Abstract
In this study, we present the application of two novel hybrid multiplecriteria decisionmaking (MCDM) techniques in the mineral potential mapping (MPM), namely FUCOMMOORA and FUCOMMOOSRA, as robust computational frameworks for MPM. These were applied to a set of exploration targeting criteria of skarn. The multiobjective optimization method on the basis of ratio analysis (MOORA) and the multiobjective optimization on the basis of simple ratio analysis (MOOSRA) approaches are used to prioritize and rank individual cells. What makes MOORA and MOOSRA more reliable compared to many other methods is the fact that the optimizations procedure is applied to calculate the prospectivity score of individual unit cells. This reduces the uncertainty stemming from erroneous mathematical calculations. The full consistency method (FUCOM), on the other hand, is useful for assigning weights to the spatial proxies. The FUCOM method, as a pairwise comparison method, reduces a large number of pairwise comparisons of similar and popular approaches such as analytic hierarchy process (AHP) with \(n\left( {n  1} \right)/2\) and the best–worst method (BWM) with \(2n  3\) number of pairwise comparisons with \(n  1\) which leads to a less timeconsuming and more consistent performance compared with AHP and BWM. These were applied to a set of exploration targeting criteria of skarn iron deposits from Central Iran. Two potential maps were retrieved from the procedures applied, the comparison of which using correct classification rates and field checks revealed the superiority of FUCOMMOOSRA over the FUCOMMOORA.
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1 Introduction
A great deal of attention has been recently focused on greenfields’ mineral potential mapping (MPM), in which the intent is to reduce the search space for the possible detailed surveys (e.g., [24, 44, 79, 82, 91, 92, 96, 97, 112, 125]). In these studies, expertbased methods are applied for weighting and integrating exploration targeting criteria into potential maps. Of the various expertbased methods employed in this context, multicriteria decisionmaking (MCDM) methods have gained a considerable reputation (e.g., [8, 14, 89, 95, 100, 102]). These methods are either comparisonbased or matrixbased approaches [71]. The former and the latter methods are used for assigning weights to the targeting criteria and integrating the weighted criteria into potential maps, respectively.
The matrixbased MCDM methods are often too complex [26, 77, 142, 143], making it challenging decision makers to follow their mathematical procedures. The multiobjective optimization method on the basis of ratio analysis (MOORA: [21]) and the multiobjective optimization on the basis of simple ratio analysis (MOOSRA: [32]) have been proposed to provide more straightforward mathematical procedures to follow. Notwithstanding the robustness and myriad applications of these methods (e.g., MOORA: [4, 20, 22, 25, 47, 48, 70, 84, 98, 103, 137], MOOSRA: [7, 11, 33, 75, 116, 129, 137]), seldom have they been applied to the context of MPM.
The comparisonbased methods and, on the other hand, a large number of pairwise comparisons (e.g., AHP: [113], BWM: [109]) make these methods timeconsuming and less consistent (e.g., [9, 42, 83, 89, 99, 100, 102, 124]). The full consistency method (FUCOM: [94]), a novel comparisonbased procedure, has reduced the number of comparisons required. This method results in a higher consistency ratio by determining the deviation from utmost consistency ([12, 17, 35, 94, 105]) compared to those of similar procedures, making its outputs more reliable. Although this method has been applied in different decisionmaking procedures (e.g., [12, 17, 18, 35, 41, 90, 105, 127]), it is yet to be applied in MPM.
The intent of this study is to showcase the application of two novel hybrid MCDM techniques in MPM, namely FUCOMMOORA and FUCOMMOOSRA. The FUCOM technique was used in various scientific fields after it was published in 2018 because of two outstanding reasons: (1) this approach has reduced the number of comparisons required (which is less timeconsuming) and (2) has more reliable outputs in comparison with previous approaches [17, 35, 94]; however, this method has been never used in MPM. In addition of applying the FUCOM method in MPM, we combined it to MOORA and MOOSRA to present twostep methodologies, namely FUCOMMOORA and FUCOMMOOSRA. MOORA and MOOSRA, like the FUCOM approach, have been never used in MPM. MOORA and MOOSRA with approximately similar and authentic mathematical backgrounds have been well validated in various scientific fields based on comparison with other methods. The superiority of MOORA and MOOSRA methods in comparison with other similar methods is related to the optimization procedure in their mathematical theory, which reduces the uncertainty stemming from erroneous mathematical calculations and causes having more reliable outputs [7, 33, 98, 129, 137]. In this paper, FUCOMMOORA and FUCOMMOOSRA were applied on a set of regionalscale targeting criteria of iron skarn deposits from Varan area in Central Iran to show the robustness of the proposed approaches in MPM. The intrusion of the Eocene plutonic rocks into the sediments of Qom formation, Cretaceous in age, yielded several cases of calcic skarn iron mineralization in the study area.
