4.1. Fuzzy Analytic Hierarchy Process (FAHP) Method
The Analytic Hierarchy Process (AHP) is considered a heuristic method. It was developed by the American mathematician Thomas Saaty [
40]. It was created in response to the lack of a simple tool to support decision makers in the process of decision making in multi-criteria problems. There was no structured, systematic approach to decision making. Priorities were often determined arbitrarily [
41]. AHP method helps to make optimal choices in the case of multi-criteria decision making problems by reducing them to a series of pairwise comparisons, which are undertaken by experts. It enables a numerical measure of the validity of the analyzed features. AHP is conducted in two fundamental phases:
- (1)
creating a hierarchical structure of the problem,
- (2)
developing the final priorities as a result of considering criteria and alternatives.
In the first phase the structure of the problem is created. In this hierarchical model the highest level of the hierarchy is a primary objective and below it, at a lower level, there are sub-goals, called criteria. The number of criteria and sub-criteria levels usually does not exceed two. At the lowest level of the hierarchy there are possible variants of the decision, referred to as alternatives.
In the second phase, appropriate weight is assigned to each element of the hierarchical structure. The weight takes into account the opinion of the individual participants in the decision making process. Weights are obtained by creating a pairwise comparison matrix of all criteria at the selected level of the hierarchy after taking into account the position of the weights/criteria in the hierarchical structure of the problem.
Saaty proposed the comparison of pairs to be made in nine-relative rating scale. The comparison result is expressed in the descriptive way, which corresponds with the respective number from 1—denoting equal importance to 9—denoting absolute advantage [
40].
Pairwise comparison matrix takes the following form:
It should be noted that the pairwise comparison matrix should be consistent, it additionally allows to verify the quality of judgments made by an expert. One of the most practical issues in the AHP methodology is that it allows for slightly non-consistent pairwise comparisons because perfect consistency of the matrix of comparisons rarely occurs in practice.
To analyze the consistency of the matrix of comparisons Saaty proposed the calculation of the consistency index (
CI). The lower the consistency the value of consistency index (
CI) is increasing. The consistency index takes a following form:
where
—maximum eigenvalue, and
n—number of comparison elements.
The major measure of the consistency is consistency ratio (
CR). This measure is based on a comparison of the expert ratings and average value of the random pairwise comparisons. The pairwise comparisons made by experts should differ significantly from random comparisons, the consistency ratio takes the form of:
where
CI—Consistency Index,
RI—Random Index, the consistency index when pairwise comparisons are completely random. In the AHP the pairwise comparisons in a judgment matrix are considered to be adequately consistent if the corresponding consistency ratio (
CR) is less than 10% [
40].
Estimation of priorities from the pairwise comparison matrix is based on finding maximum eigenvalue of this matrix and then finding the eigenvector corresponding to that eigenvalue. The resulting eigenvector becomes vector of weights of judgment matrix enabling identification of the priorities. The literature indicates at least a few methods for obtaining weight vector, from the simplest method, based on an average, to the right-hand matrix method postulated by Saaty (for more on the methods of obtaining preferences, see [
40,
42]).
The AHP method is one of the most often used in the practice of the methods of multi-criteria decision-making, and as such has become a base for modifications and upgrades. One of the first adjustments already proposed by Saaty in 1996 was the inclusion of feedback into the structure of hierarchy [
43]. In this way, the AHP method has become a special case of the Analytic Network Process (ANP) method, taking into account feedback connections between the various levels of the hierarchy [
44]. Another important modification of AHP method is the use of fuzzy numbers for pairwise comparisons. Linguistic ratings proposed by Saaty may lead to some confusion (especially when the comparisons are made by many experts and then are aggregated), because it is difficult to distinguish between for example: “big advantage” from “huge advantage”. Therefore, instead of assigning one value to a linguistic assessment, as proposed by Saaty, the fuzzy number is assigned. This is the major characteristic of the FAHP method and key modification of AHP. The first paper taking into account the problem of fuzzy numbers in the method of AHP was published by Van Laarhoven and Pedrycz [
45]. A wider review of works devoted to this approach can be found in Demirel et al. [
46]. The method has been used also to assess energy technologies, i.e., [
47,
48,
49].
