4.1. Results
In the preliminary stage, the assessment of criterion significance was conducted through the integration of the IMF SWARA method with the fuzzy Dombi operator. Given the participation of eight experts in this collective decision making endeavor, 32 models were computed for the main and sub-criteria. At each decision level, encompassing both main and sub-criteria within respective principal categories, the fuzzy Dombi operator was employed to establish the ultimate criterion weights, which are subsequently incorporated into the subsequent phase of the model. The calculation models using the IMF SWARA method for each individual expert are delineated in
Table 3.
When determining the weights of the main criteria, the experts first had to assess the importance of these criteria and rank them. Consequently, experts E1, E2, E3, E4, and E8 ranked the criteria in the following order: C1 > C2 > C3. In contrast, experts E5 and E7 ranked these criteria as C2 > C1 > C3, while expert E6 ranked the main criteria as C1 > C3 > C2. This discrepancy highlights the differing opinions among the experts and their varying levels of importance assigned to the criteria. Subsequently, the importance of criterion C1 in comparison to criterion C2 was determined, taking expert 1 (E1) as an example. According to E1’s perspective, C1 holds greater significance than C2. Consequently, E1 assigned the value, “Moderately less significant”, to criterion C2. Similarly, E1 regarded C2 as more important than C3 and assigned it the same value of, “Moderately less significant”. The most important criterion was then assigned the fuzzy number value, (0, 0, 0) based on the membership function, while the other criteria were assigned the fuzzy number value, (0.222, 0.250, 0.286). This procedure led to the determination of the values in column sj. Column kj values were obtained by adding one (1) to each of the individual fuzzy numbers. Criterion qj values were determined by copying the value of the best criterion (C1). To calculate the value for criterion C2, it involved dividing the value of C1 for qj by the value of kj for criterion C2 (. Similarly, the value of qj for criterion C3 was computed by taking the value of criterion C2 for qj and dividing it by the value of criterion C3 for kj. The resulting qj values were then summed. To determine the wj values for the criteria, the individual values of qj for each criterion were divided by the aggregate value qj. Using criterion C1 as an example, the calculation is as follows: . The same procedure was applied to the other criteria. This process was consistently applied to all expert evaluations, including auxiliary criteria.
Subsequently, the acquired wj values were subjected to aggregation using the Fuzzy Dombi operator, leading to the determination of final weights for the principal criteria as follows:
w1 (ecological) = (0.357, 0.365, 0.374)
w2 (economic) = (0.332, 0.343, 0.354)
w3 (social) = (0.364, 0.280, 0.296)
The analogous process was repeated for the sub-criteria within each grouping, yielding the final weights presented in
Table 4.
Following the criterion weight determination, the task of evaluating the best sustainability rating among the observed lodges emerged. This was approached through expert-based decision making, wherein experts evaluated the lodges using linguistic expressions. The linguistic scale spanned from “Absolutely bad (AB)” to “Absolutely good (AG)”, as outlined in
Table 5. To facilitate rank-based decisions, linguistic values were translated into fuzzy numbers using a decision function (
Table 2). Each linguistic expression was corresponded with a distinct fuzzy number. For instance, “Absolutely bad (AB)” was assigned a fuzzy number of (1, 1, 2), while “Very bad (VB)” corresponded to (2, 3, 4), and so forth, as shown in
Table 2. These fuzzy numbers are derived with careful consideration to the possibility of partial overlap among individual numerical values. Additionally, it is ensured that the upper limit of a specific fuzzy number exceeds the preceding fuzzy number while remaining lower than the subsequent one.
The transition from linguistic values to fuzzy numbers established the initial fuzzy decision matrix. Given the involvement of eight experts, a harmonization process was undertaken by applying an arithmetic mean, wherein all experts held equal importance, each influencing 12.5% of the overall decision. This approach ensures that each expert’s opinion is taken into account individually, without prioritizing any of the experts. The aggregated fuzzy decision matrix then served as the foundation for executing subsequent stages of the fuzzy CRADIS method.
