An improved fuzzy preference programming to evaluate entrepreneurship orientation

Applied Soft Computing 13 (2013) 2749–2758

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An improved fuzzy preference programming to evaluate entrepreneurship orientation Jafar Rezaei ∗ , Roland Ortt 1 , Victor Scholten 2 Faculty of Technology Policy and Management, Delft University of Technology, Jaffalaan 5, 2628 BX Delft, The Netherlands

a r t i c l e

i n f o

Article history: Received 20 September 2011 Received in revised form 3 September 2012 Accepted 19 November 2012 Available online 6 December 2012 Keywords: Entrepreneurship orientation (EO) Small to medium-sized enterprises (SMEs) Multi-criteria decision-making (MCDM) Fuzzy preference programming Fuzzy analytic hierarchy process (AHP) Model validation

a b s t r a c t This paper describes an approach to measuring the entrepreneurship orientation (EO) of firms. EO is a widely accepted way to measure the degree in which a firm is entrepreneurial. The scale has three dimensions – innovativeness, risk-taking and proactiveness – each of which is assessed using multiple items. Measuring EO is important for entrepreneurial firms and for organizations like venture capitalists, business angels, investment banks and governments investing in these firms. Both the traditional statistical and the simple approach of assessing the overall level of EO (adding item scores) have their disadvantages. The aim of this article is to discuss these disadvantages and describe how some of them can be removed by using fuzzy analytic hierarchy process (AHP), which is a multi-criteria decision-making (MCDM) method that is particularly suited to tackle multi-dimensional, fuzzy, and perception-based constructs such as EO. We first improve a fuzzy AHP and then apply it using the pairwise comparisons of three experts to evaluate the EO of 59 small to medium-sized enterprises (SMEs) and rank the firms based on their EO score. The results indicate that proactiveness is by far the most important dimension, followed by innovativeness. Furthermore, there are considerable differences when it comes to the weights of the items. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Today, in a period of rapid change and innovation, companies need to acquire entrepreneurial competences to survive [1:144]. The processes of strategy-making and the styles of firms engaging in entrepreneurial activities are together referred to as “entrepreneurship orientation” (EO) [2], a term that was first introduced in the 1980s [3,4] and that has since become widely accepted as a tool to assess how entrepreneurial a firm is (e.g. [5–15]). Several studies have found a positive relationship between EO and firm performance (e.g. [16–19]). Furthermore, EO is found to be stable over time [20]. Consequently, measuring EO is of special importance for firms and for organizations, such as venture capitalists, business angels, investment banks and governments. Firms need to know their entrepreneurial level if they are to invest in entrepreneurial activities and improve their performance. The entrepreneurship orientation construct reflects the strategic posture of firms. Based on the decision-making style captured by the EO construct, firms configure their knowledge-based resources, including their marketing-related and technological capabilities in

∗ Corresponding author. Tel.: +31 15 27 81716; fax: +31 15 27 82719. E-mail addresses: [email protected] (J. Rezaei), [email protected] (R. Ortt), [email protected] (V. Scholten). 1 Tel.: +31 15 27 84815. 2 Tel.: +31 15 27 89596. 1568-4946/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.asoc.2012.11.012

such a way as to increase their ability to pursue innovative opportunities [21] and improve their performance [19]. The EO of firms is also a vital tool for venture capitalist in assessing the potential of their investments [22]. Despite the recognition of the importance of the construct, several authors discuss the dimensionality of the EO construct, its interrelatedness of the sub-dimensions [5,21] and the representations of the construct and its sub-dimensions [23,24]. These representations can affect the type of methodology to analyze the construct. Building on recent advancements of applying multi-criteria decision-making (MCDM) techniques in social sciences and management (please see Section 2.1) we view measuring EO as a multi-criteria decision-making task and introduce an MCDM method to measure EO in a real-world situation. The paper is organized as follows. In Section 2, we discuss existing literature regarding the use of MCDM in entrepreneurship and innovation, and literature regarding the construct of entrepreneurship orientation (EO). In Section 3, the methodology and our improvements are described. Section 4 discusses the implementation of the proposed methodology in a real-world situation while the conclusions and future research are addressed in section five. 2. Literature review In this section, we first review existing MCDM applications in the field of entrepreneurship and innovation and then focus on literature describing how to measure entrepreneurship orientation.

