A comparative assessment of prediction capabilities of modified analytical hierarchy process (M-AHP) and Mamdani fuzzy logic models using Netcad-GIS for forest fire susceptibility mapping

Abstract

The main purpose of this study is to assess forest fire susceptibility maps (FFSMs) and their performances comparison using modified analytical hierarchy process (M-AHP) and Mamdani fuzzy logic (MFL) models in a geographic information system (GIS) environment. This study was carried out in the Minudasht Forests, Golestan Province, Iran, and was conducted in three main stages such as spatial data construction, forest fire modelling using M-AHP and MFL, and validation of constructed models using receiver operating characteristic (ROC) curve. At first, seven conditioning factors, such as altitude, slope aspect, slope angle, annual temperature, wind effect, land use, and normalized different vegetation index, were extracted from the spatial database. In the next step, FFSMs were prepared using M-AHP and MFL modules in a Netcad-GIS Architect environment. Finally, the ROC curves and area under the curves (AUCs) were estimated for validation purposes. The results showed that the AUCs for MFL and M-AHP are 88.20% and 77.72%, respectively. The results obtained in this study also showed that the MFL model performed better than the M-AHP model. These FFSMs can be applied for land use planning, management, and prevention of future fire hazards.

1. Introduction

Forests are major natural resources which play a crucial role in maintaining environmental balance. The health of forest in a given area is a true indicator of the ecological condition prevailing in that area (Saklani 2008). In general, fire is a natural component of many forest ecosystems and cannot be avoided (Dimopoulou & Giannikos 2001). Forest fires cause major damages to environment, human health and property, and endanger life (Rawat 2003). Six million square kilometre of forests has been lost around the world in less than 200 years mainly due to forest fire (Dimopoulou & Giannikos 2002). In Iran, forest fire is one of the most natural occurring hazards. According to the ECE/FAO database (Economic Commission for Europe/ Food and Agriculture Organization) on forest fires in 1982–1995, the number of forest fires per year is 130 and the burnt average area and its maximum is 54 km² and 330 km², respectively (Allard 2001). During the period 1991–1997, nearly 3063 fires have been reported, of which 13,700 ha was burnt. In the year 1998, there were 998 fires reported and the burnt area was estimated at 206,713 ha covering mostly shrubs. Losses were estimated at more than 5.6 million Rials (almost USD 3200 in the year of 1998), including 8761 tons of cattle feed lost (Allard 2001). In a recent paper, Janbaz Ghobadi et al. (2012) reported that, in the last decade, 9086 ha of the forests have been affected by forest fire. Also, in Iran, it is difficult to control forest fire naturally; however, it is possible to map different hazard levels for minimizing fire hazards and avoid potential damage.

In the literature, several different methods and techniques for forest fire susceptibility and risk mapping have been proposed and tested. Many studies have evaluated forest fire using geographic information system (GIS) and remote sensing (RS) technologies (Chuvieco & Congalton 1989; Prosper-Laget et al. 1995; Castro & Chuvieco 1998; Jaiswal et al. 2002; Erten et al. 2004; Wulder & Franklin 2006; Pradhan et al. 2007; Razali 2007; Saklani 2008; Chuvieco et al. 2010; Pradhan & Assilzadeh 2010; Adab et al. 2013; Teodoro & Duarte 2013). Several studies have applied probabilistic-based models such as fuel moisture content (FMC), fire area simulator (FARSITE), and Maxent models (Chuvieco et al. 2004; García et al. 2008; Krasnow et al. 2009; Renard et al. 2012).

In the past decade, some methods, such as artificial neural networks (ANNs) (Betanzos et al. 2002; Maeda et al. 2009; Bisquert et al. 2012; Safi & Bouroumi 2013), fuzzy logic (Nadeau et al. 2005; Carvalho et al. 2006; Agarwal et al. 2013), and adaptive neuro-fuzzy inference system (ANFIS) (Angayarkkani & Radhakrishnan 2011), have been proposed. Recently, new forest risk assessment methods, such as support vector machine (SVM) (Cortez & Morais 2007; Koetz et al. 2008; Zhao et al. 2011), decision tree methods (Stojanova et al. 2006), and random forest (Cortez & Morais 2007; Pierce et al. 2012; Leuenberger et al. 2013), were employed and their performances were assessed.

