Fuzzy Logic Expert System for Classifying Solonchaks of Algeria.
Soil classification is considered as an important means of communication at both national and international levels [1, 2]. However, few soil classification studies have been published . The lack of soil classification reduces our knowledge and affects our land use decision. This difficulty is compounded by the fact that the hierarchical classifications are often built on criteria that vary greatly from one to the other. The classical reference proposed by Baize and Girard  reduces the number of hierarchical levels, mitigates these challenges, and represents a significant improvement. Both conventional classifications (i.e., hierarchical and classical reference) are the most used. However, there are many other national classifications, such as the Australian classification system , Canadian , and French . Currently, the International Union of Soil Science promotes the development of a universal soil classification system  in which all the soils of the world find a place in its hierarchy. Preliminary results suggest that the objective and pedometric approaches can support the planned development of a universal soil classification system.
As the soil is part of an ecological continuum, the usual classifications are facing major challenges which require a choice, often questionable , between the base characters and their importance on the hierarchy of taxonomic units. Conventional classifications define several intergrades between the main units. Hierarchical classification systems are based partly on the judgment of the expert on soil formation. 40 years ago, the first attempts at the numerical soil classification was made [10, 11]. McBratney and Odeh  argued that a system of discrete soil classes is not adequate for soil classification and proposed a numerical classification based on fuzzy sets. Numerical approaches can deal with a large number of properties simultaneously. Currently, there are numerical classification systems that attempt to be an objective classification, which are based on the actual differences between morphological and analytical characteristics of the soils. Their main goal is to minimize intragroup variations and maximize intergroup variations according to objective criteria . WRB  has been favored by the International Union of Soil Science and the European Union as a correlation system between the soils . It defines the different groups of soil horizons in terms of references, properties, and diagnostic materials; each criterion is quantitative and well differentiated. Some studies have shown that WRB compared to Soil Taxonomy  is well suited for classifying calcareous soils  and gypsum soils [18, 19].
Similarly, at the end of the 16th World Congress of Soil Science, it was recommended to strengthen conventional methods of mapping by other methods, such as fuzzy logic and artificial intelligence to assess the inherent uncertainties in soil mapping . Fuzzy logic has become widespread in recent years in many scientific fields, such as soil science [21-23]. It aims at dealing with the uncertainty due to the imprecision . Fuzzy systems belong to the class of systems based on knowledge or expert systems. Their main purpose is to implement a human skill, or linguistic rules, by a computer program. Fuzzy logic provides a mathematical formalism with uncertain linguistic concepts. This mathematical method, which is based on set theory, has been introduced by Zadeh . Thus, many studies have focused on fuzzy logic to the study of soils and their classifications. It follows that fuzzy logic allows the creation of nonhierarchical continuous classes defined by their centers of gravity . The notion of intergrade soils has been formally recognized by using the concept of fuzzy sets . The fuzzy logic-based algorithms can estimate the number of soil intergrades . The combination of fuzzy clustering to other techniques is currently used in the development of models for the prediction of soil properties [27, 28]. In general, this theory has great potential in soil science . The use of this system can replace the Boolean variable, which is poorly suitable to the presentation of most natural phenomena, by using linguistic concepts that will be transformed into multilanguage values. There are several fuzzy inference systems that were used in different applications; the most commonly used is the Mamdani fuzzy inference system (MFIS), which will be used in this research. The advantages of MFIS are reputed as intuitive; it is the most widespread acceptance and better suited to human cognition .
In arid and semiarid regions of the North of Africa, the calcium carbonate accumulations are frequently associated with gypsum and soluble salts. In many cases, soils are at the same time saline, calcareous, and gypsic . Rahmouni  studied soil classification in Algeria (semiarid area) using WRB. This author revealed high similarity between Gypsisols and Solonchak and concluded that the soil studied could be considered as an intermediary group between Gypsisols and Solonchaks. To improve WRB soil classification, the fuzzy classification (continuous) is of great importance to group all soil types into continuous classes with membership values , to avoid imprecise and ambiguous classification. In this context, the expert system based on MFIS was used to (1) determine the degree of membership between Solonchaks in northern Algeria and both Calcisols and Gypsisols based on WRB criteria and (2) to see to what extent these Solonchaks may constitute Calcisols or Gypsisols.
2. Materials and Methods
2.1. Studied Soil Characteristics. This research focused on the study of 194 profiles identified by Djili  (Figure 1) in the north of Algeria. Using WRB  criteria, all these profiles were considered as Solonchaks. The characteristics of the diagnostic horizons of all profiles are shown in Table 1.
The main features of the whole horizons are summarized as follows:
(i) Electrical conductivity ([EC.sub.e]) of saturated soil-paste varies between 15 and 96 dS/m with an average of 30 dS/m. These Solonchaks are marked by a very high salinity  that varies highly (CV = 56%) from a soil to another.
(ii) Calcium carbonate equivalent is variable (CV = 56%) and is between 1% and 67% with a mean of 23%. These Solonchaks can therefore be very little calcareous, or, conversely, very heavily filled in calcium carbonate equivalent. Some of these horizons follow the criteria of the calcic horizon.