The initial step in implementing the fuzzy CRADIS method entailed the normalization of the initial fuzzy decision matrix. This normalization was conducted by determining the maximum value for each criterion’s alternatives and subsequently dividing the alternatives’ values by this maximal value (Expression 6). Notably, normalization solely encompassed benefit criteria, given the uniform evaluation potential facilitated by the linguistic scale, eliminating the necessity to differentiate between cost and benefit criteria. It is worth noting that while fuzzy CRADIS allows for the use of other normalization methods, this research adhered to the standard normalization procedure prescribed by the method. The exploration of different normalization techniques and their impact on ranking is a subject that can be addressed in future research, particularly in the context of methodological studies.
For instance, in the context of criterion C11, a maximum value of 9.87 is identified. Consequently, each value corresponding to the alternatives within this criterion undergoes division by this identified maximum. To illustrate, consider the first alternative, which is associated with fuzzy numbers (7.2, 8.3, 8.9). When divided by this maximum value, the result is a set of normalized values, exemplified by (. This process is systematically applied to all criteria, thereby establishing the maximum value for each.
The subsequent step involves the weighting of the normalized decision matrix. During this phase, the normalized values are multiplied by their respective weights. Take, for instance, criterion C11, where the weights are specified as (0.06, 0.06, 0.07). In this scenario, for the first mountain lodge, the normalized values are subjected to multiplication with these designated weights, resulting in calculations such as (0.73 × 0.06 = 0.04, 0.84 × 0.06 = 0.05, 0.91 × 0.07 = 0.06). Each distinct fuzzy number is subjected to multiplication by its corresponding weight, generating weighted normalized decision matrix.
Following the formation of the weighted normalized decision matrix, the process proceeds to calculate the maximum and minimum values within this matrix, denoted as the ideal and anti-ideal values, respectively. The quest for the maximum value for an individual criterion entails extracting the highest value among all corresponding alternatives. This procedure yields the ideal value, represented as a fuzzy number (0.07, 0.08, 0.09). Conversely, in the pursuit of the anti-ideal value, the minimum value is identified for each individual criterion, drawing from the collection of minimal values. This process results in the acquisition of an anti-ideal value in the form of the following fuzzy number (0.02, 0.03, 0.04).
Subsequent to this determination, the next stage in the application of the fuzzy CRADIS method involves the computation of deviations from the ideal and anti-ideal values. Within this phase, the deviation of all weighted values from both the ideal and anti-ideal values is meticulously determined. Initially, the values of the weighted decision matrix undergo subtraction from the ideal value, followed by subtraction of the anti-ideal value from the weighted value. This dual computation yields two matrices, one representing deviation from the ideal value, and the other from the anti-ideal value. The overarching objective for each alternative is to approach the ideal value as closely as possible while distancing itself from the anti-ideal value. Consequently, optimal values are computed based on these criteria. Given the existence of two decision matrices, two distinct optimal values are derived. In cases where deviation is from the ideal value, the optimal value comprises the alternatives with the lowest value for each criterion. Conversely, when deviating from the anti-ideal value, the optimal value entails the alternatives with the highest value for each criterion.
Following the calculation of these optimal values, the subsequent step involves quantifying the collective deviation of alternatives, encompassing all deviations for specific alternatives, including those designated as optimal (
Table 4). Subsequently, the process proceeds to defuzzify these aggregated deviations, thereby converting fuzzy numbers into crisp numerical values. Standard defuzzification is employed here, as defined in the original fuzzy CRADIS method, where the central fuzzy number is given four times higher priority in relation to the other two numbers. In practice, various types of defuzzification exist; thus, future research should investigate whether this phase affects the final ranking of alternatives or not. Upon completing this defuzzification, the utility function is computed. In instances where deviations from the ideal value are in question, the optimal alternative is divided by the value of the aggregate deviations among alternatives. Conversely, when deviations are from the anti-ideal value, the value of the aggregate deviations among alternatives is divided by the value of the optimal alternative.