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2.1. Multi-criteria decision-making in entrepreneurship and innovation Multi-criteria decision-making (MCDM) is one of the most recognized branches of decision-making. In short, MCDM involves selecting the best alternative based on a set of decision criteria and alternatives [25]. MCDM methods have been applied to address a variety of practical problems (see, for example [26,27]). We found some applications of MCDM methods in the field of entrepreneurship and innovation, but their number is small, when considering the many multi-criteria decision-making problems in those fields. The ones we did find are briefly discussed below. Nijkamp and Reggiani [28] proposed an MCDM method that is based on Regimes Analysis and is designed to determine the key entrepreneurial innovation factors at the local level. Capaldo et al. [29] proposed an MCDM approach, based on Ordered Weighted Average (OWA) operators, to determine the values of market-related and technological innovation capabilities of small entrepreneurial knowledge-based firms. Chen et al. [30] proposed an MCDM approach, based on analytic network process (ANP), to evaluate the teaching cases in entrepreneurship education at ˇ cer and Knez-Riedl [31] applied AHP to evalbusiness schools. Canˇ uate the creditworthiness of entrepreneurial firms’ partners. Lu et al. [32] proposed an MCDM approach, based on AHP and fuzzy set theory, to evaluate a firm’s technological innovation capability, using several qualitative and quantitative criteria. Wang et al. [33] used a fuzzy measure and non-additive fuzzy integral method and, by considering different aspects and criteria, evaluated the performance of synthetic technological innovation capabilities in high-tech firms. Wu et al. [34] applied a combination of two MCDM methods, fuzzy AHP and VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), to evaluate the intellectual capital of universities in Taiwan, based on innovation capital indicators. Incorporating the weights of the innovation capital indicators obtained by fuzzy AHP, types of universities were ranked by VIKOR. Mouzakitis et al. [35] proposed a fuzzy MCDM method, based on the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), to select companies in which to invest in, adopting the perspective of business angels. They selected criteria based on the business angels’ opinions and firm performance. Tsai and Kuo [36] applied a hybrid approach, combining decision-making trial and evaluation laboratory (DEMATEL), ANP and zero-one goal programming methods, to evaluate entrepreneurship policies, using the criteria proposed by Stevenson and Lundstrom [37], such as reducing entry and exit barriers, promotion, entrepreneurship knowledge, and financing and business support. DEMATEL and ANP were used to determine the weights of the criteria and a zero-one goal programming was used to determine the optimal alternatives considering the optimal weights of the criteria and resource restrictions. Grimaldi and Rippa [38] applied AHP to select the most suitable set of knowledge management tools to support the innovation processes in organizations. Most recently, Rezaei et al., [39] applied four different methodologies to measure EO of firms: naive, DEA-like, factor analysis and fuzzy logic. They compared the results of those methodologies and showed under which condition which methodology performs best. This overview shows that different MCDM methods have been applied in the field of entrepreneurship and innovation, a field where constructs like the innovative capabilities of firms, the intellectual capital of universities and the quality of entrepreneurship policies are typically multidimensional and fuzzy in nature. These types of constructs are typically measured using perception-based evaluations.

2.2. Entrepreneurship orientation Entrepreneurship orientation (EO) is a construct that reflects the strategic orientation of firms [3,4]. Miller [3:771] defines an entrepreneurial firm as “one that engages in product market innovation, undertakes somewhat risky ventures, and is first to come up with ‘proactive’ innovations, beating competitors to the punch”. This definition contains the three dimensions of EO: innovativeness, risk-taking and proactiveness. In fact, a firm is considered entrepreneurial when (1) technological and product innovations are created frequently; (2) the risks involved in introducing new products and services and or entering new markets are faced deliberately; and (3) the firm is more proactive than its competitors when it comes to exploiting new market opportunities [4,7]. The three dimensions are defined below. “Innovativeness reflects a firm’s tendency to engage in and support new ideas, novelty, experimentation, and creative processes that may result in new products, services, or technological processes” [21]. Risk-taking is reflected in “the degree to which managers are willing to make large and risky resource commitments, i.e. those which have a reasonable chance of costly failures” [40]. Proactiveness is reflected in anticipating and acting on future needs of firms by “seeking new opportunities which may or may not be related to the present line of operations, introduction of new products and brands ahead of competition, strategically eliminating operations which are in the mature or declining stages of the life cycle” [21,41]. As mentioned by Wiklund and Shepherd [7], several researchers have agreed that EO is a combination of these three dimensions. Covin and Slevin [4] devised a scale to evaluate the three dimensions using different items for each dimension. The assessment of the items representing innovativeness, risk-taking and proactiveness is typically based on perceptions that are measured using 5or 7-point scales. By contrast, the combination of the items within the different dimensions and of these dimensions in a value of the overall construct is often assessed using simple algorithms (e.g. add the values for the items). Although this is a straightforward approach to determining the final score for the construct, it is hard to believe that all the different items have the same importance (weight). Although statistical approaches can overcome this main shortcoming by assigning different weights to the items in question, this requires a relatively large number of cases, which are rarely available in most real-world situations. The statistical approaches do not incorporate the preferences of the decisionmakers either. We believe, however, that using a fuzzy MCDM method like fuzzy AHP allows us to overcome the inefficiencies inherent in the statistical approaches. Using fuzzy AHP, we can find the importance (weight) of different items and dimensions, take into account the decision-makers’ preferences, prevent the number of cases from affecting the reliability of the results, and properly handle the vagueness that is inherent in all perception-based problems. If the level of a firm’s EO is assessed using fuzzy AHP the construct EO is considered a goal, while the three dimensions are viewed as criteria and the items that are used to evaluate the individual dimension as sub-criteria. In that case, the evaluation of EO can be seen as an MCDM problem. Because of the advantages of fuzzy AHP, we use this method to evaluate the EO of firms and rank them based on their final evaluation. 3. Fuzzy AHP Analytic Hierarchy Process (AHP), first introduced by Saaty [42], is a systematic approach to solving complex and multi-level decision-making problems. The approach is applicable in situations