(iii) Gypsum content is highly variable (CV = 115%). They range from less than 1% to 73% (by mass) with an average of 9%. Therefore, diagnostic horizons of these soils are extremely gypsic. Some of these horizons follow the criteria of the gypsic horizon.
(iv) Soil pH of the saturation extract values is between 7 and 8.9 with an average of 7.83, which indicates an alkaline soil reaction.
(v) The thickness of the diagnostic horizons (E) is highly variable (CV = 55%), and these Solonchaks may have diagnostic horizons moderately thick to very thick. These characteristics suggest that these Solonchaks are related to Calcisols than Gypsisols.
The variables or physical values used for the three groups studied soils (Solonchaks, Calcisols, and Gypsisols) are presented in Table 2. All studied Solonchaks have [EC.sub.e] [greater than or equal to] 15 dS/m, and therefore the pH is no taken into account according to WRB classification.
Among the 194 studied Solonchaks profiles, 74% are Calcic Solonchak, 10% are Gypsic Solonchak, 4% are Gypsic Calcic Solonchak, and 12% are Solonchak, which are neither Gypsic nor Calcic. Despite the high content of calcium carbonate equivalent and gypsum, we observed a lack of petrocalcic and petrogypsic qualifiers because of the absence of more diagnostic criteria.
2.2. Decision-Making. The expert system based on MFIS requires three steps, the fuzzification, inference, and defuzzification, as shown in Figure 2.
2.2.1. Fuzzification. The fuzzification is a process of converting numeric values (or physical parameters of the diagnostic criteria) of each group of soil (Table 2) into fuzzy variables. Compared to other numerical classifications as distance metrics method , neither crisp data (nonfuzzy) nor model assumptions are required [34-37], which is considered as one of the major advantages of MFIS.
During this step, we firstly defined the membership function of all variables, and then, we proceeded to the passage from the physical quantities to the linguistic variables. The membership functions describe the membership degree of a fuzzy variable (the [EC.sub.e] in this case) to a fuzzy subset A (little [EC.sub.e] value, medium, or great), and it is noted as [[mu].sub.A](x) =  six [member of] Aet [[mu].sub.A](x) = 0 six [not member of] A.
Fuzzification of all physical variables has been applied using the Gaussian membership function and the fuzzy set. The fuzzy variables (input) were divided into three subsets using linguistic variables (little value (L), medium value (M), and great value (G)). On the other hand, the output was also divided into three subsets (little value (L), medium value (M), and great value (G)) (Table 2, Figures 3 and 4). The advantage of this method, using linguistic variable, is to avoid threshold values that are not adequate for continuum soil.
The boundaries of linguistic variables of calcium carbonate equivalent, gypsum, electrical conductivity, secondary carbonates (SC), and thickness of diagnostic horizon L (0-30%), M (30-80%), and G (80-100%) are shown in Figure 3. The electrical conductivity was divided into L (0-30 dS/m), M (30-80 dS/m), and G (80-100 dS/m) linguistic variables. For the thickness of the diagnostic horizon, three subsets were defined as cited above (L (0-30 cm), M (30-80 cm), and G (80-100 cm)), and finally, for both thickness of the diagnostic horizons x [EC.sub.e] and thickness of the diagnostic horizon x gypsum, the linguistic variables were L (0-2000), M (2000-7000), and G (7000-9000). These boundaries of linguistic variables are based on the human knowledge from field experiences. The same procedure was performed for the output variables which have been translated into Solonchaks indices, Calcisols indices, and Gypsisols indices as shown in Figure 4.
2.2.2. The Inference Rules. The inference rules were developed using the 9 input data (diagnostic criteria or physical variables) previously divided into three subgroups that represent Solonchak, Calcisol, and Gypsisol, respectively (Table 2). The soil was classified Solonchak if all its diagnostic criteria were great (G). The same was applied for Calcisol and Gypsisol. For example, if our soil presented little calcium carbonate equivalent and (SC) (that characterize Calcisol), medium gypsum content (that characterize Gypsisol), and great [EC.sub.e] (that characterize Solonchak), the soil will be classified as Solonchak. These rules are expressed as single conditions (IF) or combined with other conditions (AND, OR) to achieve a linguistic result. Each rule consists of an antecedent part (condition or input) expressed by IF and a substantial portion (conclusion or output) expressed by THEN. For example, IF [EC.sub.e] is G AND ([EC.sub.e] x EE) is G AND E is G (Solonchak criteria), AND calcium carbonate equivalent is L AND SC is L (Calcisol criteria), AND gypsum content is L AND (E x gypsum) is L (Gypsisol criteria) THEN Solonchak is G, Calcisol is L, Gypsisol is L.
In this study, the degree of membership between the soils studied was highlighted using 9 physical variables (three for each soil) and 3 linguistic variables (Little, Medium, and Great). (1) In total, 171 inference rules that represent all diagnostic criteria combinations were developed by the following relation:
((3 x [C.sup.1.sub.3] + 3 x [C.sup.2.sub.3] + [C.sup.3.sub.3]) x 9) (1)
where C is combination.