In FAHP approach fuzzy pairwise comparisons are presented in the form of the fuzzy pairwise comparison matrix:
where
is a triangular fuzzy number of expert ratings or geometric average of expert ratings, Weights can be established on the basis of procedure proposed by Chang [
50]. In the first step the value of fuzzy synthetic extent with respect to
kth object (fuzzy normalized values) is defined as:
then the degree of possibility is calculated as:
Next, the minimum degree of possibility of fuzzy number versus other
p − 1 fuzzy numbers is calculated as:
Normalized values of the minimum degree of possibility for all fuzzy numbers stand for weights of criteria. Global weights for sub-criteria are obtained by multiplying local weights by the weight of the superior criterion.
4.2. Evaluation of Economic, Social and Environmental Effects of the Development of Low-Emission Energy Technologies with Fuzzy Analytic Hierarchy Process (FAHP)
In this study the FAHP method will be used in order to realize the goal of the research stated as to determine the ranking of low-emission energy technologies in the context of their impact on social well-being within the meaning of the sustainable development paradigm. Five technologies (decision-making variants) are considered: wind on-shore, wind off-shore, solar, biomass and biogas, nuclear. There are three main criteria under the concept of sustainable development i.e., environment, economy and society. For each of the main criteria, the sub-criteria (intermediate criteria) were selected. The hierarchical assessment model of low-emission energy technologies in Poland is shown in
Figure 1.
A survey was conducted on the sample of 15 experts. In the first phase, environmental economics and energy professionals were asked to fill in the given questionnaire. The FAHP method was used to determine the priorities of each criterion (objective). Due to the large number of comparisons between alternatives with respect to criteria, the method of pairwise comparisons has been abandoned with respect to peer-to-peer evaluation of particular technologies. Each technology was assessed on a scale that determines the impact of a given energy technology on a particular criterion (without reference to other technologies). This effect could be both positive and negative, and was determined on a scale from −4 to 4 (where −4 denotes maximum negative influence, 0 no effect, and 4—maximum positive influence). The scale for the impact assessment is shown in the
Table 2.
The consistency coefficient was calculated for aggregated pairwise comparison matrix. In the case of pairwise comparison matrices for sub-criteria, the consistency ratios were less than 6%, while for matrix for main criteria CR slightly exceeded the arbitrarily set value of 10%. Exceeding CR maximum value was so small that it was considered that the matrix was consistent.
Estimation of weights was started by calculating the weights for the main criteria. Experts’ opinions were aggregated into one fuzzy pairwise comparison matrix for main criteria (see
Table 3), then fuzzy normalized values for each main criteria
were calculated.
The procedure of calculating the
value is shown for the first main criterion (
k = 1), i.e., the economy:
The remaining normalized values for the main criteria were calculated in the same way. Results are shown in
Table 4.
The fuzzy normalized values from
Table 3 allowed to determine the minimum value of the degree of possibility and the priorities, consequently. The ability level for each fuzzy number was calculated, followed by their minima and priorities of the main criteria (see
Table 5).
The remaining priorities for sub-criteria were calculated in the same way, final results are shown in
Table 6.
Experts assigned the highest priority to the criterion economy (0.42). Priorities of the criteria society and environment are close (0.304 and 0.276, respectively), although slightly higher priority was assigned to the first one.
The greatest differences in the priorities of individual sub-criteria occurred in the main criterion of economy, but these differences are still small (the highest difference between the sub-criterion: innovation and competitiveness of the economy with a priority of 0.167 and the trade balance with the priority of 0.110).
In the criterion of society, only three sub-criteria were distinguished and each was assigned with a priority slightly higher than 0.3. Within the criterion environment six sub-criteria were listed, with priorities slightly above 0.15.
At the last stage of the analysis, an attempt was made to create a ranking of energy technologies. Experts have assessed impact (on the scale from −4 to +4) of each technology on each of the sub-criteria. Experts’ ratings have been averaged and are presented in
Table 7.
Analyzing the average scores assigned for each criterion, it can be noticed that technologies that contribute the most to social wellbeing through the economy criterion are biomass and biogas technologies, with the score of 11.3 points. The following technologies hold remaining positions: solar (photovoltaic) with a score of 9.9 points, wind on-shore (7.4 points), wind off-shore (5.9 points) and last place, with a significantly lower result—nuclear technology (4.4 points).
The highest score was attributed to such sub-criteria as energy security of enterprises and innovation and competitiveness of the economy. It turns out that according to experts, developing any low-emission technology, in principle, will have a significant positive impact on these sub-criteria. This seems to be in line with the intuitive understanding of these phenomena, i.e., the development of any energy technology, besides the dominant coal power industry, leads to increased energy security due to the diversification of energy sources and to increased innovation and competitiveness of the economy.