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where decision-makers (DM) and experts are available. The DM needs to have a (quantifiable) goal and can distinguish alternative solutions to attain that goal. In addition, experts are required to evaluate the alternative solutions based on criteria. In some cases where the evaluation requires criteria on multiple levels, a hierarchical evaluation process is formed. Based on the expert judgments, the criteria are compared in a pairwise fashion to assess how they contribute to the goal. Finally, alternative solutions are compared by the experts using the criteria that have been identified. Following a mathematical process, the alternative solutions are ordered in terms of their ability to attain the goal. The most challenging step of this methodology involves quantifying the expert judgment using crisp ratios. This makes the methodology inefficient when it comes to dealing with vague and imprecise knowledge. To overcome this inefficiency, fuzzy AHP, as a fuzzy extension of AHP, was proposed by van Laarhoven and Pedrycz [43] and extended by other authors (e.g. [44–51]). However, one of the main criticisms of these works is that they mostly fail to deal with the issue of consistency. Although consistency is also important in conventional AHP, because fuzzy AHP uses fuzzy numbers, inconsistency is more likely to emerge [52]. There are a few studies that have tackled this issue in fuzzy AHP [52–56]. According to Buckley [44] a consistent fuzzy positive reciprocal matrix is defined as follows: ˜ = [˜aij ] is conDefinition 1. A fuzzy positive reciprocal matrix A sistent if and only if a˜ ik ⊗ a˜ kj ≈ a˜ ij where the fuzzy positive matrix ˜ = [˜aij ] is reciprocal if and only if a˜ ji = a˜ −1 and a˜ ii = 1∀i. A ij Recently, however, Cakir [57], based on Bana e Costa and Vansnick [58], identified a fundamental problem in fuzzy AHP when he determined that not only it is impossible to ensure the preservation of the preference intensities (ratios) in the resulting priority vector, but even when the pairwise comparisons are consistent, the order of the preference intensities may not be preserved. Mikhailov [59] has applied fuzzy preference programming (FPP) to derive the priority vector in fuzzy AHP. His proposed approach not only guarantees the preservation of the preference intensities [57], but also provides a well interpretive consistency index. Although it solves various shortcomings of the previous versions of fuzzy AHP, it fails to fully handle the skewness and non-linearity of the reciprocal fuzzy numbers. In the next section we describe Mikhailov’s fuzzy AHP [59], and our improvement.

3.1. Fuzzy AHP using FPP In this section, we describe the procedure of fuzzy AHP as follows. Step 1. Establish the hierarchy In this step, the aim is to construct a hierarchy, including the goal, criteria and alternatives. Step 2. Determine the pairwise comparison matrices This step includes the constructing of comparison matrices for comparing the criteria and alternatives.

⎡

a˜ 11

a˜ 12

···

a˜ 1n

⎤

⎢ a˜ ⎥ ⎢ 21 a˜ 22 · · · a˜ 2n ⎥ ⎥ .. .. ⎥ .. ⎣ ... . . . ⎦

˜ =⎢ A ⎢

a˜ n1

a˜ n2

···

(1)

~ 1

~ 2

~ 3

~ 4

~ 5

~ 6

1

2

3

4

5

6

~ 8

~ 7

7

8

~ 9

9

Fig. 1. Triangular fuzzy numbers (TFNs).

Definition 2. ([43]) Triangular fuzzy number (TFN): A fuzzy number N on  is defined to be a TFN if its membership function N (x) :  → [0, 1] be:

N (x) =

⎧ x−l ⎪ , ⎪ ⎪ ⎨ m−l

l ≤ x ≤ m,

u−x

(2)

, m ≤ x ≤ u, ⎪ u−m ⎪ ⎪ ⎩ 0,

otherwise,

where l, and u are the lower and upper bound of the support N / m = respectively and m is the modal value (l = / u). This triangular fuzzy number can be noted by the triple (l, m, u). In this paper we use the TFNs shown in Fig. 1 for the comparisons. The operational laws of two TFNs N1 = (l1 , m1 , u1 ) and N2 = (l2 , m2 , u2 ) are as follows. Fuzzy number addition ⊕: N1 ⊕ N2 =(l1 , m1 , u1 ) ⊕ (l2 , m2 , u2 ) = (l1 + l2 , m1 + m2 , u1 + u2 )

(3)

Fuzzy number multiplication ⊗: N1 ⊗ N2 = (l1 , m1 , u1 ) ⊗ (l2 , m2 , u2 ) ∼ = (l1 × l2 , m1 × m2 , u1 × u2 ) (4) where li , mi , ui , are all positive real numbers. Fuzzy number division (/): N1 (/)N2 = (l1 , m1 , u1 )(/)(l2 , m2 , u2 ) ∼ =

l

1

u2

,

m1 u1 , m2 l2

(5)

where li , mi , ui are all positive real numbers. It suffices that the DM provides at most n(n − 1)/2 pairwise comparisons a˜ ij , i = 1, 2, . . ., n − 1, j = 2, 3, . . ., n, j > i. Step 3. Derive a crisp priority vector w = (w1 , w2 , · · ·, wn )T using fuzzy prioritization programming (FPP) In this step, the aim is to determine the relative weight of the criteria w = (w1 , w2 , · · ·, wn )T such that the ratios wi /wj are approximately within the scopes of the pair wise judgment a˜ ij , or equivalently: ˜ lij ≤

wi ˜ ij ≤u wj

(6)

For each i and j, there may be many wi and wj that satisfies the inequality (6). However, different ratios wi /wj provide different DM’s satisfaction that can be measured by a membership function as:



a˜ nn

where a˜ ij is a triangular fuzzy number (TFN) to show the decisionmaker (DM)’s preference of i over j and a˜ ji = 1/˜aij . Here, we present the definition of TFN and their operational laws.

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ij

wi wj

 =

⎧ w i ⎪ − lij ⎪ ⎪ wj ⎪ ⎪ ⎨ m −l , ij

ij

w ⎪ uij − i ⎪ ⎪ wj ⎪ ⎪ , ⎩ uij − mij

wi ≤ mij , wj wi ≥ mij wj

(7)

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As the judgments aij are uncertain, lij < mij < uij and therefore dividing by zero do not take place. The membership function (7) may take the following values:



ij

 ij

wi wj wi wj



∈ (−∞, 0),

if

 ∈ [0, 1],

wi wi < lij or > uij wj wj

if lij ≤

wi ≤ uij wj

(8)

(9)

It takes the maximum value of 1 when wi /wj = mij The FPP is aimed at finding the optimal crisp priority vector w* of the fuzzy feasible area P on the (n − 1)-dimensional simplex Qn−1 Q

n−1

 n   = {wi  wi = 1, wi > 0} 

˜ Fig. 2. Triangular fuzzy number 2.

