Evaluation model of competitive and innovative tourism practices based on information entropy and alternative criteria weight

Abstract

An evaluation model of competitive and innovative tourism practices in Portugal based on information entropy is proposed. The relative evolution of each criterion/construct is explored in the light of its predictability/randomness in Portuguese companies by calculating and analysing the information entropy of different perceptions on competitive and innovative tourism practices. This article presents a novel approach by using information entropy to handle probabilistically different competitive and innovative practice weights computed by alternative models such as (a) the Fuzzy Rasch model that combines the item response theory and the fuzzy set theory, (b) the fuzzy analytic hierarchy process (AHP) model and (c) the crisp AHP model based on eight different judgment scales on the relative evolution of each criterion/construct. The results show that the total information entropy suggests a strong heterogeneity in Portuguese companies in terms of innovation for competitiveness. They also reveal a significant relationship between innovative tourism practices and tourism competitiveness models.

Keywords

AHP fuzzy logic information entropy managerial practices Portugal tourism innovation and competitiveness

Introduction

Accelerated tourism growth in emerging economies increases competition among hospitality providers and demands innovative services, thus resulting in the need of a better understanding of the current status of managerial practices to improve marketing positioning and sustain a competitive advantage in the light of different perceptions.

Although some studies attempt to emphasize the role of productivity in achieving any form of competitiveness, which is emphasized by some economists, there is a gap in the literature on destination competitiveness, business relationship and innovative practices in the tourism sector (Cvelbar et al., 2016).

Despite the existence of several studies in this research field of innovation strategies in tourism, there are still very few studies that explore the relationships and variations of innovation practices in relation to business and regional competitiveness models (Abreu Novais et al., 2018; Divisekera and Nguyen, 2018; Rodríguez et al., 2014; Zehrer et al., 2016).

We approach the current knowledge gap by creating a model based on information entropy and alternative criteria weight of tourism as a construction of meaning to take a step forward in the tourism theory and practice based on innovation criteria for competitiveness (Fernandez et al., 2013; Zhang et al., 2011).

One major contribution from this article is that competitiveness and tourism business innovation practices are analysed in-depth by means of a survey conducted with 119 hospitality providers in the Autonomous Region of Madeira (RAM, Portugal).

While a 7-point Likert-type scale is used in several criteria/constructs, the main objective of this research is to compare the weights assigned to each criterion/construct by means of different methods and fuzzy logic to infer their degree of randomness/predictability, so that innovation and competitiveness practices and perceptions could be discussed in terms of homogeneity among hospitality providers.

This article also unveils how these different practices and perceptions are tied together in terms of weight importance. In this research, information entropy is the cornerstone method used to assess the randomness/predictability of each practice based on the weights computed from alternative multicriteria methods such as the item response theory (IRT) and the analytic hierarchy process (AHP) in both its fuzzy and its crisp versions.

Compared with other methods, information entropy provides higher accuracy and superior objectivity, which can bring a more comprehensive interpretation of the results. Also worth mentioning is that information entropy is suitable for all the decision-making processes that require weight determination. Therefore, information entropy is used here to determine the weights of various constructs/criteria and to provide support for the IRT and AHP methods used.

This article has four more sections. A literature review is given in the second section, while data and methods are presented in the third section. The fourth section analyses and discusses the results, and the conclusions are elaborated in the final section.

Literature review

Innovative tourism practices

Innovation is understood as a process by which opportunities are transformed into practical utilities and may occur within a social, cultural, economic and specific context in the business world (Bowie, 2018; Zhang and Hartley, 2018).

Some previous studies have addressed the importance of stimulating various factors for the practice of innovation (Batle et al., 2018; Darroch, 2005; Li, 2014), while others have shown some advances in understanding the factors or barriers that determine favourable or unfavourable conditions of competitiveness for tourist destinations. Innovation practices are identified as an important tool for developing a company’s growth capacity and have been discussed at a variety of levels by academics and local policymakers rather than by regional and national policymakers (Backman et al., 2017; Farinha, et al., 2016).

Literature in the field of tourism has paid little attention to developing more or less complex innovation strategies by means of either technological or non-technological innovation (Martin-Rios, 2019). There are several practices and metrics used to measure innovation performance over time and what impact they may have on the performance of new products or services, thus reflecting on the competitiveness of companies (Grillo et al., 2018).

Some academic perspectives when incidentally commenting on knowledge transfer studies and innovative competitive practices in tourism organizations sometimes refer to the growing interest in acquiring competitive knowledge within companies and destinations (Stejskal et al., 2016; Teixeira et al., 2019). One suggestion is that the relative absorptive capacity of acquisition and the ability to exploit external knowledge by organizations differentiates them as innovators from non-innovators in relation to both firms and destinations (Thomas and Ormerod, 2017).

At the regional level, there is a direct cross-reference between the creators of innovation and the users of innovation (Wokoun, 2010). Regional prosperity (Corvers, 2003), therefore, depends on a region’s ability to identify and compensate for deficiencies in the competitiveness of tourism, innovation and clusters applied to regions and enterprises in this sector.