2.2.3. Defuzzification. Inference methods provide membership function [[mu].sub.res] (y) for the output variable "y" (Solonchak, Calcisol, and Gypsisol). Defuzzification is the transformation of this fuzzy information into measured information. A centroid (Z) method was employed  (Figure 5). The expression of Z is given by the following equation:
Z = (([[integral].sub.D] y x [[mu].sub.res] (y) x dy)/([[integral].sub.D] [[mu].sub.res] (y) x dy)). (2)
In this study, Z represents the Solonchak indice, Calcisol indice, or Gypsisol indice obtained by MFIS.
The correlations between indices of soil obtained by MFIS and all soil classification criteria considered by WRB ([EC.sub.e], calcium carbonate equivalent, gypsum content, and thickness of diagnostic horizons) were conducted. From the 171 rules estimated, only 21 inference rules were selected under our conditions. The selection of these 21 inference rules was based on high significant correlation (P < 0.05) between the different Solonchaks (Is), Calcisol (Ic), and Gypsisol (Ig) indices and WRB diagnostic criteria (except for diagnostic horizon thickness criteria). Finally, the key rules obtained are as follows:
Rule 1: IF [EC.sub.e] is G AND ([EC.sub.e] x E) is G AND E is G AND calcium carbonate equivalent is L AND SC is L AND gypsum content is L (E x gypsum) is L THEN Solonchak is G, Calcisol is L, Gypsisol is L.
Rule 2: IF [EC.sub.e] is L AND ([EC.sub.e] x E) is L AND E is L AND calcium carbonate equivalent is G AND SC is G AND gypsum content is L (E x gypsum) is L THEN Solonchak is L, Calcisol is G, Gypsisol is L.
Rule 3: IF [EC.sub.e] is M AND ([EC.sub.e] x E) is M AND E is M AND calcium carbonate equivalent is G AND SC is G AND gypsum content is L (E x gypsum) is L THEN Solonchak is M, Calcisol is G, Gypsisol is L.
Rule 4: IF [EC.sub.e] is L AND ([EC.sub.e] x E) is L AND E is L AND calcium carbonate equivalent is M AND SC is M AND gypsum content is L (E x gypsum) is L THEN Solonchak is L, Calcisol is M, Gypsisol is L.
Rule 5: If [EC.sub.e] is L AND ([EC.sub.e] x E) is L AND E is L AND calcium carbonate equivalent is L AND SC is L AND gypsum content is G (E x gypsum) is G THEN Solonchak is L, Calcisol is L, Gypsisol is G.
The same procedure is used, as mentioned above, for the rest of the rules.
The method of min-max [25, 39, 40] was used to calculate the fuzzy inference. A weighting coefficient (Wi) is assigned to each inference rule. This coefficient depends on the structure of the rule, that is to say the combination of OR and AND. AND is used for the min operator and OR for the max operator. The weighting coefficient is used as a constant clipping of the output membership function.
2.3. Interpretation of Indices. Classification by MFIS is in favor of the higher indices. However, when the indices have the same value, it means that soils have the same degree of membership. Therefore, the soil is considered intergrade. Thus, we can interpret the evidence as follows:
(i) If Is > Ic and Is > Ig, then the soil is classified Solonchak.
(ii) If Ic > Is and Ic > Ig, then the soil is classified Calcisol.
(iii) If Ig > Is and Ig > Ic, then the soil is classified Gypsisol.
(iv) If Is = Ic = Ig, then the soil is classified intergrade Solonchak-Calcisol-Gypsisol.
(v) If Is = Ic and Ig < Ic and Ig < Is, then the soil is classified as an intergrade Solonchak-Calcisol soil.
(vi) If Is = Ig and Ic < Gypsisol and Ic < Is, then the soil is classified as an intergrade Solonchak-Gypsisol soil.
(vii) If Ic = Ig and Is < Ic and Is < Ig, then the soil is classified as an intergrade Calcisol-Gypsisol soil.
3. Results and Discussion
Data analyses showed some differences between the three calculated indices. These data varied from 0.15 to 0.53 for Is, from 0.13 to 0.50 for Ic, and from 0.14 to 51 for Ig (Table 3). In general, Solonchaks under our study were more related to Calcisols (0.31 versus 0.25, resp.) than to Gypsisols (0.31 versus 0.19, resp.). These results suggest that the degree of membership of Solonchaks with Calcisols was more important compared to the degree of membership of Solonchaks with Gypsisols. 41% of the indices are assigned to Solonchaks, 33% to Calcisols, and 25% to Gypsisols as shown in Figure 6. This result revealed that the soils studied are dominated by Solonchaks.
The high similitude between Solonchaks and Calcisols suggests that soils studied could be classified as Calcisols. The results illustrated in Figures 6 and 7 show the following facts:
(i) Solonchaks are the most dominant followed by the Calcisols.