(10)

i=1

with the following membership function:



P (w) = min{ij (w) i = 1, 2, . . . , n − 1, j = 2, 3, . . . , n, j > i} (11) ij

According to [59], there is always an optimal crisp priority vector that has a maximum degree of membership ∗ = P (w∗ ) = max min{ij (w)} w ∈ Q n−1

ij

(12)

Using the maximin rule of Bellman and Zadeh [60], the problem (12) can be transformed to the following problem:

Fig. 3. Fuzzy number 1/2 (solid line) and the membership function of its corresponding ratio wi /wj (dashed line).

max 

 = (1/3, 1/2, 1) has The reciprocal of TFN 2˜ = (1, 2, 3), i.e. 1/2 the following membership function (see also Fig. 3) (to see the membership function of reciprocal of a TFN refer to [43]).

s.t. (mij − lij )wj − wi + lij wj ≤ 0, (uij − mij )wj + wi − uij wj ≤ 0,

n

(13)

w = 1, k=1 k

wk > 0,

 1 (x) =

i = 1, . . . , n − 1, j = 2, . . . , n, j > i, k = 1, . . . , n.

2

Mikhailov [59] claimed that by solving the above non-linear programming problem the optimal priority vector w* and * are obtained. However, we will show that this form does not fully take the skewness and non-linearity of the reciprocal fuzzy numbers into account, and needs some improvements to handle these issues in order to obtain the optimal results. 3.2. Improved fuzzy AHP using FPP Mikhailov [59] in his description of the membership function (7) mentioned that “over the range (lij , uij ) the membership function (7) coincides with the fuzzy triangular judgment a˜ ij = (lij , mij , uij ).” The membership function (7) is linearly increasing over the interval (–∞, mij ) and linearly decreasing over interval (mij , ∞). However the judgment is not necessarily a TFN. Because in fuzzy AHP we use two types of fuzzy numbers to compare the criteria: (1) TFNs ˜ . . . , 9˜ (we call them Type I), and (2) the corresponding reciprocals 1, ˜ ˜ ˜ of the TFNs of Type I which are 91 , 81 , · · ·, 21 , 1˜ (we call them Type II). TFN a˜ ij = (lij , mij , uij ) as defined in (2) is linearly increasing over the interval (lij , mij ) and linearly decreasing over interval (mij , uij ), while the reciprocal of a TFN is not linearly changing over its left and right intervals and therefore the statement is not true for the reciprocal of a TFN. For example TFN 2˜ = (1, 2, 3) is a fuzzy number of Type I and has the following membership function (see also Fig. 2). 2 (x) =

⎧ ⎨ x − 1, 1 ≤ x ≤ 2, ⎩

3 − x,

2 ≤ x ≤ 3,

0,

otherwise,

1

≤ x ≤ 1, 2 − 2x, ⎪ 2 ⎪ ⎪ ⎩

(15)

otherwise,

0,

As can be seen in Fig. 3, the increase and the decrease of the

 over its left and right intervals are not linreciprocal number 1/2 ear while changes of the corresponding satisfaction membership

 over the left and right interfunction defined for the number 1/2 vals are linear. More important, and as it can be seen from Fig. 3, the satisfaction membership function does not coincide with the fuzzy

 As we will show later, this deficiency yields misleading number 1/2. results. To overcome this problem we should first consider the set F = {˜aij } as a combination of Type I and Type II numbers (existing the fuzzy numbers of Type II in F = {˜aij } has been neglected in [59]). Therefore the goal is in fact to obtain a priority vector w = (w1 , w2 , · · ·, wn )T such that: the ratio wi /wj approximately satis˜ i /wj ≤u ˜ ij , for TFN of Type I, and fies the initial judgment a˜ ij , or lij ≤w the ratio wj /wi approximately satisfies the initial judgment a˜ ji , or ˜ j /wi ≤u ˜ ji , for fuzzy numbers of Type II. Then the satisfaction lji ≤w of decision-maker with different wi /wj and wj /wi is represented by the membership function (7) and (16) respectively.

ji (14)

⎧ 1 1 ⎪ 6x − 2, ≤x≤ , ⎪ ⎪ 3 2 ⎨

w j

wi

=

⎧ wj − lji ⎪ ⎪ w ⎪ ⎪ ⎨ mi − l ,

wj

ji

wi

uji − mji

wi

ji

≤ mji ,

wj ⎪ ⎪ uji − ⎪ wj ⎪ wi ⎩ , ≥ mji .

(16)

J. Rezaei et al. / Applied Soft Computing 13 (2013) 2749–2758 Table 1 Fuzzy pairwise comparisons of the main criteria [59].

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Table 3 Comparison matrix A.