Illustrated using the example of the first mountain lodge, ML1, the calculations yield the following results:
,
. The culmination of the fuzzy CRADIS method entails computing the final value by determining the average utility function across individual alternatives. In the case of ML1, this computation appears as follows:
. This process is replicated for all mountain lodges, leading to the formation of the final results, as outlined in
Table 6.
The analytical assessment based on expert evaluations indicates that mountain lodge ML6 exhibits the most favorable sustainability outcomes, followed by mountain lodge ML3, while mountain lodge ML1 exhibits the least favorable results. These findings will undergo validation and sensitivity analysis to ensure their robustness.
Result validation has become an integral step in the application of MCDM methodologies [
67,
68]. The goal of this analysis is to examine the robustness of the fuzzy CRADIS method, in such a way that its results are compared with the results obtained by other fuzzy methods. In this validation, the initial fuzzy decision making matrix, along with the derived weights, is employed. The sole objective is ranking alternatives using various methods. In this context, apart from the fuzzy CRADIS method, six additional fuzzy methods will be employed: fuzzy MABAC (Multi-Attributive Border Approximation Area Comparison), fuzzy WASPAS (Weighted Aggregated Sum Product Assessment), fuzzy SAW (Simple Additive Weighting), fuzzy MARCOS (Measurement Alternatives and Ranking according to the Compromise Solution), fuzzy ARAS (Additive Ratio Assessment), and fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution). The results of this analysis reveal that the fuzzy TOPSIS method is the only one with a distinct ranking order of alternatives, whereas the remaining methods yield congruent alternative rankings, affirming the consistency of the results obtained through the fuzzy CRADIS method (
Figure 2). Based on the results of this analysis, which demonstrated that the rankings generated by the fuzzy CRADIS method align with those produced by other fuzzy methods, it is evident that this method can be reliably employed in future research as the results are consistent with those obtained from various other fuzzy methods. In subsequent studies, there is no obligation to exclusively use the fuzzy CRADIS method; other approaches can also be considered. However, it is worth noting that the application of the fuzzy TOPSIS method should be approached with caution due to the observed disparity in rankings compared to other methods.
A sensitivity analysis will subsequently investigate the influence of specific criteria on the ultimate ranking of mountain lodges. Within this analysis, individual criteria weights will be varied by designated percentages, i.e., 30%, 60%, and 90%, while the weights of other criteria remain unaltered. This process serves to gauge the diminished importance of a given criterion within the final decision [
69,
70,
71]. Given the existence of 15 auxiliary criteria, and with their weights adjusted threefold, 45 distinct scenarios are established. The application of these scenarios (
Figure 3) reveals that two mountain lodges, ML6 and ML1, maintain their respective rankings throughout all scenarios. Specifically, ML1 consistently occupies the lowest rank, while ML6 consistently secures the highest rank. These two lodges demonstrated independence regarding changes in the individual weights of the criteria, and therefore the rankings of these lodges were not changed. However, for other mountain lodges, their ranking order varies with the modification of specific criteria. For instance, ML3 temporarily ascends to third place in the ranking in certain scenarios, a shift attributed to the fact that ML5 exhibits less favorable indicators than ML3 concerning tourist accessibility. The diminishing importance of this criterion results in ML5 surpassing ML3 in the ranking. Furthermore, there was a noticeable shift in the ranking of mountain lodge ML5 when the importance of the criterion related to the availability of natural resources was reduced in the scenario. In this particular instance, this lodge transitioned from the third position to the fifth. This observation underscores that compared to lodges ML2 and ML4, ML5 boasts superior access to natural resources. A similar change was observed in scenario 27, where the significance of the capacity criterion was reduced. In response to an alteration in the tourist accessibility criterion, this change propelled ML5 to the second position. This indicates that the ML2 mountain lodge offers better tourist accessibility in comparison to the ML5 mountain lodge. Analogously, all other shifts in lodge rankings can be elucidated using similar rationales. Further adjustments in rankings, compared to the initial ranking (Scenario S0), can be analyzed in a similar manner. These outcomes provide valuable insights for mountain lodges, identifying specific areas where they may lag behind others. Armed with this analysis, they can subsequently strategize improvements to enhance their sustainability. Every mountain lodge can utilize this sensitivity analysis to assess the strengths and weaknesses specific to their establishment. This assessment opens the door to the possibility of implementing tailored strategies to enhance the performance of individual lodges when engaging in mountain tourism.
