III.

Table 2, shows pilot testing from 13 ACOPI's companies, every expert went to qualifying those five reasons that comprise export capability of SMEs. Evaluations weighted according the weighting given to each item, then advance to calculate average value and export capability. Columns 3 through 13 present experts´ evaluation, column 16 presents average scores and column 17 weight for each input. Eg the value of Marketing is 28, it is result of the weighted sum of every sub factor as follows: 30.4*.30 +26.4*.35 +25.2*35 = 28.2, which match with a "Minor Fortress (FMn)" at experts judgment. If we repeats the procedure for every item,  we get   28.2  as final qualification of export capability which match with a "Minor Fortress (FMn)" also.  This result are suitable with FIS model results (figure 6).

5. Conclusions

In this paper, we propose a logical framework integrating qualitative variables to define export capability as human talent, infrastructure, innovation strategies, free trade agreements, marketing strategies and finance and built a Fuzzy Inference System to modeling  the export success determinants considering the most relevant qualitative and quantitative variables within each of the items expressed.  Model proposed has  explain through a case study from the textile-clothing cluster in Medellín, Colombia; running the model found to have a particular value of 28.2 in their export skills. The model reflects weaknesses on R&D, logistics, finance and marketing. Strengths in production, environmental management, information systems and human talent. The Model allows identify which issues should improve, where administrative action must take to  carry out a better export capability. The qualifications for Planning and HHRR=27.6, Marketing and Logistic=28.7, and finances=28.1. Qualifications for export capability in 28.2 which equal to "Minor Fortress" (FMn). We have this qualification after of evaluate the previous fuzzy systems (first and second system level).

Acopi's managers, owners and experts  identified some features to find out ECS and advantages to apply the model in different companies and manufacturing industry, due to the flexibility and wide treatment of the variables evaluated.  The model caused concern among participants about  economics relevance and priority of SMEs. Besides, the effects a free trade agreement - FTA with the U.S., to develop and carry out programs, projects and strategies to strengthen their export capability and manage to introduce themselves successfully in the globalization and its innovation. 

The SMEs, as those found Medellin city, need to leverage their export model, making inroad into scientific and technical items by making alliances with the national R&D network.  The method proposed in this paper provides a flexible and simple way to measure and assess their internal position to undertake successful export procedure.  Also, to learn which issues demand intervention, change or improving skills and investment to promote an internal organizational environment making possible to compete on the international sphere decently. 

Method emerges as an innovative management tool, linked to internal organizational spheres and their different abilities.  A set of strategic variables considered and identified screened with technical and rhetorical rigor: by reviewing literature and consulting experts, to assess SMEs export capability.  The selected variables passed through various filters suggested by consultants, entrepreneurs and international trade experts. 

The variables explaining export capability, which examined in this paper, are of linguistic and difficult to quantify. The Fuzzy Logic theory proves to be a clear tool to face this events. It allows to address —with an undefined linguistic statements focus— classifying information on events in an infinite value scale in the interval [0,1]. Last, allows representing the functions of membership and solving the bipolarity in the classical logic. 

5.1. Limitations of fuzzy systems

The main constraints to use fuzzy inference system are on the difficulty to identify the relationship's function between both input and output's variables, this procedure take time and it based on the experts criteria and it is more difficult when increase the inputs variables number. 

In the textile companies' particular case, is highlighted the lack of a continuous information record and very few studies directed towards the long-term plans development. Similarly, there is little consistency in the exports criteria and it requires participation and cooperation both than textile cluster as the Colombian state.

5.2. Future Research

The model described, can be complemented with studies of technological and management capability, as well as the analysis of external resources for a clear focus on international market. As described, the versatility of fuzzy logic systems, have an important range of services for the academic sector is linked with innovative proposal to address thematic with a high degree of inaccuracy.


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1. This project was financed with resources from the Tecnológico de Antioquia I. U. in agreement with the Fundación Universitaria Autónoma de las Américas.
2. School of Economics and Management Science, Fundación Universitaria Autónoma de las Américas, GICEA Research Group, Medellín- Colombia,,
3. School of Management and Economic Science, Universidad CEU San Pablo Madrid España,

4. School of Management and Economic Science, Tecnológco de Antioquia I.U., R.E.D. Research Group, Medellín-Colombia,

Vol. 37 (Nº 07) Año 2016


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