Goal

Pricing

Service quality

Delivery time

Goal

M

N

O

Pricing Service quality Delivery time

1 (1/4, 1/3, 1/2) (1/3, 1/2, 1)

(2, 3, 4) 1 (1, 2, 3)

(1, 2, 3) (1/3, 1/2, 1) 1

M N O

1

(4, 5, 6) 1

(1, 2, 3) (1/4, 1/3, 1/2) 1

Table 2 Comparison of three criteria (a common form of pairwise comparison in practice). Criteria

9˜

M M N

8˜

7˜

6˜

5˜ √

4˜

3˜

2˜

1˜

2˜

3˜

4˜

5˜

6˜

7˜

8˜

√ √

9˜

Criteria

Goal

N

O

M

N O O

N O M

1

(1/4, 1/3, 1/2) 1

(1/6, 1/5, 1/4) (1/3, 1/2, 1) 1

Now, following the same logic as in [59] the improved FPP is as follows, which leads to the correct results. max  s.t. (mij − lij )wj − wi + lij wj ≤ 0,

(uji − mji )wi + wj − uji wi ≤ 0

n

k=1

for fuzzy numbers of Type I,

for fuzzy numbers of Type II,

While for matrix B we have: w∗ = (w1∗ = 0.570, w2∗ = 0.112, w3∗ = 0.318) and ∗ = 0.886. The modified model (17) is however independent of the order of the criteria in the matrix and therefore applying model (17) leads to the same result for the two matrices as follows.



(uij − mij )wj + wi − uij wj ≤ 0  (mji − lji )wi − wj + lji wi ≤ 0,

Table 4 Comparison matrix B.

(17)

wk = 1,

wk > 0, i = 1, . . . , n − 1, j = 2, . . . , n, j > i, k = 1, . . . , n.

Solving the non-linear programming problem described above results in the optimal priority vector w* and *. * is interpreted as consistency index, i.e. the negative values of * means that the pairwise comparisons are strongly inconsistent while the positive values of * shows that the pairwise comparisons are consistent. * = 1 indicates full consistency. Example 1. Mikhailov and Tsvetinov [61] used ‘fuzzy AHP using FPP’ to evaluate services using three criteria: pricing, service quality and delivery time. Table 1 indicates the pairwise comparisons. Applying (13) they found the optimal vector w* and * as follows. w∗ = (w1∗ = 0.538, w2∗ = 0.170, w3∗ = 0.292) and ∗ = 0.838. In formulating the problem they used a set F = {˜aij } containing three fuzzy numbers (2, 3, 4), (1, 2, 3) and (1/3, 1/2, 1). The first two fuzzy numbers are TFN (Type I), however because the last fuzzy number (1/3, 1/2, 1) is not a TFN (it is a fuzzy number of Type II), the results are not correct. If we apply (17) to this matrix considering the two fuzzy numbers Type I: (2, 3, 4), (1, 2, 3) and the corresponding reciprocal of the fuzzy number Type II: (1, 2, 3), we will obtain the following results.

w∗ = (w1∗ = 0.575, w2∗ = 0.111, w3∗ = 0.314) and ∗ = 0.828. At face value, it appears that the differences between the weights obtained from the original model [59] and those of the modified model are not significant. However as in most real-case problems there are multiple levels of comparisons, the final results could be significantly different. 4. Implementation in real-world cases In this section, we apply the proposed methodology to evaluate the EO of 59 small to medium-sized enterprises (SMEs) and rank them based on their final EO score. We first present the process of data collection and then illustrate the implementation of the methodology. 4.1. Data collection Data was collected in a sample of start-ups in the Dutch ICT industry. We choose the ICT industry because it is a dynamic environment with rapid developments. There have been substantial

w∗ = (w1∗ = 0.535, w2∗ = 0.167, w3∗ = 0.298) and ∗ = 0.791. Example 2. Suppose we ask a decision-maker to pairwise compare the three criteria M, N, O and he/she provides the comparisons shown in Table 2. When transferring the data to a comparison matrix one may form matrix A and the other may form matrix B (Tables 3 and 4). It is obvious that the two matrices should result in a same priority vector because they are different just in their order of rows and columns. Applying the proposed model by Mikhailov [59] we however find different priority vectors. For matrix A we have: w∗ = (w1∗ = 0.576, w2∗ = 0.112, w3∗ = 0.312) and ∗ = 0.848.

Fig. 4. Hierarchy of the problem (please note that the name of sub-criteria has been shortened).

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Table 5 Criteria and sub-criteria considered to evaluate EO. Criteria

Sub-criteria

C1 : Innovativeness

C11 : Emphasis on tried and true products and services vs on R&D, technological leadership and innovation C12 : Number of marketed new lines of products and services C13 : Extent of changes in products and services lines C21 : Propensity for risk taking in projects C22 : Owing to the nature of environment C23 : Decision-making under uncertainty C31 : Initiating actions vs responding to actions of competitors C32 : Adopting vs avoiding competitive clashes

C2 : Risk-taking

C3: Proactiveness

Table 6 Fuzzy pairwise comparisons of the main criteria (dimensions).

Fig. 5. The final weights of sub-criteria.

changes in information technology in recent years. Computers and software have evolved in a rapid, complex and almost chaotic manner. These changes have a major impact on competition and strategy. As such, the new competitive landscape requires a significantly different approach compared to the past [62]. As a result, managers face major strategic decisions that are changing the nature of competition. To be included in the sample, firms had to meet the following requirements. First, they had to be operating in the Dutch ICT sector. Secondly, to make sure we included start-ups,

Goal (EO)

Innovativeness

Risk-taking

Proactiveness

Innovativeness Risk-taking Proactiveness

(1, 1, 1) (0.25, 0.33, 0.5) (1, 2, 3)

(2, 3, 4) (1, 1, 1) (4, 5, 6)