Innovation is considered a critical factor in the success of tourist destinations when facing competition and this is one of the social and economic determinants of market demand (Zach and Hill, 2017). Tourist products, for example, are key cards that attract tourists to specific destinations. Diversification, intensification and the combination of these products can be crucial for the competitiveness of companies and for the sustainable development of the regions (Benur and Bramwell, 2015).

The weaker the combination of innovation factors, the greater the difficulties in overcoming the barriers to innovation and the greater the difficulties in obtaining competitive advantages (Maury, 2018). Thus, the need arises to understand how a company can identify its own resources so as to value the rare and valuable resources that can improve levels of business competitiveness through innovation factors or other strategic factors (Ferreira and Fernandes, 2017).

Tourism competitiveness

The large increase in global competitiveness means that tourism companies face great challenges to maintain their competitiveness, which has led many researchers to seek a better approach to conceptualize and measure business tourism competitiveness (Bojnec and Ferto, 2016; Cvelbar et al., 2016). The notion of competitiveness is broad and involves any resource that a company or destination can use to gain a competitive advantage. Our analysis makes an important contribution to these studies and is interested in measuring the performance of companies in the tourism sector. The competitiveness of a tourism destination, as well as the competitiveness of its companies, depends on their capacity to reinvent themselves, innovate and face the challenges and obstacles that often prevent the insertion of innovative factors in either developing a company activity or a tourist destination.

The competitiveness of a destination, defined as its ability to highlight its local tourist attractions and provide services and experiences capable of attracting more tourists than other destinations, has undoubtedly been a matter of extreme scientific relevance in the field of tourism competitiveness studies (Cibinskiene, 2012). In this sense, tourism of events has been provoking a growing interest on the part of several researchers from the most diverse areas from both the conceptual and the empirical point of view (Cibinskiene, 2012; McKercher, 2016; Montenegro, 2017; Panfiluk, 2015; Tiew et al., 2015).

Despite the already existing contribution from the literature on competitiveness and innovation in the tourism sector, there is still a lack of clarity and consensus on how these areas relate (Henderson et al., 2018). The search for competitiveness has been a major concern for regions and companies around the world (D’Ippolito, 2014).

As tourism is an important cluster in the development and competitiveness of regions, it is relevant to analyse the potential of this sector (Chhetri et al., 2017) and it becomes important to explore, identify and analyse critical factors and barriers in the success of business models that are likely to be increasingly innovative and competitive in the market (Long et al., 2018).

Tourism is fundamental for the development of new clusters capable of sustaining regional competitiveness, bringing challenges to the tourism and cultural sector and nourishing its competitiveness (Alberti and Giusti, 2012; Jackson and Murphy, 2002; Zan et al., 2007). The Cibinskiene and Snieskiene (2015) conceptual model on the competitiveness of tourism highlights internal and external environmental factors, emphasizing that internal environmental factors constitute competitive conditions for tourism. The groups of external factors include political, economic, social, cultural, ecological, natural and technological factors, while the internal environmental factor groups include tourism companies, tourist resources, tourism and recreational infrastructures.

The competitiveness of a destination is understood as a combination of competitive and comparative advantages. Comparative advantages include inherited resources such as climate, landscapes, fauna, flora, handicrafts and typical products, while the competitive advantages are related to created items such as management quality, tourism structure, worker skills and government policies (Wilde et al., 2017). We can define regional competitiveness as the ability of regions to provide an attractive place for companies and inhabitants to live and work (Annoni and Dijkstra, 2010). Dunning et al. (1998) argue that competitiveness is a way of discussing the relative performance of the economy in a comparative sense.

Management skills, the existence of tourism programs, cooperation between the public and private sectors, resorts and wellness resorts, information and tourist guidance, casinos, nightlife and the use of e-commerce are among the key aspects for the competitiveness of any destination (Armenski et al., 2011). The vision of the destination in relation to the values of the tourism experience, the residents, the stakeholders and the community also emerge as essential factors for the competitiveness of the tourist destination according to the perspective of Armenski et al. (2011).

The planning and implementation of innovative practices is very complex and articulated with elements of success as it creates coherent synergies among stakeholders and requires a modern organisational structure. There are many stakeholders in the tourism planning process to devise participatory strategies to create and enable business opportunities that require greater effort and concentration to leverage their resources (Carrà et al., 2016; Cruz et al., 2016; D’Ippolito, 2014).

Regional competitiveness contributes positively to the competitiveness of firms located in a particular cluster and where firms can take advantage of the network-based interaction effects with other firms leading to more competitive advantages (Lechner and Leyronas, 2012).

The competitiveness of companies is also related to the competitiveness of the product and to production efficiency, position and organization’s effectiveness in terms of restructuring and sales and its stimulation in the search for these same products (Ahmedova, 2015). One of the foundations for the entanglement between the competitiveness of tourism companies and the competitiveness of the tourist destination in which the companies are located lies in the nature of the product and how a tourism product is integrated (Camisón, 2015; Go, 1992).