(ii) Solonchaks similar to Gypsisols are represented only by soil 89 with an index of 0.5. Soil 89 is qualified in WRB as Gypsic Solonchak.
(iii) Only soils 39, 107, and 138 simultaneously exhibit the same degree of similarity with Solonchaks, Calcisols, and Gypsisols because their indices are 0.21, 0.18, and 0.15, respectively. Therefore, soils 39, 107, and 138 are qualified in WRB as Gypsic Calcic Solonchak.
(iv) In contrast, soil 78 is classified Gypsisol by the fuzzy classification unlike WRB. We explain this differences that the soil 78 is very rich in gypsum (58% by mass) (Table 4). This soil is qualified by WRB as Gypsic Solonchak.
Soils 15 and 126 have a higher degree of similarity to Calcisols than to Solonchaks (Figure 7). Therefore, these soils were classified by MFIS as Calcisols and not as Solonchaks. Moreover, the soils 15 and 126 are very rich in calcium carbonate equivalent (67%), rich in SC, with values ranging from 20% to 25% (by volume) for soils 15 and 126, respectively (Table 4). These 2 soils are qualified by WRB as Calcic Solonchak. The difference observed between the WRB and MFIS was due to fact that the threshold values and priority order of classification were not considered by MFIS.
According to the overall trend of the three curves (Figure 7), we concluded that the majority of Gypsisols was affected by values below 0.2. The indices between 0.2 and 0.4 affect soils that have almost the same dominance between Solonchaks and Calcisols. These reveal the presence of a dominant overlap between Solonchaks and Calcisols compared to Solonchaks and Gypsisol. Index values above 0.4 represent essentially Solonchaks. Therefore, we can allocate indices (I) obtained by MFIS into three groups to determine the frequency of the level of soil membership studied within each group, as shown in the following breakdown:
(i) Group 1 (low indices): I < 0.2
(ii) Group 2 (average indices): 0.2 < I [less than or equal to] 0.4
(iii) Group 3 (high indices): I > 0.4
3.1. Membership Degree between the Soils Studied. Figure 8 showed that 50% of Gypsisols, 32% of Calcisols, and 19% of Solonchaks in the study area shared the group of low indices (I < 0.2). This result means that in this group, studied Solonchaks have a low degree of membership with Gypsisols and a relatively higher degree of membership with Calcisols. Similarly, some Solonchaks of this group have simultaneously the same degree of membership with Calcisols and Gypsisols. The Majority of the soils of group 1 are qualified by WRB as Gypsic Solonchak, and a small proportion of these soils are qualified as Gypsic Calcic Solonchak. In group 2 (0.2 < I [less than or equal to] 0.4), 43% of the average indices are assigned to Solonchaks, 39% to Calcisols, and 18% to Gypsisols. According to WRB, the qualifier Calcic is predominant for this group comparing the qualifier Gypsic.
This result suggests that Solonchaks, which are also dominant in this group, have a higher degree of membership with Calcisols than with Gypsisols. In group 3 (I > 0.4), 67% of the indices are assigned to Solonchaks against 26% and 6% to Calcisols and Gypsisols, respectively. This result means that Solonchaks clearly dominate this group. It also suggests that, compared to groups 1 and 2, the degrees of membership between soils (Solonchaks with both Calcisols and Gypsisols) in group 3 were low, and there are some Solonchaks that have no membership with either Calcisols or with Gypsisols. On the other hand, the proportions of the soil qualifiers in group 3 are distributed in the following way: Calcic (80%), Gypsic (12%), Gypsic Calcic Solonchak (3%), and 5% of Solonchaks, which are neither Calcic nor Gypsic.
Overall, these results showed that the studied soils were dominated by Solonchaks; 74% of these Solonchaks are Calcic Solonchak. The degree of membership of Solonchaks to Calcisols or Gypsisols was different depending on the group considered. The degree of membership between Solonchaks and Calcisols is stronger than that between Solonchaks and Gypsisols. Thus, Solonchaks with a higher degree of membership with Calcisols are qualified by WRB as Calcic Solonchaks.
The data analysis of each group of indices (Figure 8) was computed to determine Solonchaks, Calcisols, and Gypsisols frequencies and all possible intergrade soils. Figure 9 shows that Solonchak frequency increased from 39% in group 1 to 64% in group 2 and to 78% in group 3. Both Calcisols and Gypsisols were only detected in group 3 (3% and less than 2%, resp.). In each group, the soils which are neither Solonchaks, nor Gypsisols, nor Calcisols may be considered as intergrade soils with Solonchaks. As conclusion, the MFIS-based algorithms could estimate the number of soil intergrades and the degree of membership values (indices) of these soils with more precision [12-25] compared to WRB soil classification.
Figure 9 shows three types of intergrade soils, Solonchaks-Calcisols, Solonchaks-Gypsisols, and Solonchaks-Calcisols-Gypsisols. These intergrade soils represent 60% of Solonchaks in group 1 with a clear predominance of Solonchaks-Calcisols (45%) followed by Solonchaks-Gypsisols (11%) and Solonchaks-Calcisols-Gypsisols (3%). These inter-grade soils represent only 34% of soils in group 2 and 16% in group 3. The use of MFIS revealed that Solonchaks previously classified by WRB have strong similarities with Calcisols and Gypsisols.