4.2. Discussion
The allure of mountain regions is progressively drawing diverse tourists, playing a pivotal role in the advancement of tourism development [
72]. The assessment of sustainability within mountain tourism constitutes a multifaceted undertaking that necessitates a holistic framework capable of effectively addressing the multifaceted dimensions inherent to this industry. Sustainability within the realm of tourism holds profound significance, primarily due to the utilization of a nation’s resources in the tourism sector. Consequently, safeguarding these resources for posterity becomes an imperative endeavor, achieved through the practical application of sustainability principles. Sustainability, in this context, is attained through the harmonization of three pivotal dimensions, namely environmental, economic, and social facets [
73]. In the provisioning of mountain tourism services, it becomes essential to harness the ecological resources inherent to a specific region, facilitating economic outcomes while concurrently drawing upon social resources. Furthermore, the integration of mountain tourism with other forms of tourism becomes indispensable in order to furnish tourists with a comprehensive experiential package [
74]. Tourists exhibit a heightened proclivity towards visiting specific mountain lodges when the destination boasts an array of tourism resources. Thus, it is incumbent upon destinations to leverage the entirety of their assets to offer tourists diverse experiences while ensuring the conservation of natural resources.
In this research, a comprehensive sustainability model for mountain tourism is developed. This model introduces a novel approach for assessing the sustainability of mountain lodges with the aim of enhancing the overall quality of mountain tourism experiences. The model is designed to accommodate the inherent uncertainties and subjectivity often encountered in expert assessments, making it a robust tool for evaluating the sustainability of mountain tourism. Each sustainability factor under consideration is further subdivided into five distinct criteria, ensuring that none of the examined sustainability factors is afforded undue preference, particularly when assessing the relative importance of these criteria. The determination of criterion importance is carried out systematically, commencing with the prioritization of the main criteria, followed by the auxiliary criteria. The final weights used for ranking the alternatives are obtained by multiplying the weights of the main criteria with their corresponding sub-criteria weights. In cases where one of the main criteria features a smaller number of associated auxiliary criteria, these criteria are given higher weighting, and vice versa. Consequently, adjustments to the weights are deemed necessary in such scenarios. To mitigate this, it is advisable to employ an equal number of sub-criteria within each main criterion, thus ensuring a more equitable weight distribution. Consequently, the results obtained through this approach cannot be directly compared with similar research, as it differs fundamentally in terms of methodology. Unlike previous studies, MCDM methods have been uniquely leveraged to first determine criterion weights and subsequently ascertain the ranking of mountain lodges. This innovative approach allows the identification of which of these lodges exhibits the most favorable performance in sustainable mountain tourism. Moreover, the specific evaluation of mountain lodges in this manner as a function of sustainable mountain tourism is a novel contribution to the field, further differentiating this research.