(0.33, 0.5, 1) (0.17, 0.2, 0.25) (1, 1, 1)

we limited our selection firms with a founding date between 2002 and 2004. Younger firms were excluded because we aimed at young firms that had survived the early stages, which can be considered the most critical years for small firms. Once a firm has managed to survive for three years, it has successfully passed through the “valley of death” [63,64]. After surviving the first three years, firms have to decide on a strategy that will determine their future direction. Also, their business practices presumably approximate those of established firms rather than new ventures. Finally, we used a third condition that no firm in our sample has more than 65 fulltime employees. As such, all the firms in our sample can be classified as small firms. We selected our sample from the REACH database and the Dutch Chambers of Commerce. The initial sample consisted of 67 companies (157 respondents). We asked at least two members of the management team of each firm to fill out the survey. Using a 66 percent inter-rater validity as response rate criterion, as suggested by Schippers et al., [65], and based on the criteria outlined above, the final sample consisted of 59 management teams of 59

Table 7 Fuzzy pairwise comparisons of the sub-criteria (items). Innovativeness

Innovation emphasis

No. of new lines

Change in lines

Innovation emphasis No of new lines Change in lines

(1, 1, 1) (0.2, 0.25, 0.33) (0.25, 0.33, 0.5)

(3, 4, 5) (1, 1, 1) (1, 2, 3)

(2, 3, 4) (0.33, 0.5, 1) (1, 1, 1)

Risk-taking

Risk in projects

View the environment

Cautious vs aggressive

Risk in projects View the environment Cautious vs aggressive

(1, 1, 1) (0.17, 0.2, 0.25) (0.25, 0.33, 0.5)

(4, 5, 6) (1, 1, 1) (1, 2, 3)

(2, 3, 4) (0.33, 0.5, 1) (1, 1, 1)

Proactiveness

Being introducer

Competitive behavior

Being introducer Competitive behavior

(1, 1, 1) (0.25, 0.33, 0.5)

(2, 3, 4) (1, 1, 1)

Table 8 Results -weights of criteria and sub-criteria. Criteria

Criteria weights

Sub-criteria

Sub-criteria weights

Local weights

C1 : Innovativeness

0.314

C2 : Risk-taking

0.111

C3 : Proactiveness

0.575

C11 : Innovation emphasis C12 : No. of new lines C13 : Change in lines C21 : Risk in projects C22 : View the environment C23 : Aggressiveness C31 : Action strategy C32 : Being introducer

0.622 0.143 0.235 0.646 0.125 0.229 0.750 0.250

0.195 0.045 0.074 0.072 0.014 0.025 0.431 0.144

J. Rezaei et al. / Applied Soft Computing 13 (2013) 2749–2758

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Table 9 The final aggregated EO scores of the firms. Firm #

C11

C12

C13

C21

C22

C23

C31

C32

EO

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

5 4.5 4.5 5 5.5 6 4 5 5 5 6.5 5.5 5 4 5 5 4.5 5.5 5 5 3.5 4.5 5 3.5 4.5 6.5 6 3.5 5 2.5 6.5 4.33 3.67 2.67 6.33 5.5 5.67 4.5 5.67 4.33 4.5 5.67 6.5 4 6 4.5 4.67 5.67 3.33 4.33 4.67 3.33 4.67 3.67 3.33 4.5 5 4.8 6.33

5 5 3.5 4.5 5.5 6 3.5 4.5 4.5 5.5 5.5 5 5.5 3.5 4.5 4 3 5 6 4 4 5 4 2 5.5 4.5 4.5 4 3.5 3 4.5 4 2.67 3.33 5.33 5.5 4.67 5.5 5.33 4.67 5 4.67 6.5 3.5 5.5 6.5 6.33 4.67 2.67 4.67 5.67 2.67 3.33 4.33 2.33 4.75 5.5 4.2 5.67

4 5 5.5 5 6 5.5 4 4.5 5.5 5 6 5 5 4 5.5 5 4.5 5.5 5.5 4 3 4.5 5.5 4 5 6.5 7 4 5.5 2.5 7 3.67 4.33 3.67 5.67 5 5.33 5.5 5.33 4.33 4 5.67 6 3.5 6.5 5.5 5.67 6.67 4.33 3.67 5.33 2.67 5.33 3.33 3.67 3.25 5.25 5.2 6.33

4 5.5 5.5 5 4.5 3.5 4.5 5 4.5 5 6 5.5 6 4.5 4 4 5 5.5 4.5 4.5 3.5 3.5 4.5 4.5 5.5 5.5 5.5 4.5 4.5 4 5.5 3.33 4.33 5.33 4.67 6 4.67 4.5 5.33 4.67 5 4.67 5.5 5 5.5 5.5 5.33 4.33 3.67 4.33 4.67 5.33 4.33 5.33 4.33 4.25 5.25 3.6 6.33

4.5 5.5 3.5 4.5 5 4.5 4.5 4.5 5 5.5 6.5 5 5.5 4.5 3.5 4.5 5.5 4 5 5 4 4 3.5 4 6 4.5 5.5 4 4 3.5 5 3 4.67 4.67 5.67 6 5.67 5 4.67 4.33 4.5 4.67 5 4.5 4 4.5 4.67 4.67 4.33 4.33 3.67 3.33 3.67 3.67 4.67 4.5 4.75 4.2 5.33

4.5 5.5 5 5 5 4 5 4 5.5 5.5 6 4.5 5 4.5 3.5 5 6 5.5 5 4.5 3 3.5 3.5 5.5 5.5 5.5 5.5 4.5 4.5 4.5 5.5 3.33 3.67 4.67 5.67 5.5 4.33 4.5 3.67 4.33 4.5 5.33 5.5 4 6.5 4 4.67 4.33 5.33 4.33 5.67 4.67 4.33 4.33 3.67 4.75 4.5 4.4 6