The aim of the current research is to assess forest fire susceptibility maps (FFSMs) using modified analytical hierarchy process (M-AHP) and Mamdani fuzzy logic (MFL) models developed in Netcad GIS 6. The assessment was performed in the Minudasht forests situated in Golestan Province, Iran. The main difference between this research and the approaches described in the aforementioned publications is that an M-AHP model is applied and the result is compared with MFL model in the study area. Also, expert opinions are used in the mentioned models for defining the rules and conditioning factor scores in MFL and M-AHP models, respectively. This contribution provides originality to this study.

2. Study area

The study area is located in the eastern part of Golestan Province, in the north of Iran, between latitudes 37° 00′ 27″ to 37° 27′ 53″ N, and longitudes 55° 14′ 00″ to 56° 00′ 39″ E (figure 1). It covers an area about 1531 km². This county shares boundaries with other Golestan Province counties such as Kalaleh county in the north and Azadshahr county in the west (Shadman Roodposhti et al. 2014). The elevation of the study area ranges between 100 and 2500 m above the mean sea level. The climate of Minudasht ranges between temperate and semi-humid types. The mean annual precipitation within the study area varies from 138 to 335 mm (Shadman Roodposhti et al. 2014). Based on Iranian Meteorological Organization, maximum and minimum of temperature were reported as +40 and −5 °C, respectively. Agriculture is the main economic activity of the region. In addition, part of the Golestan National Park is located within the county and it is known as tropical dry forests.

Figure 1. Forest fire location (black and pink dots) map in the study area. Modified from Pourtaghi et al. (2014). To view this figure in colour, please see the online version of the journal.

3. Methodology

The overall methodology flow chart of the study is shown in figure 2. The flowchart consists of three phases: (1) data integration and analysis, (2) forest fire susceptibility modelling using M-AHP and MFL approaches, and (3) validation of the constructed models using receiver operating characteristic (ROC) curve.

Figure 2. Flow chart of used methodology in the study area.

3.1. Data integration and analysis

In general, data collection and construction of a database of effective factors in any study area are the most important parts of the process (Ercanoglu & Gokceoglu 2002). At first, fire occurrences and locations were collected from MODIS (Moderate-Resolution Imaging Spectro Radiometer) satellite images (collected in year 2010), extensive field surveys, and national reports. Forest fires are related to year 2010, at 1:25,000 scale (table 1). Out of 151 forest fire locations, 70% were used in the model training and the remaining 30% were used for validation (Pourghasemi et al. 2012a; Zare et al. 2012; Pourghasemi et al. 2014; Regmi et al. 2014). For FFSM in the study area, seven effective factors were considered. These factors include altitude, slope aspect, slope angle, annual temperature, wind effect, land use, and normalized different vegetation index (NDVI). The spatial database for the study area is shown in table 1.

Table 1. Data used for forest fire susceptibility mapping (FFSM).

Data layers	Data format	Source of data	Scale
Forest fire locations map	Point	Satellite image, aerial photos, and extensive field surveys	1:25,000
Topographic map	Line and point	National Cartographic Center (NCC)	1:50,000
Land use	Polygon	National Geographic Organization (NGO)	1:100,000
Normalized difference vegetation index (NDVI)	Grid	National Geographic Organization (NGO)	30m × 30m
Meteorological data	Excel data	Iranian Meteorological Organization (IRIMO)	–

One of the important factors in any fire hazard rating system is topography data. In the literatures, the impacts of elevation, slope aspect, and slope angle in fire behaviour have been widely reported (Chuvieco & Congalton 1989; Erten et al. 2004; Renard et al. 2012; Adab et al. 2013).

In the current research, a digital elevation model (DEM) was created by digitizing contours (30 m interval) and survey base points. The DEM map has a grid size of 30 m with 2323 columns and 1657 rows. Using the DEM, altitude, slope aspect, and slope angle were extracted (figures 3(a) and (b)).

