What is the difference between ahp and fuzzy ahp

We need to define the problem according to the criteria used to determine the gemstones of quality. Specific gravity, color, hardness, cutting, and clarity are used as the main criteria for determining gemstone quality. This is some data from the gemstone certificate see Table 1. The weight of the stone has a unit of carat ct ; the greater the weight of a gemstone, the greater its size.

Stone hardness unit is called Mohs because the name of the first person to do research on the hardness of a gemstone was Friedrich Mohs, a geologist and mineralogist from Germany in The level of cutting quality is seen from its proportional and symmetrical shape of gemstones pieces. Step 2 create a comparison matrix see Figure 1. After we know the data and criteria stone in Table 1 we need to create a comparison matrix.

The matrix used is simple, has a strong position for the consistency framework, obtains other information that may be required with all possible comparisons, and is able to analyze the overall priority sensitivity for changes in consideration. Here are the equations used to define pairwise comparisons: where n denotes the number of criteria compared, are weights for the i criterion, and is the ratio of the weight of the i criterion and j. After knowing the comparison of its criteria in Table 2 , the next thing done is to normalize each column into the matrix form by dividing each value in the column i and row j with the largest value in column i.

Then the results of the matrix normalization from Table 2 are obtained as follows:. Step 3 checking for consistency see Figure 1. The comparison of the consistency index with a random generator RI value is listed in Table 3 set by Saaty [ 10 ].

This value depends on the matrix order n. First we must recognize the value of the eigenvector which is the weighted value of the criterion. To calculate the eigenvector, we use the following equation: is the eigen vector, where is the sum of the matrix normalization values and is divided by the number of criterion. The largest eigenvalue is the number of times multiplying the number of columns with the main eigenvector see Table 4.

So it can be obtained by the equation After obtaining maximum lambda value, the value of CI can be determined. If the value of CI is zero 0 , this means the matrix is consistent. Testing is measured using Consistency Ratio CR , i.

The RI value used is in accordance with the order n matrix. The consistency value of 0. So each fuzzy set will be divided into 2 see Figure 2 , except for the same comparison set, or can be seen on the TFN scale see Table 5. Step 5 calculate the weight value of the fuzzy vector see Figure 1.

The process to get fuzzy synthesis value is shown using equation of the following formula: Information:. After the comparison of fuzzy synthesis values see Table 7 , we will get the defuzzification ordinate value. From the above calculation, we can calculate the values of v and. To calculate we use the equation of the following formula. Calculating the value of the fuzzy vector weight , calculation of the fuzzy weight value is shown using the equation of the following formula collecting ordinate values that have been previously obtained, as below.

Normalization of vector weight values is obtained by the equation of the following formula,. Step 6 ranking and selection of decisions see Figure 1. Next is to do an alternative value calculation where the alternative settlement measures are the same as the completion steps on the criteria. The built system consists of several menus that are the stages in running the decision support system.

The first thing to do is login first. To be able to use this system we need to login. After login, we will enter into the main menu. On the main page the F-AHP algorithm and any data needed to start the system process are explained. After that alternative data and criteria are entered into the system. The gemstone data we have need to be input into the alternate data input page according to the criteria along with the criteria data we input into the input data page criteria.

The next thing to do is to provide a comparison of the criteria and the value of alternative comparison to each criterion. After all has been done, next we can do the following process. In the process page we can see the value of criteria comparison and TFN set of criteria. When the process is completed, this will result in the ranking of each alternative; the decision-maker can determine which gemstones are qualified from the gemstones being compared.

From the ranking results in Figure 3 and Table 9 , it can be concluded that alternative 1 has the most optimum weight value compared with other alternatives. Therefore, a decision can be made that Rubi 1 is the highest-quality gemstone of all stones compared. The conclusion of this research is as follows: we created a system that can assist decision-making in assessing and choosing quality gemstones accurately and effectively by using F-AHP algorithm.

The focus on the decision of the system is more on the decision of stones based on the same type of stone name; this is because, for the decision system to be more appropriate and relevant for use as a consideration in decision-making, it is impossible to compare one stone with stones of different types, not in the same class quality, so the end result of the system is based on the classification of the type of stone name.

As shown in Figure 3 we obtained the result by using the F-AHP model in the selection of quality gemstones Rubi 1 with a weight value of 0. This weighting value indicates that a gemstone of the highest quality is Rubi 1 with a weight value of 0. The data used to support the findings of this study are available from the corresponding author upon request.

This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article of the Year Award: Outstanding research contributions of , as selected by our Chief Editors. Read the winning articles. Journal overview. Special Issues. Guest Editor: Qi Zeng. Received 25 May Accepted 13 Sep Published 01 Oct Abstract The selection of quality gemstones requires a special ability to select and assess the quality of gemstones to be traded.

Introduction Many times, we are always faced with several options for the right decision-making. Table 1. Data of gemstones containing specific gravity, color, hardness, cutting, and clarity as the main criteria.

The data can be seen from the gemstone certificate. Figure 1. Table 2. While at FAHP, experts' decisions are driven by the consideration of triangular fuzzy numbers, which can have a large impact on the final weight of the criteria. Although this comparison shows differences in AHP and FAHP weights and rankings, it does not recognize the true impact of this difference on the final result. Therefore, the next section is done to see the difference between the outcomes of both methods.