According to MFIS, Solonchaks have a higher degree of membership with Calcisols (29%) (Figure 10) than with Gypsisols (5%), and only 1% was Solonchaks-Calcisols-Gypsisols. Consequently, the classification of Solonchaks intergrades will be Solonchaks-Calcisols, Solonchaks-Gypsisols, and Solonchaks-Calcisols-Gypsisols. MFIS also showed that 61% of soils were strictly Solonchaks and only 1% and 0.5% were strictly Calcisols and Gypsisols, respectively. Based on WRB, from the 61% Solonchaks detected by MFIS, only 26% were classified as Solonchaks, 43% as Calcic Solonchaks, 3% as Gypsic Solonchaks, and 1% as Gypsic Calcic Solonchaks.
3.2. Correlation between the Indices of Soil Obtained by MFIS and Diagnostic Criteria of WRB. The correlation data analyses were conducted to determine the relationship between the indices obtained by MFIS, and its diagnostic criteria are defined by WRB ([EC.sub.e], calcium carbonate equivalent, SC, gypsum, thickness of horizon (E), (E x [EC.sub.e]), (E x gypsum)). The statistical parameters of these relationships presented in Table 5 showed that all correlations were positive and significant (0.49 < r < 0.77; P < 0.05) except for (E) (0.01 < r < 0.06; P > 0.05). Solonchaks indices (Is) presented significant and positive correlation with [EC.sub.e] (0.76), and Gypsisols indices (Ig) showed high correlation with gypsum content (0.70), while Calcisols indices (Ic) soil presented significant correlation with calcium carbonate equivalent and SC (0.77 and 0.70, resp.). The majority of WRB diagnostic criteria were highly correlated with the indices obtained by MFIS. These results suggest that MFIS gives the same soil classification as WBR; however, its application provides more precision concerning the degree of membership values between soils (reference group soil).
Data analyses showed that the relationships between the three soil indices were positive and significant (P < 0.05) (Table 6). The relationship Is x Ic (r = 0.7) is stronger than Is x Ig (r = 0.52) and Ic x Ig (r = 0.32). The high correlation between Is and both Ic and Ig suggests the presence of some intergrade soils under our conditions (Solonchak-Calcisol, Solonchak-Gypsisol, and Solonchak-Calcisol-Gypsisol) (Figure 10).
Therefore, Solonchaks studied are actually a mixture of Solonchaks, Calcisols, and Gypsisols. However, the results showed that the indices assigned to Solonchaks were the most dominant (about 41%) followed by those assigned to Calcisols (33%) and Gypsisols (25%). In general, Solonchaks presented the highest indices, followed by Calcisols and Gypsisols.
In total, Solonchaks have a higher degree of membership with Calcisols (29% of soil or Solonchak-Calcisol) than with Gypsisols (5%). Data analyses also confirmed these results by the high correlation between Solonchaks and Calcisols (r = 0.7; P < 0.05) and between Solonchaks and Gypsisols (r = 0.52; P < 0.05). Solonchaks-Calcisols (29%) intergrade soils were the most important in the north of Algeria compared to Solonchaks-Gypsisols (5%). These results confirm the conclusion of Hughes et al.  who showed that fuzzy logic allows the determination of intergrade groups. Also, Viscarra Rossel et al.  use the fuzzy approach to provide information on the group of soil overlaps. MFIS showed that the degree of overlapping membership of these Solonchaks-Gypsisols-Calcisols intergrades was poorly represented (<2%). Similarly, it was found that 1% and 0.5% of 194 Solonchaks classified by WRB are respectively recognized as Calcisols and Gypsisols by MFIS. This small difference between the two classification systems is due to the fact that the threshold values of diagnostic criteria defined by conventional classifications would not be suitable for soil that is considered as a continuum system . Consequently, significant information is lost , especially for both taxonomic fragmentation and soil mapping. However, fuzzy classification is continuous and numerical  that use the linguistic variables and Gaussian membership functions.
These results revealed that the two used systems (WRB and MFIS) provide the same classification (predominance of the Solonchak group). Based on fuzzy logic, the soil previously classified by WRB as Calcic Solonchak has high degree of membership to Calcisols, and some of these Calcic Solonchaks are now classified by MFIS as Calcisol. Solonchaks qualified previously by WRB as Gypsic Solonchak has a high degree of membership to Gypsisol, and some of these soils were classified by MFIS as Gypsisol. The differences noted between the two soil system classifications are attributed to the fact that the WRB depends on the order of priority and weights attributed to diagnostic criteria. MFIS exhibited more precision concerning intergrade soils and degree of membership compared to WRB. This precision is very useful in soil management practices and land evaluation systems [23-43].