2 Methods
2.1 FUCOM
The full consistency method (FUCOM: [94]) is a comparisonbased MCDM procedure applying the principles of pairwise comparison and deviation from maximum consistency [18, 35, 94, 136]. FUCOM requires only n − 1 pairwise comparisons for assigning weights to n mappable targeting criteria in MPM. The deviation from maximum consistency (DMC) of comparisons is used for validating the results of FUCOM [18].
FUCOM is implemented with regard to the following steps [18, 35, 94, 136]:

Step 1: The set of exploration targeting criteria, \(C = \left\{ {C_{1} , C_{2} , \ldots , C_{n} } \right\}\), are initially ranked according to their importance; that is, the higher the initial rank is, the more critical the criterion is to mineralization. This is shown by the following formulation:
$$C_{j\left( 1 \right)} > C_{j\left( 2 \right)} > \cdots > C_{j\left( k \right)}.$$(1) 
Step2: The ranking criteria are compared and the comparative priority (\(\varphi_{{k/\left( {k + 1} \right)}} , k = 1,2, \ldots ,n,\) in which \(k\) represents the rank of the criteria) of the criteria is determined according to Eq. (2):
$$\varphi = \left( {\varphi_{1/2} ,\varphi_{2/3} , \ldots , \varphi_{k/(k + 1} } \right).$$(2) 
Step3: Weight coefficients of the targeting criteria \(\left( {w_{1} , w_{2} , \ldots , w_{n} } \right)^{T}\) are calculated. These values should meet the following conditions:

1.
The weight coefficients (w_{k}) are proportional to the comparative priorities \((\varphi_{k} ):\)
$$\frac{{w_{k} }}{{w_{k + 1} }} = \varphi_{{k/\left( {k + 1} \right)}}.$$(3) 
2.
The mathematical transitivity must be met among all the comparative priorities \((\varphi_{k} ):\)
$$\varphi_{{k/\left( {K + 1} \right)}} \times \varphi_{{\left( {K + 1} \right)/\left( {K + 2} \right)}} = \varphi_{{k/\left( {k + 2} \right)}}.$$(4)

1.

Step 4: The following optimization problem should be solved for calculating the optimal weights \(\left( {w_{1} , w_{2} , \ldots , w_{n} } \right)^{T}\) of the targeting criteria:
$$\begin{aligned} &{\text{Min}}\,X \\ & {\text{s}}.{\text{t}}{.} \\ & \left {\frac{{w_{j\left( k \right)} }}{{w_{{j\left( {k + 1} \right)}} }}  \varphi_{k/k + 1} } \right = X,\,\, \forall j \\ & \left {\frac{{w_{j\left( k \right)} }}{{w_{{j\left( {k + 2} \right)}} }}  \varphi_{{k/\left( {k + 1} \right)}} \times \varphi_{{\left( {k + 1} \right)/\left( {k + 2} \right)}} } \right = X,\,\, \forall j \\ & \mathop \sum \limits_{j = 1}^{n} w_{j} = 1 \\ & w_{j} \ge 0, \forall j. \\ \end{aligned}.$$(5)
2.2 MOORA
The multiobjective optimization method on the basis of ratio analysis (MOORA) has been proposed by Brauers and Zavadskas [21]. This method can be applied for integrating a set of weighted targeting criteria (cf. [10,25]) into maps of mineral potential. In the first step, targeting criteria are marked by positive and negative signs. The positive sign refers to the criteria in which higher values should be prioritized. Negative criteria, on the other hand, are those in which lower values are more important (cf. [25]). Next, the following matrix is developed in which m and n refer to the number of unit cells in the area and the number of targeting criteria, respectively [23]:
For individual targeting criteria, each x_{ij} in the above matrix is normalized to ^{*}x_{ij} in which the values vary in a [0, 1] range. This is implemented according to the following equation [23]:
Finally, the potential values assigned to individual unit cells, y_{i}, are derived from the following optimization function [10, 25, 70]:
where g is the number of positive criteria [21] and w_{j} refers to weight of jth criterion [19, 73].