The assessment of criteria and auxiliary criteria significance, as well as the evaluation of how these criteria are realized by the observed alternatives, was accomplished through expert decision making. The insights and judgments of eight experts, all holding Doctor of Science degrees and possessing substantial experience in the field of mountain tourism, were solicited for this purpose. This group comprised university professors and seasoned scholars within the domain of tourism. The experts evaluated both the criteria and the alternatives employing linguistic values. To employ these values effectively in the assessment of mountain lodges’ sustainability, a transformation into fuzzy numbers was necessitated. In the process of determining criterion weights, the experts initially ranked these criteria based on their perceived importance. Subsequently, they employed linguistic evaluations adapted to the IMF SWARA method. It is noteworthy that this method diverges from the conventional fuzzy SWARA method primarily in its utilization of specific linguistic values [
66]. Initially, weights were assigned for each individual expert, followed by the harmonization of these weights using Fuzzy Dombi Aggregation Operators. Within this research, this aggregator was strategically employed to attain a final set of harmonized weights as assessed by these experts [
75]. The outcomes of this weight assignment exercise revealed a remarkable consistency, indicating that none of the observed criteria held a significantly different level of importance relative to the others. Consequently, it can be inferred that all these criteria exert an equal influence on the final evaluation.
In the context of this research’s examination of sustainable mountain tourism, particular attention is directed towards mountain lodges. This choice is informed by the pivotal role that mountain lodges play in mountain tourism, offering visitors accommodations and gastronomic services. This transformation of visitors into tourists is a well-established concept [
76], allowing individuals to extend their stay in these regions, providing ample time to explore the various attractions on offer. Consequently, mountain lodges are required to adapt by significantly enhancing their service offerings to cater to tourists’ needs. Typically, mountain lodges are owned and operated by specific mountaineering societies [
77], with access traditionally granted to members of these organizations. However, to leverage mountain resources for tourism purposes effectively, it is imperative to open access to these lodges for all. This inclusive approach is essential for optimizing the utilization of mountain resources for tourism development.
To investigate and assess the utilization of mountain lodges for tourism purposes, the first step was to identify the specific mountain lodges in Bosnia and Herzegovina suitable for this research. This selection process was carried out using a random number generator, resulting in the choice of six mountain lodges. These lodges were then evaluated against sustainability criteria. The research aimed to determine the extent to which these lodges fulfilled the sustainability criteria. The expert ratings obtained through this assessment indicated that these mountain lodges performed exceptionally well in meeting the sustainability criteria.
However, the primary objective of this research was to identify which of these mountain lodges best achieved the sustainability goals. To achieve this, the fuzzy CRADIS method was employed to rank these lodges and ascertain which one most effectively met the sustainability objectives. This method revealed that, based on expert assessments, mountain lodge ML6 exhibited the most favorable indicators. The dominant factor contributing to the superior performance of this lodge was criteria C24—capacities and C25—accessibility to tourists. It is noteworthy that while this lodge may not boast extensive sleeping accommodations, it does offer two substantial halls where tourists can spend their daytime hours. Hence, this lodge was selected as the most effective in meeting the sustainability objectives. This particular mountain lodge should serve as a benchmark for comparison with other lodges, motivating them to strive for improved ratings in order to enhance sustainability within mountain tourism.
This model, encompassing economic, ecological, and social criteria, serves as a valuable tool for facilitating well-informed decision making among stakeholders. It encourages the prioritization of sustainable practices, thereby ensuring the enduring appeal of mountainous regions to tourists while concurrently safeguarding their natural splendor and fostering the welfare of local communities. Furthermore, this model offers an avenue for individual mountain lodges to enhance their business operations. This is achieved through a comprehensive analysis that compares these lodges with their counterparts. Consequently, insights are derived regarding areas where experts believe certain lodges excel or fall short in comparison. Building upon this analysis, mountain lodges can refine their offerings and align them more effectively with sustainability objectives. As a result, they are better positioned to harness the abundant resources that mountainous regions offer for their benefit in the future. Consequently, the outcomes of this research extend beyond the borders of BiH, finding relevance in the enhancement of mountain tourism worldwide.
To initiate this process, a preliminary evaluation of these mountain lodges is imperative to identify areas requiring improvement in order to boost mountain tourism. Key areas of focus include streamlining accessibility to these lodges for tourists, as the current requirement of approval from mountaineering societies often hinders accessibility. Furthermore, efforts should prioritize the enhancement of surrounding infrastructure and the expansion of tourist offerings [
78].