The soil classification by MFIS of 194 profiles previously classified as Solonchaks (Calcic Solonchak, Gypsic Solonchak, and Gypsic Calcic Solonchak) by WRB revealed 6 different soil groups represented by Solonchaks, Solonchaks-Calcisols intergrades, Solonchaks-Gypsisols intergrades, Solonchaks-Calcisols-Gypsisols intergrades, Calcisols, and Gypsisols. In addition, this study showed that Is, Ic, and Ig were highly correlated with almost diagnostic criteria established by WRB except for horizon thicknesses. Moreover, the correlation between Is and Ic (r = 0.7) was more important than Is and Ig (r = 0.52) and Ic and Ig (r = 0.32).
These relationships between indices suggest the presence of intergrade soils. On the other hand, these results confirm that Solonchaks-Calcisols intergrade is more dominant than Solonchaks-Gypsisols intergrade, as previously reported by Halitim  and Djili . Our results showed that soil groups determined by WRB are analogous to those determined by MFIS. However, the application of MFIS provides us the degree of membership between all these soils and their intergrades and takes into account the continuous complex nature of soil. As general conclusion, MFIS improved soil classification by using the degree of membership. Therefore, fuzzy logic could be considered as the basic tool for both classification and soil mapping and an undeniable support in precision agriculture. The application of the MFIS to other soils of the world is possible because of the flexibility of inference rules.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
 T. Zadorova and V. Penizek, "Problems in correlation of Czech national soil classification and World Reference Base 2006," Geoderma, vol. 167-168, pp. 54-60, 2011.
 X. Z. Shi, E. D. Warner, and H. J. Wang, "Cross-reference for relating genetic soil classification of China with WRB at different scales," Geoderma, vol. 155, no. 3-4, pp. 344-350, 2010.
 A. E. Hartemink, "The use of soil classification in journal papers between 1975 and 2014," Geoderma Regional, vol. 5, pp. 127-139, 2015.
 D. Baize and M. C. Girard, Referentiel Pedologique, Edition Quae, Versailles, France, 2008.
 Commonwealth Scientific and Industrial Research Organisation, Australian Classification System, August 2015, http:// www.clw.csiro.au/aclep/asc_re_on_line/soilhome.htm.
 Soil Classification Working Group, The Canadian System of Soil Classification, Agriculture and Agri-Food, Ottawa, ON, Canada, 1998.
 National Institute of Agronomic Research, Referentiel Pedologique, INRA, Paris, France, 1995.
 FAO, Systeme Universel de Classification des sols, 2017, http:// www.fao.org/soils-portal/soil-survey/soil-classification/universal-soilclassification/en/.
 P. Duchaufour, "Raflexions sur les classifications des sols," Etude et Gestion des Sols, vol. 5, pp. 201-205, 1998.
 J. H. Rayner, "Classification of soils by numerical methods," Journal of Soil Science, vol. 17, no. 1, pp. 79-92, 1966.
 A. W. Moore, J. S. Russell, and W. T. Ward, "Numerical analysis of soils: a comparison of three soil profile models with field classification," Journal of Soil Science, vol. 23, no. 2, pp. 193-209, 1972.
 A. McBratney and I. O. A. Odeh, "Application of fuzzy sets in soil science: fuzzy logic, fuzzy measurements and fuzzy decisions," Geoderma, vol. 77, no. 2-4, pp. 85-113, 1997.
 FAO, Les Systemes Numeriques, 2017, http://www.fao.org/ soils-portal/soil-survey/soil-classification/numerical-systems/ en/.
 IUSS Working Group WRB, "World reference base for soil resources. International Soil Classification System for Naming Soils and Creating Legends for Soil Maps," World Soil Resources Reports, no. 106, FAO, Rome, Italy, 2014.
 A. Jones, L. Montanarella, and R. Jones, Soil Atlas of Europe, Joint Research Centre, Ispra, Italy, 2005.
 Soil Survey Staff, Soil Taxonomy, USDA National Resources Conservation. Services, Washington, DC, USA, 2nd edition, 1999.
 I. Esfandiarpour, M. H. Salehi, and A. Karimi, "Correlation between Soil Taxonomy and World Reference Base for Soil Resources in classifying calcareous soils: (a case study of arid and semi-arid regions of Iran)," Geoderma, vol. 197-198, pp. 126-136, 2013.
 N. Toomanian and A. Jalalian Karimian, "Application of the WRB (FAO) and US taxonomy systems to gypsiferous soils in Northwest Isfahan, Iran," Journal of Agricultural Science and Technology, vol. 5, pp. 51-66, 2003.
 A. Mojiri, A. Jalalian, and N. Honarjoo, "Comparison between keys to soil taxonomy and WRB to classification of soils in Segzi plain, Iran," Journal Applied Science, vol. 11, no. 3, pp. 579-583, 2011.
 M. Jamagne, "Compte rendu succinct des travaux. 16eme Congre Mondial de la Science du Sol, Montpellier, 20 au 26 Aout 1998," Etude et Gestion des Sols, vol. 6, pp. 1-3, 1999.
 J. V. Vliet, A. Hagen-Zanker, J. Hurkens, and H. V. Delden, "A fuzzy set approach to assess the predictive accuracy of land use simulations," Ecological Modelling, vol. 261-262, pp. 32-42, 2013.