3 MOOSRA
The multiobjective optimization on the basis of simple ratio analysis (MOOSRA: [32]) is a matrixbased MCDM, with its procedure bearing a striking resemblance to that of MOORA [12]. The matrix alignment and the normalization of arrays in MOORSA are identical to those of MOORA. However, the optimization procedure used for deriving the potential values assigned to individual unit cells is applied according to Eq. (9) as follows [11,32]:
where g and w_{j} refer to the number of positive criteria and the weight assigned to the jth criterion, respectively.
4 The Varan area and input data
4.1 Geological setting and the deposit model
The NW–SE trending metallogenic belt of Zagros [46, 121, 123, 139], as a segment of AlpineHimalayan orogenic system [27, 93, 110, 117, 128] in the western section of Tethyan domain [63, 67, 132, 134, 135], is developed by the collision of the Arabian and Eurasia platforms [52, 87, 108, 126, 131] (Fig. 1). The Zagros orogenic belt includes three aligned tectonic zones of (1) the Zagros fold–thrust belt, (2) the Sanandaj–Sirjan magmatic–metamorphic zone, and (3) the tertiary Urumieh–Dokhtar magmatic belt (UDMB) [5, 6, 60, 118, 122]. The Varan area is situated in the UDMB (Fig. 2) resulted from a convergent tectonic regime [2, 3, 31, 66, 141]. This Andean volcanic arc, having extended over a length of some 2000 km, hosts plutonic complexes included intrusive, extrusive, and volcanosedimentary units post Eocene volcanic, plutonic, and volcanic–sedimentary complexes [31, 60, 61, 66, 69, 74, 115, 119, 138, 141]. The magmatism of the UDMB is associated with continual steps of the NeoTethys closure within Paleogene–Neogene times, started at ∼ 50 Ma [16], continued into middle Eocene, and followed by magmatic activities of Oligocene–Miocene intrusions [2, 3, 141]. The magmatism of UDMB is of calc–alkaline affinity [60, 61, 69, 138, 141]. However, Jamali et al. [65] stated alkaline rocks locally, related to younger plutonic activity in some components of the UDMB. This tectonic setting emplaced extensive magmatism constituting the trigger and heat source, and the convention forces developed a vast array of metallic ore deposits [51], especially copper [58, 104, 139, 140, 141] and Iron [42, 81, 83, 88, 138]. According to the existence of carbonate rocks, which are mostly older than plutonic complexes of the UDMB (mainly at the age of Cretaceous), there is remarkable potential for skarn mineralization in this tectonic setting.
Skarn mineralization is genetically and temporally associated with mafic to intermediate plutons that intruded an older sedimentary basement comprising limestones and dolostones [15, 29,29,30, 34, 36,38,−38, 53, 55, 57, 86, 120]. Three consecutive steps occur are required for developing skarn mineralization: (a) contact metamorphism, (b) ascending the temperature of the plutonic body and the release of orebearing content, and (c) developing the orebearing and alteration mineral assemblages [56]. Steps b and c are associated with skarn mineralization and deposition [56]. This style of mineralization can be divided into two categories that include endoskarn or exoskarn on the basis of the host rock [34, 40,41,−38, 56, 86]. Endo and exoskarns are the consequences of replacements of intrusive rocks within the contact zone and carbonate host rocks at or near the contact, respectively [36, 86]. Fe skarn deposits are associated with magnetite mineralization in calc–silicate contact metasomatic rocks, which can be categorized into two groups including calcic and magnesian skarn irons [28, 36, 37, 42, 81, 83, 86, 138]. The former is mostly developed by the replacement of limestone, tending to occur in convergent tectonic environments, especially in island arc settings. The latter, however, is mostly developed by the replacement of dolomite and is associated with orogenic belts along continental margins [28, 34, 36, 37, 86]. The majority of the world's economic iron skarn deposits are calcic iron, while magnesian iron skarns are less documented [38]. Calcic skarn iron deposits are large deposits averaging some 300 million tons of iron content [133]. Calcic skarn irons are characterized by less silicic intrusions compared with magnesian skarns, minor amount of alkaline rocks, somewhat great amount of endoskarn mineralization, the extensive event of Na metasomatism, in association with magnetite, pyrite, hematite, garnet, pyroxene, and calcite, with geochemical enrichments of Fe, Cu, Zn, Au, and As [28, 34, 36, 37, 42, 56, 106]. Magnesian iron skarns are characterized by more silicic intrusions compared with calcic skarns, mostly occurred in dolomitic strata, in association with magnetite, forsterite, spinel, diopside, apatite, tremolite, phlogopite, talc, amphibole, serpentine, talc, chlorite, chondrodite, magnesite, and clinohumite [36, 37, 55,56,57].