5 4.5 3.5 6 4.5 4.5 5.5 5 5 4.5 5.5 6.5 4.5 4.5 5 3 4 6.5 6.5 5.5 2.5 5 4.5 6.5 4.5 7 6.5 4.5 4.5 4 6 3.67 5.33 3.67 5.67 5.5 4.67 5 4.67 5 5.5 4.67 6.5 4.5 7 4.5 5.67 4.33 4.67 3.67 3.67 3.33 4.67 4.33 5.33 3 5.25 4.2 5.67

5.5 4 4 5.5 4.5 5 5 3.5 5.5 4.5 5.5 6.5 3.5 4 4.5 3.5 4.5 6.5 6 3.5 3 6 5 5.5 3.5 6 6 5 6.5 3.5 6 4.33 5.67 4.33 5.33 4.5 5.33 5 5.67 4.67 4.5 5.67 6 4 6.5 6 5.67 3.67 5.33 4.33 5.33 4.33 5.67 4.67 3.67 3.75 4.75 3.8 4.67

4.906 4.599 4.097 5.473 4.871 4.922 4.836 4.693 5.063 4.755 5.795 5.983 4.670 4.249 4.812 3.799 4.305 6.031 5.836 4.833 2.977 4.849 4.682 5.179 4.556 6.429 6.166 4.310 4.907 3.485 6.042 3.866 4.738 3.713 5.663 5.362 5.014 4.913 5.110 4.707 4.952 5.100 6.273 4.235 6.466 4.938 5.440 4.690 4.328 4.012 4.439 3.573 4.755 4.239 4.320 3.653 5.115 4.296 5.755

Table 10 Local weights of sub-criteria: fuzzy AHP and conventional AHP. Sub-criteria

C11 : Innovation emphasis C12 : No. of new lines C13 : Change in lines C21 : Risk in projects C22 : View the environment C23 : Aggressiveness C31 : Action strategy C32 : Being introducer

Local weights Fuzzy AHP

Conventional AHP

0.195 0.045 0.074 0.072 0.014 0.025 0.431 0.144

0.193 0.042 0.074 0.071 0.013 0.025 0.436 0.145

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Table 11 Comparison results of the local weights obtained by fuzzy AHP and conventional AHP (Wilcoxon Signed Rank Test). Ranks (FAHP-AHP)

N

Sum of ranks

Mean rank

Test Statistics (FAHP-AHP)a

Negative ranks Positive ranks Ties

2 4 2

8.00 13.00

4.00 3.25

Z Asymptotic Sig. (2-sided test)

a b

−0.530b 0.596

The significance level ˛ = 0.01. Based on negative ranks.

different firms (131 respondents). The management team averaged 2.71 members (SD = 0.87); the average age was 38.7 (SD = 4.86).

average, for the set of 59 firms, the EO is 4.844 with a standard deviation of 0.757. 4.3. Validation of the model

4.2. Results and discussion As the first step of the proposed methodology and to evaluate the EO of each firm, three criteria and eight sub-criteria are considered, as shown in Table 5. The hierarchy of the problem can be also found in Fig. 4. As the second step, we pairwise compare the criteria and subcriteria constructing the matrices of type Eq. (1). To this end, three experts in a joint meeting provided the comparisons by using the ˜ ˜ ˜ ˜ fuzzy numbers 91 , 18 , . . . , 21 , 1, . . . , 9˜ as shown in Tables 6 and 7. As the third step of the proposed methodology, solving the improved non-linear programming model, as presented in Eq. (17) for each comparison matrix we obtain crisp weights of criteria and sub-criteria, as shown in Table 8. To obtain the local weights of sub-criteria, we multiply their relative weights by the weights of the main criteria (see column 5 of Table 8 and Fig. 5). The second column of Table 8 shows that, based on the experts’ pairwise comparisons, proactiveness is considered to be by far the most important dimension of the EO. In turn, innovativeness is seen as much more important than risk-taking. The fourth column of Table 8 shows how sub-criteria, or items in the EO-scale, contribute to the dimensions. Again, considerable differences in weights were found on the basis of the experts’ evaluations. For the innovativeness dimension, the item ‘Innovation emphasis’ is the most important, for the risk-taking dimension, the item ‘Risk in projects’ is the most important, and finally, for the proactiveness dimension, the item ‘Action strategy’ is the most important. To compare the actual (or local) weights of all sub-criteria, it is important to look at the criteria weights of the three dimensions and the sub-criteria weights of the items. The actual weight of a subcriterion is the multiplication of the weight of that sub-criterion and the weight of the main criterion to which it belongs. The fifth column of Table 8 shows the multiplication of these weights for all the sub-criteria. The difference in actual weights is now emphasized: the most important sub-criterion (‘Action strategy’) has a weight that is more than 30 times bigger than the weight of the least important sub-criterion (‘View the environment’). The actual weights are shown in Fig. 5. Clearly, action strategy and innovation emphasis are the most important sub-criteria for an entrepreneurial firm, while aggressiveness and view the environment are the least important criteria. The final aggregated EO score of firm k, EOk is calculated as n EOk = w ϕ , k = 1, . . . , K, where wi is the local weight of i=1 i ik sub-criterion i; ϕik is the assigned score to firm k with respect to sub-criterion i; n is the number of sub-criteria and K is the number of firms. The final aggregated scores of the firm are shown in Table 9. In the last column of Table 9, we find the relative level of entrepreneurship of the various firms. For example, firm 45, with EO = 6.466, is considered the most entrepreneurial firm, while firm 21, with EO = 2.977, is considered the least entrepreneurial. On