 M. Elaalem, "A Comparison of parametric and fuzzy multi-criteria methods for evaluating land suitability for Olive in Jeffara Plain of Libya," APCBEE Procedia, vol. 5, pp. 405-409, 2003.
 A. Sharififar, H. Ghorbani, and F. Sarmadian, "Soil suitability evaluation for crop selection using fuzzy sets methodology," Acta Agriculturae Slovenica, vol. 107, pp. 32-35, 2016.
 H. J. Zimmermann, Fuzzy Set Theory and its Applications, Kluwer Academic Publishers, London, UK, 4th edition, 2001.
 L. A. Zadeh, "Fuzzy sets," Journal of Information and Control, vol. 8, no. 3, pp. 338-353, 1965.
 P. Hughes, A. McBratney, and B. Minasny, "End members, end points and extragrades in numerical soil classification," Geoderma, vol. 226-227, pp. 365-375, 2014.
 P. Verma, P. Singh, and K. George, "Uncertainty analysis of transport of water and pesticide in an unsaturated layered soil profile using fuzzy set theory," Applied Mathematical Modelling, vol. 33, no. 2, pp. 770-782, 2009.
 M. Fajardo, A. McBratney, and B. Whelan, "Fuzzy clustering of Vis-NIR spectra for the objective recognition of soil morphological horizons in soil profiles," Geoderma, vol. 263, pp. 244-253, 2015.
 E. H. Mamdani, "Application of fuzzy logic to approximate reasoning using linguistic synthesis," IEEE Transactions on Computers, vol. 26, pp. 1182-1191, 1977.
 K. Djili, "Contribution a la connaissance des sols du Nord d'Algerie. Craation d'une banque de donnaes informatisees et utilisation d'un systaeme d'information gaeographique pour la spatialisation et la valorisation des donneaes peadologiques," Thease doctorat, p. 227, ENSA, El-Harrach, Algeria, 2000.
 A. Rahmouni, "Morphologie et propriates des gypsisols references du Hodna," Magister Thesis, p. 188, Superior National School of Agronomics, Oued Smar, Algeria, 2010.
 United States Salinity Laboratory Staf, Diagnosis and Improvement of Saline and Alkali Soils, Agriculture Handbook, no. 60, Govt. Printing Office, Washington, DC, USA, 1954.
 F. Carre and M. Jacobson, "Numerical classification of soil profile data using distance metrics," Geoderma, vol. 148, no. 34, pp. 336-345, 2009.
 E. H. Mamdani, "Application of fuzzy algorithms for simple dynamic plants," Proceedings of the IEEE, vol. 121, no. 12, pp. 1585-1588, 1974.
 A. Uyumaz, A. Altunkaynak, and M. Ozger, "Fuzzy logic model for equilibrium scour downstream of a Dams vertical gate," Journal of Hydraulic Engineering, ASCE, vol. 132, no. 10, pp. 1069-1075, 2006.
 M. Ozger, "Comparison of fuzzy inference systems for stream flow prediction," Hydraulic Science Journal, vol. 54, no. 2, pp. 261-273, 2009.
 A. Ahumada, A. Altunkaynak, and A. Ashraf, "Fuzzy logic-based attenuation relationships of strong motion earthquake records," Expert Systeme with Applications, vol. 42, no. 3, pp. 1287-1297, 2015.
 J. T. Ross, Fuzzy Logic with Engineering Applications, McGraw-Hill, Inc., New York, NY, USA, 1995.
 C. Negoita, Expert Systems and Fuzzy Systems, Benjamin Cummings, Redwood City, CA, USA, 1985.
 G. Klir and T. Folger, Fuzzy Sets, Uncertainty and Information, Prentice-Hall, Englewood Cliffs, NJ, USA, 1988.
 R. A. Viscarra Rossel, T. Behrens, and E. Ben-Dor, "A global spectral library to characterize the world's soil," Earth-Science Reviews, vol. 155, pp. 198-230, 2016.
 A. Zhua, E. Lawerence, B. D. Band, D. Thomas, and J. Nimlosd, "Automated soil inference under fuzzy logic," Ecological Modelling, vol. 2, no. 90, pp. 123-145, 1996.
 E. Van Ranst and H. Tang, "Fuzzy reasoning versus Boolean logic in land suitability assessment," Malaysian Journal of Soil Science, vol. 3, pp. 39-58, 199.
 A. Halitim, Sols des regions arides d'Algerie, OPU, Alger, Algeria, 1988.
Samir Hadj Miloud (iD),(1,2) Kaddour Djili, (1) and Mohamed Benidir (3)
(1) Soil Science Department, Higher National Agronomic School (ENSA-ES1603), BP 16200 El Harrach, Algeria
(2) Department of Agronomics, Faculty of Natural Science and Life, University Saad Dahlab, Soumaa, BP 270 Blida, Algeria
(3) Unit of Setif, Institut National de la Recherche Agronomique (INRAA), El Harrach, Algeria
Correspondence should be addressed to Samir Hadj Miloud; email@example.com
Received 29 November 2017; Accepted 13 June 2018; Published 8 July 2018
Academic Editor: Claudio Cocozza
Caption: Figure 1: Solonchaks location map.