Most of the skarns are related to magmatic arcs and subduction zones, which also host porphyry copper deposits [55] such as the UDMB which has the same situation. Iron deposits of Iran, especially the ones located in the UDMB, are the consequence of magmatic activities pending Eocene to Miocene [122]. The Sarvian deposit, hosting some 2 million tons of Iron [138], is one of the calcic skarn irons of the UDMB [83], situated in the Varan area. This deposit is resulted from a quartz diorite intruding an early Permian to Tertiary limestone of Qom formation, with the temperature of 370–550 °C according to Garnet–pyroxene thermometry [138]. Mansouri et al. [83] implemented successfully the potential mapping of calcic skarn iron in the Sarvian area, which is considered in this study for the Varan area, with using intrusive rocks of tonalites and quartz diorites as the source of mineralization, a reducedtopole map of ground magnetic data representing a further proxy for the source, the outcropping limestones and skarn units representing the trap; unielement geochemical signatures of orerelated elements derived from lithogeochemical samples including Fe, Cu, Zn, Au, and As; and the remotely sensed derived accumulation of minerals include magnetite, pyrite, hematite, garnet, pyroxene, and calcite. Figure 1 shows a schematic representation of the subductionrelated tectonic regime and ore formation model of calcic skarn iron deposit in the Varan area (after Lowell and Guilbert 1978).
The Varan area is marked by the presence of Eocene plutonic rocks and the sediments of Qom formation, Cretaceous in age [49]. The intrusion of the former into the latter yielded several cases of calcic skarn iron mineralization in the area [42]. Figure 2 depicts a simplified geological map of the study area, thoroughly discussed in Feizi et al. [43]. In the area confined by this study, calcic skarn iron mineralization [133] occurs in the contact of basic to intermediate intrusions and crystalline limestones, sandstones, and shales of Qom formation. The Qom formation has been reported as a proper trap of Skarn deposits in the UDMB [42, 81, 83, 88, 138].
4.2 Translating the deposit model to spatial proxies with using mineral system approach
Proper insight into mineral systems leads to defining the exploration targeting criteria in regional and districtscale exploration targeting systems [62, 80, 85] which should be translated to mappable spatial proxies with the goal of targeting undiscovered mineralization [71, 72, 78, 111]. The same suit of targeting criteria exploited in Feizi et al. [42] was employed to vector toward skarn iron mineralized zones. They used a minerals system framework [76] to translate critical processes to the formation of calcic skarn iron deposits—source, trap, and deposition—to a set of targeting criteria. This set comprises the outcropping tonalites and quartz diorites representing the source of mineralization (Fig. 3a), the outcropping limestones of the Qom formation representing the physiochemical trap (Fig. 3b), the remotely sensed derived accumulation of ore minerals as a criterion representing the deposition (Fig. 3c), unielement geochemical signatures of orerelated elements derived from lithogeochemical samples (Fig. 3d), and a reducedtopole map of aeromagnetic data representing another proxy for the source (Fig. 3e) (Feizi et al. [42]). Table 1 provides a summary of these criteria. Readers are referred to Feizi et al. [42] for further details.