All low-emission technologies have a positive impact on GDP, trade balance and unemployment, although the impact is strongly dependent on technology. The highest positive impact on GDP is due to the development of biomass, biogas and photovoltaic technologies (2 points each), followed by wind on-shore (1.27 points) and wind off-shore (1.2 points). Nuclear technology holds the last place, with a significantly lower result of 0.73 point.
Photovoltaic technology (0.87 points) and biomass and biogas (0.8) have the highest impact on trade balance. Wind technologies are on the second place and again in the last place, with a score close to zero (0.07 point)—nuclear technology. The ranking looks the same for the next sub-criterion, which is the impact on the unemployment rate. Biomass and biogas technologies are clearly distinguished as having the highest potential for job creation. Also photovoltaic and wind on-shore have shown significant positive impact. Nuclear power occupies the last place, with a score close to zero.
With regard to the impact of balanced development of regions, biomass and biogas technologies are again in the top positions, which is intuitively understandable. The second place is taken by photovoltaics, followed by wind on-shore. Nuclear and wind off-shore have achieved close to zero score, which also seems understandable. With regard to the land occupancy, each technology, except for biomass and biogas with zero score, negative impact was appointed. In this case, the distribution of points may be surprising because the experts' highest negative impact was appointed to nuclear power, despite a clear description of the sub-criterion indicating energy technologies based on renewable energy as having a low energy yield per unit of occupied land (see
Table 1). Nuclear power, on the contrary, is characterized by high energy yield per unit of occupied land. All RES technologies were generally assigned with a very small negative impact, while for nuclear power the negative impact was significantly higher.
Within the society criterion the first place with the score of 7.8 points is occupied by photovoltaics, second-biomass and biogas technologies with a score of 7.2 points, third−wind on-shore with a score of 4.9 points. Wind off-shore, with a score of 2.4 points, is significantly less important. The last place, again, belongs to nuclear power with the result of 1.07 points.
Almost the same ranking applies to each sub-criterion within this main criteria, i.e. photovoltaics, biomass and biogas technologies and wind on-shore have a significant positive effect on the elimination of social inequalities (it seems understandable given the possibility of locating investments in rural areas throughout the country), shaping a new energy culture and energy security of households. With regard to the last two sub-criteria, it seems that the development of the prosumer energy industry based on these energy technologies seems appropriate. Therefore, it is not surprising that significantly lower impact on these sub-criteria has wind off-shore and nuclear energy (lack of influence on the shaping of a new energy culture and even a slight increase in social inequalities).
Within the main criterion of: environment, the results of the experts’ survey indicate a significant, sometimes diametric, differences between the technologies in question. All technologies based on renewable energy sources have a positive impact, with wind off-shore in the first place (7.73 points), followed by photovoltaic (7.4 points) and by wind on-shore with a score of 6.1 points. Much lower but still positive impact is shown by biomass and biogas technology with a score of 3.4 points. Nuclear power has a strong negative impact with −3.1 points.
Experts have appointed the greatest positive impact within the criterion of the environment to such sub-criteria as resource efficiency, greenhouse gas emissions and emissions of other air pollutants. In principle, the development of each of the low-emission technologies will have a significant positive impact on these sub-criteria, which is obvious, and is a fundamental reason why these technologies are implemented.
Implementation of any low-emission energy technology replaces the dominant coal-fired power industry, leading to higher air quality. In regards to greenhouse gas emissions, nuclear power holds the first place, with a score of 2.5 points. Second place belongs to wind on-shore and wind off-shore (2.47 and 2.4 points respectively), followed by photovoltaics with the score of 2 points and biomass and biogas technologies, with a score of 1.53 points.
Regarding the emission of remaining air pollutants, the ranking is slightly different i.e., wind on-shore, wind off-shore and photovoltaic technologies reached the highest, similar results (2.33, 2.3 and 2.1 points respectively). Next in the ranking is nuclear power (1.67 points) and just behind—biomass and biogas with a score of 1.4 points. The last place in the ranking is unchanged, which seems reasonable, due to the presence of pollutants emission in the operational phase of the power plant, but it is not quite possible to interpret the shifts in the rest of the ranking.