Tourist products are a conglomerate, an amalgam and a set of tangible and intangible elements that from the point of view of the competitiveness of companies located in a certain destination. In this sense, in a way, integrated tourism products offer all companies potential for competitiveness, which includes complementary activities and products such as accommodation, transportation, catering and entertainment companies incorporating attributes that highlight value when deciding to buy (Camisón, 2015; Loukissas and Triantafyllopoulos, 1997).

Applying a macroeconomic approach, business competitiveness highlights comparative advantages that tourism companies can obtain with different allocations and costs with the resources available in their environment and another broad set of institutional, economic and social variables along with legal policies that help define a given space as more attractive for the development of the business activity (Camisón, 2015).

Methodology

The data

This study uses primary data collected from a sample of 119 Portuguese companies that maintain activity in the RAM, a Portuguese island region located in the Atlantic Ocean. The data were collected between June 2017 and April 2018 in which a first phase was carried out through an online questionnaire sent to each company and in a second phase by means of personal interviews directly with the company representative.

The sample universe consisted of the 500 largest companies operating in the Portuguese tourism sector as registered in 2017. This was the total amount of companies initially targeted in the study. The actual sample of respondents was formed according to the size and its main activity areas in tourism and in terms of their willingness to respond to the online questionnaire.

Before actual data collection and with the objective of ensuring clarity, quality and a complete understanding of the questionnaire, we conducted a pilot test with 21 entrepreneurs from the tourism sector so as to improve the adequacy of the questions (Atapattu, 2018; Boley et al., 2018; Yen and Tang, 2019; Zainuddin et al., 2013). On the basis of the observations considered, we modified and improved some issues to avoid any ambiguity. The pilot study contained 13 questions with 184 sub-items, and at this stage, data were gathered from 25 companies with an overview of activities related to innovation practices and models of business tourism competitiveness and destination competitiveness with responses by email and personal interviews.

As for the data collection in relation to the percentage of respondent entrepreneurs, who are the owner or manager of the company, we can mention that 68.1% were male with an average age of 47.8 ± 10.2 years and 55.5% had a higher education degree. As for the companies in the activity sector, 40.3% were concentrated in lodging as the main activity, 21.0% were service companies and 18.5% worked with artistic performance, sports and entertainment activities and have been in business for an average of 15.6 ± 27.2 years. Around 52.1% had their location in Funchal while 89.9% had no capital controlled by any other company, whereas 41.2% had 2017 turnover levels lower than € 20,000 with 28.6% of these companies recording a volume of € 500,000 and an average of 19.1 ± 54.2 staff members (see Table 3). The aim here is to empirically contribute to analysing the importance of the factors and barriers to innovation in the tourism business competitiveness.

Table 1.

Example of judgement scales used in AHP.

Scale type	Mathematical description	Parameters	Approximate scale values
Linear (Saaty, 1977)	S = x	x = {1,2,…,5}	1;2;3;4;5
Power (Harker and Vargas, 1987)	S = x ²	x = {1,2,…,5}	1;4;9;16;25
Square root (Harker and Vargas, 1987)	S = √x	x = {1,2,…,5}	1;√2;√3;2;√5
Geometric (Lootsma, 1989)	$s = 2^{x - 1}$	x = {1,2,…,5}	1;2;4;8;16
Inverse linear (Ma and Zheng, 1991)	$s = \frac{9}{(10 - x)}$	x = {1,2,…,5}	1;1.13;1.29;1.5;1.8
Asymptotical (Dodd and Donegan, 1995)	$s = tan h^{- 1} (\frac{\sqrt{3} (x - 1)}{14})$	x = {1,2,…,5}	0;0.12;0.24;0.36;0.46
Balanced (Salo and Hamalainen, 1997)	$s = \frac{w}{(1 - w)}$	w = {0.5, 0.55, 0.6,…,0.9}	1;1.22;1.5;1.86;2.33;4;5.67;9
Logarithmic (Ishizaka et al., 2010)	$s = {log}_{2} (x + 1)$	x = {1,2,…,5}	1;1.58;2;2.32,2.58

Note: AHP: analytic hierarchy process.

Table 2.

Membership function of linguistic scales for pairwise comparison of performance criteria.

Intensity of importance of each criterion	Linguistic scale or verbal judgement of preference in pairwise comparison	TFN scale	Reciprocal TFN scale
1	Equal importance	(1, 1, 1)	(1, 1, 1)
2	Intermediate values between adjacent scale values	(1/2, 3/4, 1)	(1, 4/3, 2)
3	Moderate importance	(2/3, 1, 3/2)	(2/3, 1, 3/2)
4	Intermediate values between adjacent scale values	(1, 3/2, 2)	(1/2, 2/3, 1)
5	Strong importance	(3/2, 2, 5/2)	(2/5, 1/2, 2/3)
6	Intermediate values between adjacent scale values	(2, 5/2, 3)	(1/3, 2/5, 1/2)
7	Extreme importance	(5/2, 3, 7/2)	(2/7, 1/3, 2/5)
8	Intermediate values between adjacent scale values	(3, 7/2, 4)	(1/4, 2/7, 1/3)
9	Extremely high importance	(7/2, 4, 9/2)	(2/9, 1/4, 2/7)

Note: TFNs: triangular fuzzy numbers.