Caption: Figure 2: Reasoning of the database schema by a fuzzy inference system.
Caption: Figure 3: Membership function of input variables.
Caption: Figure 4: Membership function of the output variables.
Caption: Figure 5: A method of the centroid used for defuzzification.
Caption: Figure 7: Classification of soils obtained by the MFIS.
Table 1: Characteristics of diagnostic horizons of studied Solonchaks. Parameters Minimum Maximum Mean pH 7 8.9 7.83 [EC.sub.e] (dS/m) at 25[degrees]C 15 96 30 Calcium carbonate equivalent (%) 1 67 23 Gypsum (%) (by mass) 0 73 9 E (cm) 15 1.5 69 Parameters SD CV (%) pH 0.3 4 [EC.sub.e] (dS/m) at 25[degrees]C 17 56 Calcium carbonate equivalent (%) 13 56 Gypsum (%) (by mass) 10 115 E (cm) 38 55 Note. E: thickness of the diagnostic horizons; [EC.sub.e]: electrical conductivity; SD: standard deviation; CV: coefficient of variation. Table 2: Physical quantities of soil groups recommended by WRB . Soil groups Variables used  (input variables) (output variables) Solonchaks (i) [EC.sub.e] (dS/m) (ii) E (cm) (iii) [EC.sub.e] x thickness of the diagnostic horizons ([EC.sub.e] x E) Calcisols (iv) Calcium carbonate equivalent (%) (iv) E (cm) (vi) Secondary carbonate (%) by volume Gypsisols (vii) Gypsum content (%) (by mass) (viii) E (cm) (ix) Thickness of diagnostic horizons x content in gypsum (E x gypsum) Table 3: Statistical parameters of the indices of three soils. Soils Minimum Maximum Mean SD Is 0.15 0.53 0.31 0.12 Ic 0.13 0.50 0.25 0.1 Ig 0.14 0.51 0.19 0.06 Table 4: Characteristics of Solonchaks 15, 126, and 78. Parameters Soil 15 Soil 126 Soil 78 pH 8.6 7.5 7.6 [EC.sub.e] (dS/m) 23 15 15 Calcium carbonate equivalent (%) 67 67 22 Secondary carbonate (%) by volume 20 25 1 Gypsum (%) by mass 5 8 58 E (cm) 70 40 100 Note. E: thickness of the diagnostic horizons; [EC.sub.e]: electrical conductivity. Table 5: Correlations between indices of Solonchaks (Is), Calcisols (Ic), and Gypsisols (Ig) and different diagnostic criteria. Relations df r [R.sup.2] Is, [EC.sub.e] 192 0.76 * 0.58 Is, E 192 0.01 0.0001 Is, (E x [EC.sub.e]) 192 0.49 * 0.24 Ig, gypsum 192 0.7 * 0.49 Ig, E 192 0.06 0.04 Ig, (Ex gypsum) 192 0.6 * 0.36 Ic, E 192 0.04 0.002 Ic, SC 192 0.7 * 0.5 Ic, calcium carbonate equivalent (CE) 192 0.77 * 0.6 Note. * Significant at probability P < 0.05; r: coefficient of correlation; R: coefficient of determination; df: degree of freedom. Table 6: Relations between indices of Solonchaks, Calcisols, and Gypsisols Relations df r [R.sup.2] Is, Ic 192 0.7 * 0.46 Is, Ig 192 0.52 * 0.27 Ig, Ic 192 0.32 * 0.1 Note. * Significant at probability P < 0.05. Figure 6: Histogram of frequency indices. Soil groups Indices (%) Calcisol 33 Solonchak 41 Gypsisol 25 Note: Table made from bar graph. Figure 8: Histogram of frequencies of groups of indices. Groups of indices Indices (%) [less than or 0.2-0.4 0.4-0.6 equal to] 0.2 Calcisol 32 39 26 Solonchak 19 43 67 Gypsisol 50 18 6 Note: Table made from bar graph. Figure 9: Histogram of soil group frequencies and their intergrades. % Group 1 Group 2 Group 3 Calcisol Solonchak 39 64 3 Gypsisol 78 Solonchak-Calcisol 45 32 <2 Solonchak-Gypsisol 11 <2 10 Solonchak-Gypsisol-Calcisol 3 <2 5 Note: Table made from bar graph. Figure 10: Histogram of soil group frequencies and their intergrades. Calcisol 1 Solonchak 61 Gypsisol 0.5 Solonchak-Calcisol 29 Solonchak-Gypsisol 5 Solonchak-Gypsisol-Calcisol 1 Note: Table made from bar graph.
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|Title Annotation:||Research Article|
|Author:||Miloud, Samir Hadj; Djili, Kaddour; Benidir, Mohamed|
|Publication:||Applied and Environmental Soil Science|
|Date:||Jan 1, 2018|
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