5 Mineral potential mapping
5.1 Weighting spatial proxies
Spatial proxies for calcic skarn iron mineralization comprising surficial heat sources (C_{1}), physiochemical trap (C_{2}), mineral assemblages (C_{3}), geochemical anomalies (C_{4}), and subsurficial heat sources (C_{5}) were procreated (Fig. 3). According to step 1 of FUCOM, the ranking of spatial proxies was determined as \(C_{1} > C_{2} > C_{3} > C_{4} > C_{5}\). Then, based on step 2, a comparison was applied based on the ranking criteria, determining the significance (\(\varphi_{k}\)) of the proxies, which led to computing the comparative priority of the proxies (Table 2). Step 3 was performed to calculate the final values of the weight coefficients, which satisfied two conditions of Eqs. 3 and 4. (Table 3). After that, Step 4 was accomplished with solving an optimization problem in Lingo software as follows:
Thus, the optimal weights \(\left( {w_{1} , w_{2} , \ldots , w_{n} } \right)^{T}\) acquired are given in Table 4. The spatial proxies were, therefore, ranked from the most to the least critical as heat sources (C_{1}: \(w\) = 0.434), trap (C_{2}: \(w\) = 0.255), mineral assemblages (C_{3}: \(w\) = 0.128), geochemical anomalies (C_{4}: \(w\) = 0.096), and subsurficial heat sources (C_{5}: \(w\) = 0.087).
5.2 Prioritization and ranking of alternatives (pixels)
The targeting criteria were converted to raster maps with a cell size of 50 × 50 square meters according to the distribution of geochemical samples [59] and flightline distancing of aeromagnetic data [64] used in this work. These criteria were converted to the matrix represented in Eq. (6). Given the weights of the FUCOM method in Table 4, Eqs. (7–10) are used for integrating the weighted criteria into maps of mineral potential (Figs. 4, 5).
5.3 Validation of the results
Natural breaks [68] were employed for the initial classification of prospectivity maps (Figs. 4, 5). Nevertheless, for a more robust delineation of exploration targets, favorability–area [9, 42] fractal modeling was employed. Figure 6 represents the favorability–area model applied to the potential maps of MOORA (Fig. 4) and MOOSRA (Fig. 5). This process retrieved two classified maps represented in Figs. 7 and 8. Also, the thresholds derived from the fractal model are illustrated in Tables 5 and 6. According to these tables and figures, each map is divided into five classes. Field surveys were carried out to groundcheck the anomalies derived from the two potential maps. Evidence of skarn iron mineralization has been observed in the area as illustrated in Fig. 9. In each ground control point illustrated in Fig. 9, lithogeochemical sampling was conducted. These samples were analyzed for their iron content using XRF. We sought the opinion of many experts regarding the concentration of iron in calcic skarn iron deposits. The average opinion of experts is represented in Table 7, according to which we classified our collected samples into five classes (Table 7). Table 8 provides a comparative tool through which one can opt for the more robust potential map. According to the result of the last column in Table 8, the accuracy of the MOOSRA method is 80% (8 correct predictions of 10), but the MOORA method is 70% (7 correct predictions of 10). Based on this comparison, the method of MOOSRA outperformed MOORA in MPM.
In addition, with respect to high prospective classes retrieved from the two methods, the method of MOOSRA is superior to MOORA. This is because the former has reduced the search space to some 1.7 square kilometers, while this number is some 3.7 square kilometers for the latter (cf. [79]). An illustration of this comparison is provided in Fig. 10.
We also applied confusion matrixes [1, 71] to compare the two modeling methods using the correct classification rate (CCR) (Tables 9, 10). We qualitatively translate the values of very low, low, moderate, high, and very high derived from Table 8 into the values of 1, 2, 3, 4, and 5, respectively. The sum of values of diagonal lines in confusion matrixes is divided by the total number of control points, which is 10 in this study. The value of CCR is therefore 0.7 and 0.8 for MOORA and MOOSRA, respectively. This also implies that MOOSRA provides a more robust map of mineral potential.