Table 3.

Descriptive statistics of each contextual variable used in the neural network analysis.

		N	%
Gender	Female	38	31.9
Gender	Male	81	68.1
Age (in years), average ± SD/median (range)		47.8 ± 10.2/48 (26–78)
Higher education qualifications	Without higher education degree	53	44.5
Higher education qualifications	With higher education degree	66	55.5
Sector of activity	Lodging	48	40.3
	Restaurants and similar	10	8.4
	Services	25	21.0
	Artistic performance, sports and recreation	22	18.5
	Transportation	6	5.0
	Others	8	6.7
Years of company in business, average ± SD/median (range)		15.6 ± 27.2/6 (0–181)
Company location	Funchal	62	52.1
Company location	Other municipalities	57	47.9
Company capital controlled by another company?	No	107	89.9
	Yes: from 25% to 50%	1	0.8
	Yes: over 50%	11	9.2
Turnover	Less than €20,000	49	41.2
	From €20,001 to €40,000	12	10.1
	From €40,001 to €60,000	3	2.5
	From €60,001 to €100,000	6	5.0
	From €100,001 to €200,000	7	5.9
	From 200,001 to €300,000	2	1.7
	From €300,001 to €400,000	5	4.2
	From €400,001 to €500,000	1	0.8
	Over €500,000	34	28.6
Total number of employee, average ± SD/median (range)		19.1 ± 54.2/3 (0–504)

Note: SD: standard deviation

The methods

Multiple criteria decision-making (MCDM) is a research field focused on evaluating a set of alternatives based on multiple criteria/constructs (Tsaur et al., 1997; Wang and Lee, 2009). The most common methods used to determine the weights of the criteria/constructs include the entropy method (Singh and Benyoucef, 2011; Tsaur et al., 1997), information entropy weight (Zhang et al., 2011), AHP (Dagdeviren et al., 2009; Tsaur et al., 1997; Yu et al., 2011), fuzzy AHP (FAHP) (Gumus, 2009; Sun, 2010; Wang et al., 2009), and rough AHP (Aydogan, 2011).

Liang and Ding (2003) particularly focused on expert knowledge and experience to determine the weights of the criteria/constructs based on perceptual Likert scales. However, the inherent uncertainty and subjectivity of this scale can result in weighting errors and problems in the criteria/constructs weight selection process. As a result, the subjectivity of the criteria/constructs weight selection process varies among experts. A growing research field comprises the association of fuzzy numbers with linguistic variables so that the vagueness of expert opinions on criteria/constructs could be adequately assessed. For example, Mahdavi et al. (2008) and Hsieh et al. (2004) have used linguistic variables proposed by Buckley (1985) ranging from ‘very unimportant’ to ‘very important’ to express the fuzzy numbers. Kaufmann and Gupta (1991) and Mon et al. (1994) have also used linguistic variables to express the fuzzy numbers assigned by the experts.

However, the linguistic variables defined by Buckley (1985), Kaufmann, and Gupta (1991) and Mon et al. (1994) assume that different experts assign the same fuzzy numbers to each criterion/construct, whereas in reality the inherent uncertainty of the criteria/constructs weight selection process still varies among experts in an uncertain fashion. Therefore, this research focuses on this gap by assessing how weights may vary among different MCDM methods as an attempt to explore the underlying preferences among experts. This is the focus of the next sections.

Item response theory

The IRT is a discipline devoted to analysing criteria/constructs and scale performances as well as the relationships between these performances and the criteria/constructs measured by the scale itself (Meads and Bentall, 2008). One method applied in this study is the Fuzzy Rasch model, which combines the Rasch model with the fuzzy theory (Rasch, 1960). Basically, the Rasch model is used to generate fuzzy weights for each expert and subsequently an arithmetic average is used to integrate the fuzzy weight of each expert. Lastly, the defuzzification weights are obtained for the sake of comparability with other models such as AHP and FAHP, as discussed in the following sections.

The rating scale model (RSM) devised by Andrich (1978) applies Rasch’s model to polytomous rating scale instruments, which include the 5-point Likert scale. The Rasch model is based on the concept that the probability of correctly measuring a criterion/construct on the scale is a function of a latent trait or ability (Kastrin and Peterlin, 2010). Since Andrich (1978) developed RSM, it has been extensively adopted by scholars to assess the values of criterion/construct and expert parameters as shown in the following equation:

log (\frac{P_{n i j}}{P_{n i (j - 1)}}) = θ_{n} + (δ_{i} + τ_{j})

where $P_{n i j}$ and $P_{n i (j - 1)}$ represent the probability that the criterion/construct n obtains j and $j - 1$ scores from the expert i. $θ_{n}$ represents the measure score of criterion/construct n, $δ_{i}$ represents the scores assigned by expert i and $τ_{j}$ represents the linguistic score j assigned by expert i to criterion/construct n. The step difficulty of RSM is identical for all criterion/construct (Wright and Masters, 1982). Thus, RSM is useful if the distances between scores are identical for all criterion/construct (Kim and Hong, 2004) as is the case for the Likert scales.