Here, the area that falls under the very suitable class is considered for further selection. Along with this, another consideration has also been taken that new hospital sites should be in only those wards which do not have any hospital.

The location for the new hospital is identified based on the pixel values. A higher pixel value indicates greater adherence to the criterion, thus it is more appropriate than a lower pixel value. Based on the above conditions, seven alternative locations for hospital sites are identified by both methods from a very suitable class. Here, it can be seen that three of those sites are identified at the same location by both methods.

Next, the spatial distribution and ranking order of these identified alternative sites is calculated and then compared in both methods. Here, criteria weights and PCM of each alternative site in regard to each criterion are taken part to calculate the final weight and ranking of each site. The overall weight and ranking of each criterion by both methods are shown in Tables 7 and 8 , respectively. This analysis shows that the ranking order of sites differed slightly in both methods.

For example, Site 1, Site 2, Site 3 and Site 7 are located in the same ward, but the ranking order differs in both methods. However, Site 5 and Site 6 are not only located in one place, but they ranked in the same order by both methods. Although Site 4 option from the AHP and FAHP is located in separate wards, this analysis ranked it as the most appropriate location for the hospital site.

Sensitivity analysis is used to test the reliability and robustness of alternative sites in various models. In other words, it identifies the sensitivity of alternatives to the criteria weight changes. To examine this analysis, the weight of one criterion is changed while keeping the others to the same.

In this way different combinations of weights are prepared. Experiments are then conducted to evaluate the impact of the weight variation on the output. High degree of change shows high sensitivity in output.

To perform the sensitivity analysis, weight w i of each criterion is altered at a certain percentage change PC. Weight is calculated by the following equations:. Due to having highest weight among other criteria, population density and distance to other hospital criterion is selected as the main affecting criterion for AHP and FAHP, respectively.

After generating the criteria weight changes, their impact in the overall ranking is analyzed. For this, overall weight of sites with respect to each criteria weight change is calculated using the weighted operation. The AHP result shows a continuous variation in the order of site ranking in respect to criteria weight change. From the results, it can be seen that Site 4 is identified as the most suitable location for hospital siting both ways.

Thus the impact of criteria weight change in the FAHP sites is nearly negligible. The sensitivity analysis results suggest that the FAHP site ranking is more tolerant for the criteria weight change than the AHP ranking. The site selection like problems that have multiple conflicting criteria requires MCDA based decision making. AHP can be used for this purpose as it can handle both qualitative and quantitative parameters.

It integrates expert opinion, specialist experience and public feedback to assign the weights to these criteria. FAHP use the fuzzy number instead of the crisp number in the weight assignment. In this research work, a four-step methodology is proposed for hospital site selection along with the comparative analysis of AHP and FAHP.

In the first step, the parameters are picked under three broad categories, viz, socio-economic criteria, geographical criteria and environmental criteria. Eleven sub-criteria are subsequently identified under them: population density, proximity to slum, land cost, proximity to road, distance to other hospitals, proximity to railway, possibility of extension, slope, air pollution, green area and unhealthy industry. After the screening and selecting of criteria and sub-criteria, thematic layers are generated and weight is assigned to them on a nine-point scale.

In FAHP, the extend analysis method is used to calculate the crisp weights. Finally, suitability maps are generated using both methods. Total of nine sites are identified in each of the methods where hospitals can be established. It shows that these methods' difference in the criterion weight assignment is ultimately reflected in the respective criterion ranking. The criterion weight change has an impact on the final suitability map which varies between these two methods.

For example, in AHP, the population density criterion greatly impacts the final suitability map, whereas in FAHP, it is the distance to other hospitals. The results of both methods on final suitability indicate high variance in the ranking of their respective alternative locations.

The result of sensitivity analysis shows high differences in the outcomes of both methods. This difference is not only due to distinct sets of alternative sites from AHP and FAHP but also due to the spatial extent of site location. It could help the local administrators in the handling of the emerging health threats in a more efficient manner. The solution can reduce the widening gap between the patients and the availability of health infrastructure in present COVID like situations.

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Correspondence to Ashutosh Kumar Tripathi. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Reprints and Permissions. GeoJournal Download citation. Accepted : 20 May Published : 28 May Anyone you share the following link with will be able to read this content:.

Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content. Search SpringerLink Search. Download PDF. Abstract Identification of hospital sites and their ranking is important for the planning and development of any country's health infrastructure. Introduction Over the period of time, the demand for healthcare facilities has increased exponentially all over the world Pantzartzis et al.

AHP AHP is a multi-criteria decision-making approach in which the criteria are organized in a hierarchical structure. Study area. Full size image. Methodology The flowchart of the proposed methodology is given in Fig. Table 3 Description of the evaluation criterion Full size table. Criteria hierarchy for hospital site selection. Table 4 Spatial data and its associated spatial analysis tool Full size table. Thematic layer map of socio-economic criteria.

Thematic layer map of geographical criteria. Thematic layer map of environmental criteria.