In this section we study the validity of the improved fuzzy AHP to evaluate a firm’s EO. There are different approaches in existing literature to validate the models involving AHP (see e.g. [66,67]). In this study, we used two approaches to validate the improved fuzzy AHP: (1) Consistency index; and (2) A comparison of the results of the improved fuzzy AHP and conventional AHP. As proposed by [59,61] and as mentioned before, the values of  (see Eqs. (7) and (17)) can be interpreted as a consistency index such that, for  < 0 the initial judgments are inconsistent while for 0 ≤  ≤ 1, the initial judgments are consistent. The consistency rate is increased when it goes from 0 to 1 such that when  = 1 the corresponding initial judgments are said to be completely consistent. The values of  for the main criteria are 0.828 and for the sub-criteria innovativeness, risk-taking and proactiveness are 0.646, 0.828, and 1 respectively. As these values are positive and close or equal to 1, we conclude that the final weights are approximately consistent and satisfy the experts’ opinion, and that the model is valid. As the second approach to validate the model, we compare the results found by the improved fuzzy AHP to the results of the conventional AHP.3 To this end, we compare the final local weights found by the improved fuzzy AHP to the results of applying conventional AHP (geometric mean method used to find the weight vector) (see Table 10). As mentioned by Da˘gdeviren and Yüksel [67], close results can demonstrate the validity of the model. However, they did not use any measure to test the closeness. In this paper, we use the non-parametric Wilcoxon Signed Rank Test to study the median difference between the obtained results (local weights) from the two models fuzzy AHP and conventional AHP. The comparison results in Table 11 indicates that, at the level ˛ = 0.01 of significance, there is no significant difference between the results of the two models, which indicates the validity of our improved fuzzy AHP. 5. Conclusion and future research The ability to assess the level of entrepreneurship of firms is an important management tool for the firms themselves and for other organizations, such as investment bankers and incubators that are systematically evaluating such firms. Entrepreneurship orientation (EO) is a widely accepted measurement method consisting of three dimensions (innovativeness, risk-taking and proactiveness), each of which is measured using multiple items. In practice, a committee of experts can use the tool in a simple fashion by rating firms on the items and by simply adding the ratings in dimensions, and in turn, in an overall EO-score. If more firms are to be evaluated (between about forty and a hundred firms), a hybrid approach is often used in which items are combined to form dimensions using weights

3 Here, for the purpose of model validation, we assume that the criteria and subcriteria can be compared pairwise using crisp numbers.

J. Rezaei et al. / Applied Soft Computing 13 (2013) 2749–2758

that have been derived from factor analysis. These dimensions are then simply added up. When more than hundred firms are rated, a full statistical approach can be applied where the weights are also derived for the dimensions. As pointed out by some researchers (e.g. [68,69]), to increase the quality of research in the field of small firms and entrepreneurship, we should benefit from rigorous methodologies. We contribute to the existing knowledge in this field by proposing and illustrating an alternative approach, using expert evaluations as input for a fuzzy AHP. We used the EO item scores of 59 small firms. Three experts were requested to compare items in a pairwise fashion to indicate their relative contribution to their respective dimensions. In a similar fashion, these experts rated the relative importance of the dimensions within the overall EO-construct. We improved one of the best fuzzy AHPs in existing literature which was then used to assess the weights of all the items and dimensions on the basis of these pairwise comparisons. The results clearly indicate that the ‘proactiveness’ is the most important dimension in the EO-construct, followed by ‘innovativeness’ and ‘risk-taking’. The fuzzy AHP results indicate a consistent solution with the pairwise comparison data provided by the experts. It is remarkable how big the differences in weights are, both for the dimensions and for the separate items within the dimensions. The implications of these findings are profound. Assuming that the opinion of these experts is representative for other experts, we can conclude that a simple approach, for instance adding item scores to arrive at an overall EO-score, would have yielded completely different results. Firstly, fuzzy AHP allows for a deliberate weighing of the items and dimensions and thereby delivers results that match the ideas of these experts more closely. Secondly, if a simple tool was to be constructed, fuzzy AHP would have indicated that similar EO-scores could have been assessed using a very limited number of items that are simply added. Fuzzy AHP recognizes that EO is a fuzzy, multi-dimensional and perception-based tool. Although statistical approaches do so as well, they have certain disadvantages. Firstly, the statistical approach requires a relatively large number of firms, which is not always the case in practice. Secondly, the way the items and dimensions are weighed and calculated is not known by experts. Thirdly, the weights (both for items and dimensions) depend on the sample [39]. Fuzzy AHP can be applied when a limited number of cases are evaluated, the weights are assessed independently from the sample of firms and the procedure of pairwise comparisons is easier to understand for experts invited to the evaluation process. The evaluation task for fuzzy AHP can form the basis for a thorough discussion among experts, which adds to the validity of the results and the likelihood that these results will be used by these experts. In future research, other MCDM and fuzzy approaches can be applied to assess the EO of firms. We think that the social sciences in general and the field of innovation and entrepreneurship in particular can benefit from the experiences with fuzzy approaches gained in the engineering sciences. Finally, we believe that fuzzy AHP can be used, in addition the simple and statistical approaches, to assess the degree of entrepreneurial behavior of firms using the EO-construct. References [1] P.F. Drucker, Innovation and Entrepreneurship: Practice and principle, HarperBusiness, New York, 1993. [2] G.T. Lumpkin, G.G. Dess, Linking two dimensions of entrepreneurial orientation to firm performance: the moderating role of environment and industry life cycle, Journal of Business Venturing 16 (5) (2001) 429–451. [3] D. Miller, The correlates of entrepreneurship in three types of firms, Management Science 29 (7) (1983) 770–791. [4] J.G. Covin, D.P. Slevin, Strategic management of small firms in hostile and benign environments, Strategic Management Journal 10 (1) (1989) 75–87.

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