δ_{i j} = \sum_{n} δ_{n i} + τ_{j}

where $i = 1, \dots, E$ and E represents the number of experts. $j = 1, \dots, m$ and $m$ represents the number of linguistic scores, which range from ‘very unimportant’ to ‘very important’.

Analytic hierarchy process

AHP is a well-known MCDM developed by Saaty (1977) that can help in achieving better judgments based on hierarchy, pair-wise comparisons, judgment scales, allocation of criteria/constructs weights and selection of the best alternative from a finite number of variants by calculating their utility functions. Since its inception, there has been a growth of applications and mathematical developments related to this method.

Specifically, AHP uses a ratio scale that is dimensionless, different from measurements on interval scales. The judgment is a relative value of two criteria/constructs having the same scale. The decision maker does not need to provide a numerical judgement, but a relative verbal appreciation is sufficient instead. The results of paired comparisons for n criteria/constructs are organised into positive reciprocal matrices (Saaty, 1977).

One of the most prominent features of AHP is to evaluate quantitative as well as qualitative criteria/constructs on the same preference scale. These can be numerical, verbal or graphical. Although the use of verbal responses is intuitive, it may also allow some ambiguity in non-trivial comparisons. In Saaty’s original AHP, the verbal statements are represented by a scale with increments from one to nine. Theoretically there is no reason to be restricted to these numbers and verbal gradation. Although the verbal gradation has not been a concern, several other numerical scales have been proposed (Table 1) that are used in this research for the sake of robustness and comparison of criteria/constructs weights.

Fuzzy AHP

FAHP is a development of Saaty’s AHP method (1977) to handle vagueness in criteria/constructs measurements. Analogously, the elements in the reciprocal matrices are represented by fuzzy numbers instead of crisp ones (Chiou et al., 2005; Huang et al., 2008). Many articles have been published in the literature on both the theory and the application of FAHP (Ahlatcioglu and Tiryaki, 2007; Stefanović et al., 2015). A vast literature review of the relevant techniques can be found in Kahraman et al. (2004). Operational scales for FAHP can be found, for example, in Abdel-Kader and Dugdale (2001) and Wang and Chen (2007). They are used in this research due to their widespread application. Table 2 presents the importance scale for each criterion/construct (Amiri, 2010; Kordi, 2008; Ozcan et al., 2010).

In general terms, FAHP computations should observe the following steps (Lu et al., 2007; Shaverdi et al., 2011), as described in the following:

Step 1: Determine the relative importance of the criteria/constructs. By a pairwise comparison, the matrix R̃ containing fuzzy estimates for the relative significance of each criterion/construct pair is built as follows:

\tilde{R} = \begin{matrix} C_{1}_{} C_{2} \dots C_{n} \\ \begin{matrix} C_{1} \\ C_{2} \\ ⋮ \\ C_{n} \end{matrix} & [\begin{matrix} {\tilde{r}}_{11}_{} {\tilde{r}}_{12} \dots {\tilde{r}}_{1 n} \\ {\tilde{r}}_{21} {\tilde{r}}_{22}_{} \dots {\tilde{r}}_{2 n} \\ ⋮ ⋮ ⋱ ⋮ \\ {\tilde{r}}_{n 1} {\tilde{r}}_{n 2} \dots {\tilde{r}}_{n n}_{} \end{matrix}] \end{matrix}

More precisely, pairwise comparison matrices of all the criteria/constructs in the hierarchy system’s dimensions were built through the survey developed for this research. Linguistic terms by triangular fuzzy numbers (TFNs) were assigned to these pairwise comparisons by eliciting from each expert their viewpoint criteria according to the display in Table 2, such as:

\tilde{R} = [\begin{matrix} 1_{} {\tilde{r}}_{12} \dots {\tilde{r}}_{1 n} \\ {\tilde{r}}_{21} 1_{} \dots {\tilde{r}}_{2 n} \\ ⋮ ⋮ ⋱ ⋮ \\ {\tilde{r}}_{n 1} {\tilde{r}}_{n 2} \dots 1_{} \end{matrix}] = [\begin{matrix} 1_{} {\tilde{r}}_{12} \dots {\tilde{r}}_{1 n} \\ 1 / {\tilde{r}}_{21} 1_{} \dots {\tilde{r}}_{2 n} \\ ⋮ ⋮ ⋱ ⋮ \\ 1 / {\tilde{r}}_{n 1} 1 / {\tilde{r}}_{n 2} \dots 1 \end{matrix}]

Step 2: Calculate fuzzy estimates for the weights of the criteria/constructs based on the matrix R, squaring the Triangular Fuzzy Matrices (TFMs) several times until convergence of the weights.

Step 3: Make pairwise comparisons of alternatives under each of the criterion/construct individually. Then, n matrices $(R^{1}, R^{2}, \dots R^{n})$ are built, each of which contains fuzzy estimates for the relative significance of each criterion/construct pair.