6 Discussion
Several multicriteria decisionmaking (MCDM) methods, which have their advantages and disadvantages [42, 71, 100,101,102], have been applied to knowledgedriven GISbased issues, such as mineral potential mapping studies (e.g., [13, 40, 45, 50, 107, 114, 130]). These methods are used in weighting spatial proxies [9, 13, 39, 42, 71, 99, 124]. The FUCOM method, as a pairwise comparison method, reduces the large number of pairwise comparisons of similar and popular approaches such as analytic hierarchy process (AHP: [113]) with n(n − )/2 and the best–worst method (BWM: [109]) with 2n − \(3\) number of pairwise comparisons with n − \(1\) which leads to a less timeconsuming and more consistent performance compared with AHP and BWM. Yet, the application of FUCOM in MPM is not without drawbacks. The subjectivity has been regarded as the most crucial flaw of FUCOM in MPM (cf. [94]). Further research should account for fuzziness and ambiguity to modulate this caveat in FUCOMbased MPM (cf. [94]). Turning to the MOORA [21] and MOOSRA [32] methods, this study demonstrated the application of these approaches in the integration of weighted evidence maps. Regionalscale maps of mineral potential are used for reducing the search space and thus the cost of exploratory surveys [79]. In this work, two multicriteria decisionmaking approaches, namely MOORA [21] and MOOSRA [32], were applied in the context of knowledgedriven mineral potential mapping (MPM). Both methods successfully limited the search space for field checks and further surveys. However, MOOSRA returned a more costeffective potential map, with its target zones occupying merely some 1.7 km^{2}. Groundtruth analysis of the delineated target also sheds light on the superiority of the MOOSRA method. Furthermore, the statistical comparison of the two methods using correct classification rates (CCR) revealed that MOOSRA returned a more reliable map of mineral potential.
There are a whole host of different multicriteria decisionmaking methods used in MPM. However, what makes MOORA and MOOSRA more reliable compared to many other methods is the fact that optimizations procedure is applied to calculate the prospectivity score of individual unit cells [4, 7, 11, 33, 70, 75, 84, 98, 116, 129, 137]. This reduces the uncertainty stemming from erroneous mathematical calculations. In addition, this study was applied on a suite of mineral systemsderived targeting criteria (e.g., [85]), modulating the errors embedded in the localscale deposit models [80]. Therefore, the target zones retrieved from these frameworks can be assumed as confident targets, in which the risk of exploration has been reduced.
Aside from the comparison of these methods, the delineated target zones show evidence of calcic skarn mineralization. The presence of mineral assemblages critical to the exploration of this style of mineralization, such as magnetite, crystalline calcite, and pyrite, provides compelling evidence for the presence of mineralization. The delineated targets, therefore, are worthy of detailed surveys.
7 Conclusions
This study proposed the application of FUCOM method as a MCDM approach for assigning weights to the spatial proxies and two matrixbased decisionmaking methods of MOORA and MOOSRA for intergrading a set of targeting criteria for mineral potential mapping. These methods combined to each other to present twostep methodologies, namely FUCOMMOORA and FUCOMMOOSRA. The results of combined methods were interesting and accurate because FUCOM weighting method has the minimum possible number of comparisons in its theory, which lead to having more reliable outputs in comparison with previous approaches, and both MOORA and MOOSRA methods have robust mathematical theory, which reduces the uncertainty stemming from erroneous mathematical calculations and causes having more trusty results. The proposed methods FUCOMMOORA and FUCOMMOOSRA were utilized for intergrading a set of 2D spatial proxies representing calcic skarn mineralization in Central Iran. The latter method revealed superior results as shown by field checks and statistical analyses. Both methods successfully reduced the search space for further exploratory surveys. Moreover, a mineral system approach was applied for deriving the targeting criteria, which itself reduces the bias of fallacious assumptions in geological models. As a result, the retrieved maps of mineral potential can be assumed as a high confident map, based on which further decisions can be made. The target zones suggested in the potential maps are probably worthy of conducting further exploration surveys including lithogeochemical sampling, magnetic geophysical survey, trenching, and exploration drilling. The genetic characteristics of calcic skarn deposits and the data available were used to develop a set of 2D spatial proxies representing iron skarn mineralization. In the future, the proposed methods can be used to integrate a set of 3D spatial proxies for determining exploration drilling points in the target zones.
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Feizi, F., KarbalaeiRamezanali, A.A. & Farhadi, S. FUCOMMOORA and FUCOMMOOSRA: new MCDMbased knowledgedriven procedures for mineral potential mapping in greenfields. SN Appl. Sci. 3, 358 (2021). https://doi.org/10.1007/s42452021043429
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DOI: https://doi.org/10.1007/s42452021043429