The highest level of resource efficiency of the economy is achieved by the development of photovoltaics, followed by wind off-shore and wind on-shore, followed by biomass and biogas technologies. All RES technologies received more than 2 points for this factor. Last place, with a score of 1.4 points belongs to nuclear power. This ranking may be justified by that three RES technologies with the highest score do not require the use of resources in the operational phase. Biomass and biogas technology requires the use of renewable resources, and only nuclear power requires the use of non-renewable resources such as uranium. All technologies have a positive impact on the resource efficiency of the economy compared to the currently dominant coal-based power industry.
With respect to the sub-criterion: the amount of generated waste the highest positive influence is appointed to wind off-shore and wind on-shore technologies (1.4 and 1.3 points, respectively). A significantly lower positive impact is demonstrated by photovoltaics. The positive impact of biomass and biogas is very small (close to zero). Nuclear power has a high negative impact, with a score of −2.8 points. It seems that the top three places in the ranking are assigned to RES technologies perhaps because they do not generate waste in the operating phase. One may have doubts about the ranking of biomass and biogas as it allows the use of waste from agricultural and animal production (not to mention industrial waste) and the digestate of agricultural biogas plants can be used for fertilizer purposes. It appears that the high negative impact has been attributed to nuclear power, due to the generation of long-lived radioactive waste.
Experts have attributed the negative impact to the interference in the landscape of all analyzed low-emission technologies. The strongest negative impact was attributed to wind on-shore (−2.7 points), followed by nuclear power (−2.1 points). Lower but still negative impact is appointed to wind off-shore (−1.2 point), then biomass and biogas (−1 point) and at the last position-photovoltaics (−0.53 points). It seems that this ranking is consistent with the general perception of this impact (although there may be doubts about the location of nuclear power due to lack of experience in this field in Poland).
The last, analyzed sub-criterion was the risk of failure/accident. Nuclear power is located in first place with a score of −3.8 points, which means almost the maximum negative impact on the scale used (from 4 to −4 points). The second place is held by biomass and biogas with −0.73 points. Other technologies, according to experts, have positive impact and thus reduce the risk of breakdowns in the energy cycle compared to the prevailing coal power industry. The impact is not high, with average scores of 0.5 for photovoltaics, wind off-shore and wind on-shore.
The final score obtained in the main criteria of economy, society and environment shows the following ranking of low-emission technologies: first place belongs to photovoltaics (25 points), second place-biomass and biogas (22 points), third place-wind on-shore (18 points), fourth-wind off-shore (16 points) and last place-nuclear power with a surprisingly low score of 2 points.
The experts’ evaluations were weighed with respect to global priorities of sub-criteria. The synthetic value of each low-emission technology was calculated. Results are presented in
Table 8. The results confirm the findings about nuclear power.
This ranking was created on the basis of classic approach, where weighted average is the synthetic variable. However, more sophisticated method, such as TOPSIS, could be used. The author has conducted additional tests using this method. It is one of the mostly used multi-criteria analysis methods [
51], also used for assessment of energy technologies, for example in the recent study of Akbas and Bilgen [
52]. This method was presented for the first time in the work of Hwang and Yoon [
53]). It consists of creating a ranking on the basis of the distance between particular decision variant from ideal solution. Therefore, formally the ranking is created according to the following equation:
where
—Euclidean distance of decision variant from the worst solution and
—Euclidean distance of decision variant from the best solution.
It’s important to mention that values of all variants are primarly normalized and weighted according to previously set weights. Results of conducted TOPSIS analysis are presented in
Table 9. According to expectations the ranking of technologies hasn’t change.
Regardless of the FAHP study, experts were also asked to indicate their weights for each criteria so that the weights add up to unity and to give weights to the sub-criteria within the isolated main criterion, with the weights of the sub-criteria also adding up to unity within the main criterion. These weights were averaged and are presented in
Table 10.
The aim was to test the credibility of both methods (direct weighting by experts with FAHP weightings). Despite the methodological preference for the FAHP method, it encounters difficulties in practical application. It should be noted that with a large number of criteria and sub-criteria, the number of comparisons increases considerably. According to some researchers this is an obstacle to reliable use of the FAHP method. In the next step the ranking of energy technologies was constructed, taking into account the weights provided by experts (see
Table 11).
With this approach the same ranking of low-emission technologies was obtained. Photovoltaics are located on the first position in the ranking, biomass and biogas—second, wind on-shore—third, fourth—wind off-shore and last place—nuclear power. This approach also reveals the gap between the use of RES for reaching the goals of sustainable development (scores from 1.177 to 1.783 for RES technologies) and nuclear energy (score of 0.5).