R^{i} = \begin{matrix} A_{1} \\ A_{2} \\ ⋮ \\ A_{m} \end{matrix} [\begin{matrix} {\tilde{r}}_{11}^{i} {\tilde{r}}_{12}^{i} \dots {\tilde{r}}_{1 m}^{i} \\ {\tilde{r}}_{21}^{i} {\tilde{r}}_{22}^{i} \dots {\tilde{r}}_{2 m}^{i} \\ ⋮ ⋮ ⋱ ⋮ \\ {\tilde{r}}_{1 m}^{i} {\tilde{r}}_{2 m}^{i} \dots {\tilde{r}}_{m m}^{i} \end{matrix}]

Step 4: Calculate fuzzy estimates for the weight of each alternative under each criterion separately based on the matrices $({\tilde{R}}^{1}, {\tilde{R}}^{2}, \dots, {\tilde{R}}^{n})$ . More precisely, compute the fuzzy weights of each criterion/construct by TFMs multiplication, squaring the TFM several times and using Buckley (1985) normalisation at each iteration, which is described as follows:

\tilde{r} = {({\tilde{a}}_{j 1} \otimes {\tilde{a}}_{j 2} \otimes \dots {\tilde{a}}_{i n})}^{\frac{1}{n}}

{\tilde{w}}_{i} = {({\tilde{r}}_{1} \otimes \dots \otimes {\tilde{r}}_{n})}^{- 1}

where ${\tilde{a}}_{i n}$ is a fuzzy comparison value of criterion i to criterion n; thus, ${\tilde{r}}_{i}$ is a geometric mean of fuzzy comparison value of criterion $i$ to each criterion. ${\tilde{w}}_{i}$ is the fuzzy weight of the ith criterion, which can be indicated by a TFN, ${\tilde{w}}_{i} = (L w_{i}, M w_{i}, U w_{i})$ . Here, $L w_{i}, M w_{i}$ and $U w_{i}$ stand for the lower, middle and upper values of the fuzzy weight of the ith criterion. As discussed in Thomason (1977), Hashimoto (1983), Kandel (1996), and Kolodziejczyk (1988), these three values converge to the same crisp number as a result of the convergence of the power sequence of TFMs for a large number of iterations where they are squared each time. With respect to this result, this research differs from previous studies insofar as an exact solution is found for each criterion weight (Mcaleer et al., 2007).

Step 5: Obtain a final score for each alternative by adding the weights per alternative obtained in Step 4 multiplied by the weights of the corresponding criteria obtained in Step 2.

Information entropy

Information entropy can be a measure of uncertainty is a probabilistic concept. Depending on the entropy characteristics, the randomness and dispersion of a criterion/construct can be determined by calculating the information entropy. The greater the value of the information entropy, the greater the randomness or the dispersion of the criteria/constructs weights (Núñez et al., 1996). In this article, information entropy is used to analyse the distribution of criteria weights obtained from IRT, AHP and FAHP through which a novel assessment is established to estimate the homogeneity among managerial practices, motivations, barriers and distinct stakeholders. There are some concepts based on the following considerations during the information calculation process.

Step 1. It is assumed that there are n criteria/constructs $X_{1}, X_{2}, X_{3} \dots X_{n}$ related to an event, the values of which make up the decision-making matrix D as follows:

D = [\begin{matrix} d_{11} d_{12} \dots d_{1 n} \\ d_{21} d_{22} \dots d_{2 n} \\ \dots \dots \dots \dots \\ d_{m 1} d_{m 2} \dots d_{m n} \end{matrix}]

Step 2. Transform the decision-making matrix D into a decision-making matrix R by normalization to obtain the weight of each criterion/construct as follows:

R = [\begin{matrix} r_{11} r_{12} \dots r_{1 n} \\ r_{21} r_{22} \dots r_{2 n} \\ \dots \dots \dots \dots \\ r_{m 1} r_{m 2} \dots r_{m n} \end{matrix}]

Along this line, the sum of each column element equals 1, or in other words, the decision-making matrix R satisfies the equation as follows:

\sum_{i = 1}^{m} r_{i j} = 1, j = 1, 2, 3 \dots, n

Step 3. The vectors column $(A_{1}, A_{2} \dots A_{n})$ of the normalized decision-making matrix R, namely the criteria/constructs values ( $r_{1 j}$ , $r_{2 j}$ … $r_{m j}$ ), is treated as a probabilistic distribution of information. Therefore, the information entropy E_j of the criterion/construct X_j is defined as follows:

E_{j} = \frac{1}{ln m} \sum_{i = 1}^{m} r_{i j} ln r_{i j}, j = 1, 2, 3 \dots, n

where 0 ≤ E_j ≤ 1.

Analysis and discussion of results

Density plots for the weights computed with each model for the sub-criteria/constructs are depicted in Figure 1. The respective weights for each criterion/sub-criterion are given in the Online Appendix together with their respective Cronbach’s alpha, which is a well-known measure of criterion/construct reliability. While it is possible to affirm that weights are somewhat dispersed and information entropy tends to be high, both fuzzy models (Fuzzy IRT and FAHP) presented smaller dispersion when compared to AHP models and its scale variants. This may reflect the fact that fuzzy models only capture scale vagueness apart from random effects.