Figure 3. Topographical parameter maps of the study area: (a) altitude, (b) slope aspect and (c) slope angle. Modified from Pourtaghi et al. (2014).

Elevation is a crucial physiographic variable that is associated with temperature, moisture, and wind (Xiangwei et al. 2011). Therefore, it has an important role in fire spreading (Jaiswal et al. 2002). The altitude map was extracted from the DEM and classified into five classes according to equal interval classification (Pradhan et al. 2007; Pourtaghi et al. 2014); that is, (1) <500 m, (2) 500–1000 m, (3) 1000–1500 m, (4) 1500–2000 m and (5) >2000 m (figure 3(a)).

Slope aspect is another factor that correlated with the amount of received solar energy in the area. Therefore, slope aspect layer was selected as one of the forest fire-related factors and has been categorized into nine classes: (1) flat, (2) north, (3) north-east, (4) east, (5) south-east, (6) south, (7) south-west, (8) west, and (9) north-west (figure 3(b)).

Also, one of the parameters that influence the fire spread rate is slope angle (Weise & Biging 1997). Fire can move more quickly up the slope and less quickly down the slope (Kushla & Ripple 1997). So, the slope map of the study area is derived from the DEM and divided into four classes such as 0°–5°, 5°–15°, 15°–30°, and >30° (figure 3(c)). In addition, using the meteorological database, the annual temperature and wind effect factors were calculated (figures 4(a) and (b)).

Figure 4. Meteorological parameter maps of the study area: (a) annual temperature and (b) wind effect (no dimension). Modified from Pourtaghi et al. (2014).

Temperature highly affects the moisture amount in forest combustion. High temperature led to dry combustion quickly (Antoninetti et al. 1993). The annual temperature map was classified as follows: <15, 15–16, 16–17, 17–18, and >18 °C (figure 4(a)).

Wind is an important factor because it provides fresh oxygen and the flame puts a new fuel source (Rawat 2003). Wind effect factor map was created based on three input parameters, such as DEM in grid format, wind direction (degree), and wind speed (m/s) in SAGA GIS (http://saga.sourcearchive.com/documentation/2.0.7plus-pdfsg-2/wind__effect_8cpp_source.html). In the current research, the wind effect was prepared in SAGA-GIS and classified based on the natural break classification scheme (Pourtaghi et al. 2014) into three classes such as (0.75–0.95), (0.95–1.14), and (>1.14) (figure 4(b)).

The land use map was created using Landsat-7 images of 2010. In order to create the land use map, a supervised classification using maximum likelihood algorithm was applied. A total of 370 signatures (training classes) were collected from all land use types. The signatures were collected by field survey and using GPS. Out of these 370 signatures, 250 signatures were used for land use mapping and the remaining were used for accuracy assessment. Nine land use classes were drawn such as irrigation farming (IF), dense forest (DF), sparse forest (SF), irrigated and rain-fed mixed farming (IRMF), rain-fed farming (RF), good range (GR), moderate range (MR), moderate forest (MF), woodlands and shrubbery (WS), and urban (residential) (U) (figure 5).

Figure 5. Land use map of the study area. Modified from Pourtaghi et al. (2014).

For assessment of vegetation cover, we used normalized difference vegetation index (NDVI), which is the most commonly used index to assess live FMC (Chuvieco 2003). The NDVI was prepared using Landsat-7 images (path 162 and row 34 obtained on 13 November 2010) based on the following equation (Rouse et al. 1973): (1) where NIR (band 4) and RED (band 3) values are the infrared and red portion of the electromagnetic spectrum, respectively. In this study, the NDVI map was prepared in ENVI 4.8 and divided into six classes (figure 6).

Figure 6. Normalized different vegetation index (NDVI) map of the study area. Modified from Pourtaghi et al. (2014).

For classification of conditioning factors, different methods were used such as equal interval, natural break, and normal or common standards. Finally, for application of M-AHP and MFL models, all the aforementioned conditioning factors were converted to a raster grid with 30 m × 30 m pixel size in the ArcGIS 9.3 software. All the maps are in UTM (Universal Transvers Mercator) coordinate system and WGS84 spatial reference (WGS84-UTM-Zone40N).