Figure 1.

Density plot for the sub-criteria weights computed with each model. IRT: item response theory; AHP: analytic hierarchy process.

As regards the main criteria/constructs, Figure 2 reveals that information entropy is high (above 0.85) in all of them, thus suggesting that weights assigned to tourism competition and innovation practices/perceptions in RAM-Portugal, as well as to their interrelationships with marketing positioning and other critical factors, are strongly dispersed, suggesting heterogeneity among companies on how they perceive these respective issues.

Figure 2.

Information entropy versus weight importance scatterplot.

The three criteria with higher weights are related to the perceptions on (i) how the RAM-Portugal tourist destination stands as a competitive choice in the light of several sub-criteria related to tourist attractions, infrastructure and hospitality (criterion 8); (ii) how favourably different competitive actions and strategies at the government level impact the RAM-Portugal tourist destination choice (criterion 7) and (iii) how favourably different business environmental factors impact the RAM-Portugal tourist destination choice in the light of the other destinations/competitors (criterion 9), in that order. On the other hand, the three criteria with smaller weights are related to the perceptions on (i) the importance of innovation activities at the company level (criterion 10), (ii) the importance of innovation barriers at the company level (criterion 12) and (iii) the importance of managerial competitive practices at the company level (criterion 11).

These results suggest that competitive actions taken at the government level, or the business environment per se, are perceived as more important than innovative and competitive practices taken at the company level, possibly as a consequence of the different barriers that exist to innovate at the company level, such as lack of economies of scale (business is too small) or educational background (managers do not even know how to begin their innovation task). Therefore, this may help explain why sometimes tourism innovation initiatives at the company level fail or are simply negligible despite government efforts to create an adequate business environment to promote them. These issues are further explored by means of cluster analysis, as discussed next.

Two clusters were found as the optimal split solution for the observations: cluster 1 is formed by perception weights on actions taken at the government and company levels, besides the perceptions on the business environment and the natural competitive advantages of RAM-Portugal as a tourist destination choice. Cluster 2 is formed solely by the perception weights on innovation barriers (cf. Figure 3 on the left). Results for the cluster validity tests are given in the Online Appendix. It is interesting to note that information entropy and importance weights computed for each sub-criteria are negatively correlated (−0.38), which suggests that the lower importance attributed by RAM-Portugal tourism companies to a given (sub-)criteria, the higher the heterogeneity of perceptions among them (cf. Figure 3 on the right).

Figure 3.

Results for the k-means cluster analysis on sub-criteria weight and information entropy.

Results for the cluster analysis and MCDM weights are given in the Online Appendix. It is also worth noting that while the innovation barriers sub-criteria presents the lowest weights and information entropy scores, it is still possible to affirm that the perceptions on innovation barriers by RAM-Portugal tourism companies are indeed heterogeneous among them.

The sources of this trade-off between heterogeneity (information entropy) and importance (weights) are now explored by means of artificial neural networks (ANNs) where two nested regressions are computed to assess the relative importance of each contextual variable on such behaviour so that the light can be shed on the design of policies to improve touristic inflow in RAM-Portugal while sustaining competitiveness and innovativeness in their tourism companies. The functional form of this nested regression model is given by y (information entropy, weight importance|sub-criteria) = x b, where y is a vector of the dependent variable conditional to each sub-criterion, x is a vector of the contextual variables at the company level and b is their respective coefficients that minimize the forecasting error of both dependent variables and can be assessed by means of sensitivity analysis. A linear additive functional form was assumed, and it is noteworthy that scalar contextual variables were standardized between 0 and 1 so that their relative importance could be unbiasedly assessed altogether with all other dummy variables used in the ANN regression. Table 3 reports on the descriptive statistics of the contextual variables used in the ANN regression, indicating whether they are dummy or scalar variables.

All analyses concerning this model were developed in R using a combination of existing libraries and scripts developed by the authors, which are available upon request. In this regard, the R package NeuralNetTools was used as the cornerstone for computing the relative importance (b’s) of the contextual variables in this nested ANN regression, given as the sum of the product of connection weights between y and x, as proposed by Olden et al., 2004. An advantage of this approach is that the relative contributions of each connection weight are maintained in terms of both magnitude and sign. An additional advantage is that Olden’s algorithm is capable of evaluating neural networks with multiple hidden layers. These fundamental neural network constituents are described next.

Precisely, ANNs are computational algorithms that are based on the human thinking paradigm. ANNs are made up of processing units (neurons) that are linked by weighted connections. These connections motivate the estimation of non-linear models by using a training data set. In this research, we particularly look at the multilayer perceptron (MLP) network that has been the most used in ANN architectures for forecasting (Mubiru and Banda, 2008). In an MLP, neurons are grouped in layers and only forward connections exist. This provides a powerful architecture that enables learning of any kind of continuous non-linear mapping. A typical MLP consists of an input, hidden and output layer (cf. Figure 4).

Figure 4.

Example of an MLP (left) and details of a neuron from the hidden layer (right). MLP: multilayer perceptron.

Other components include neurons, weights and a transfer function. An input x_j is transmitted through a connection that multiplies its strength by a weight $w_{i j}$ giving a product $x_{j} w_{i j}$ . This product is an argument to a transfer function f that yields an output y_i represented by $y_{i =} f (\sum_{j = 1}^{n} x_{j} w_{i j})$ , where i is a neuron index in the hidden layer and j is an input index to the neural network. In this article, our aim is to unveil the overall endogenic behaviour between heterogeneity (information entropy) and importance (weights) in RAM-Portugal tourism companies by means of MLP, taking contextual variables as the explanatory ones at the sub-criteria level (cf. Figure 3 on the right). This research, therefore, differs from previous studies in the tourism sector by applying MLP network structure to unveil information entropy and importance weights endogeneity in terms of the contextual variable set, such as y (information entropy, weight importance|sub-criteria) = f (contextual variables).

As regards the ANN training, which is known as the process of modifying the connection weights described in Figure 4, not to confuse them with the importance weights for each sub-criteria, in some orderly fashion using a suitable learning method, we observed the connection weight approach (CWA) described by Olden et al. (2004) and Olden and Jackson (2002). CWA calculates the product of the raw input-hidden and hidden-output connection weights between each input neuron and output neuron and sums the products across all hidden neurons so that the relative importance of each contextual variable in predicting information entropy or the weight importance of each sub-criteria can be adequately computed.

According to Olden et al. (2004), CWA is proven to provide the best overall methodology for accurately quantifying the relative importance of each contextual variable and should be favoured to the detriment of other approaches. CWA successfully identifies the true importance of all the contextual variables in the ANN, including contextual variables that exhibit both strong and weak correlations with the response variables information entropy and importance weights for each sub-criteria.

Results for the optimal ANN with 31 neurons and 9 layers (minimal root mean square error: 0.00174) are presented in Figure 5.

Figure 5.

Heat map for the relative importance of each contextual variable (blue indicates positive importance and red indicates negative importance).

For each combination of neurons and layers in search of the optimal architecture, 20% of the data were used for training the network in a random sample without repetition. Readers should note that, as expected, the relative importance of each contextual variable for the information entropy and importance weights are negatively correlated, thus corroborating to the fact that the higher the data heterogeneity, the lower its perceived importance. With respect to the most relevant contextual variables in explaining the barriers for innovation (criteria 12), the results show that the educational level of the expert, the size of the tourism company, the location of the company and the alternative competitive destinations are the most important drivers in explaining why innovation is low in RAM-Portugal. These results corroborate with other previous studies (Almeida and Garrod, 2016; Azagra-Caro et al., 2017; Chirieleison et al., 2013; Estevao and Ferreira, 2012; Miwa and Bell, 2017).

Conclusions

This study sought to evaluate a model of competitive and innovative tourism practices in Portuguese companies based on information entropy factors and barriers that determine the success of implementing innovation in business tourism competitiveness as well as broaden the critical thinking about companies in the tourism sector. From the theoretical point of view, this study provides and validates a set of criteria/constructs that captures innovative practices and its implications on tourism competitiveness. It also recognizes the relevant role of capital (size) and labour (human resource quality) as cornerstones for adopting innovative practices in business, which is in line with previous researches (Abdu and Jibir, 2018; Hwang et al., 2019; Pikkemaat et al., 2018; Ye et al., 2019).

From a practical point of view, this study offers managers, companies, tourism destinations and policymakers a pathway to leverage innovation and competitiveness in RAM tourism activity. It seems that a friendly tourism business environment and legislation in Portugal will not suffice to sustain tourism innovation and competition against other destinations in the world, as long as appropriate training and capacitation are not provided through tourism companies for its employees. Funding for this industry initiative may be required to structure training courses on service quality principles and on how digital innovations may help in service quality differentiation. Besides, more incentives to mergers and acquisitions are deemed necessary to scale-up small businesses into larger tourism operators leveraged by digital platforms.

Among some of the limitations of the study is that the unit of analysis is a specific sector in a particular region. Therefore, it would be interesting in future studies to apply the same questionnaire to the entire Portuguese territory and also to make international comparisons with other countries and/or tourist regions. Finally, it also could be interesting to resort to integrate quantitative and qualitative methodologies as well through the triangulation of methodologies to return the most robust results (Cunningham et al., 2017; Koc and Boz, 2014) on some of the business strategies capable of returning sustainable regional competitive advantages.

Supplemental material

supplement_material - Evaluation model of competitive and innovative tourism practices based on information entropy and alternative criteria weight

supplement_material for Evaluation model of competitive and innovative tourism practices based on information entropy and alternative criteria weight by Sérgio J Teixeira, João J Ferreira, Peter Wanke and Jorge Junio Moreira Antunes in Tourism Economics

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Peter Wanke

Supplemental material

Supplemental material for this article is available online.

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