3.2. Statistical index

In this research, the statistical index (SI) model was applied to illustrate the quantitative relationship between distributions of forest fire occurrences with predictor factors. The SI method is a bivariate statistical analysis proposed by van Westen (1997). A weight value for each categorical unit is defined as the natural logarithm of the forest fire density in the categorical unit divided by the forest fire density in the entire map (van Westen 1997; Rautela & Lakhera 2000; Cevik & Topal 2003; Pourghasemi, Moradi, et al. 2013). This method is based on the following equation (van Westen 1997): (2) where W_SI is the weight given to a certain class i of parameter j; F_ij is the number of forest fires in a certain class i of parameter j; F_T is the total number of forest fires in the entire map; P_ij is the number of pixels in a certain class i of parameter j; and P_T is the total pixels of the entire map.

3.3. Modified analytical hierarchy process

The analytical hierarchy process (AHP) is a theory of measurement for considering tangible and intangible criteria that have been applied to numerous areas, such as decision theory and conflict resolution (Vargas 1990; Yalcin 2008; Youssef et al. 2011). The AHP includes a matrix-based pairwise comparison of the contribution of different factors on forest fire occurrence. The process consists of four phases: (1) breaking a complex unstructured problem down into its component factors, i.e. conditioning factors considered in this study; (2) combine these factors in a hierarchical order; (3) assign numerical values according to the relative important of each factor (pairwise comparison); and (4) synthesize the rating to determine the priorities to be assigned to these factors (Saaty & Vargas 2001). The pairwise comparison is the process of comparing the relative importance, preference, or likelihood of two elements (for example, criteria) with respect to another element (for example, the goal) in the level above to establish priorities for the elements being compared (Saaty 1994; table 2).

Table 2. The AHP pairwise comparison scale (Saaty 1994).

Numerical values	Verbal scale	Explanation
1	Equal importance of both elements	Two elements contribute equally
3	Moderate importance of one element over another	Experience and judgment favour one element over another
5	Strong importance of one element over another	An element is strongly favoured
7	Very strong importance of one element over another	An element is very strongly dominant
9	Extreme importance of one element over another	An element is favoured by at least an order of magnitude
2, 4, 6, and 8	Intermediate values	Used to compromise between two judgments

One of the key points in AHP is calculation of consistency ratio (Saaty 1977). If consistency ratio is less of 0.1, then the mentioned matrix can be considered as an acceptable consistency (Saaty 1977). Several researchers have used AHP model in various applications and reported a reasonable accuracy (Ayalew et al. 2005; Hajeeh & Al-Othman 2005; Komac 2006; Yalcin 2008; Esmali Ouri & Amirian 2009; Wu & Chen 2009; Langenbrunner et al. 2010; Abba et al. 2013; Agarwal et al. 2013; Kayastha et al. 2013; Tierno et al. 2013; Zhang et al. 2013; Giri & Nejadhashemi 2014). However, it is based on expert opinions and thus may be subjected to cognitive limitations with uncertainty and subjectivity (Pourghasemi, Moradi, et al. 2013). Thus, for solving the limitations of the conventional AHP, an M-AHP is proposed by Nefeslioglu et al. (2013) and applied in the current research. The differences between the M-AHP and the conventional AHP can be classified into two groups:

1. The preparation of the factor comparison matrix. In this step, there are following differences:

   • The factor comparison matrix in the M-AHP model is not according to the expert opinion,

   • The expert viewpoints in M-AHP only used to define the maximum scores for each factor in order to prepare factor score matrix,

   • Normalization of the factor score values according to maximum score factor,

   • Finally, construction of factor comparison matrix based on modified importance value scale (Nefeslioglu et al. 2013).

2. The evaluation of the importance distributions of the conditioning factors on the decision points (Nefeslioglu et al. 2013). In this step, at first, each factor will be normalized based on its own maximum score. Subsequently, linear distance between the normalized factor score and decision points will be calculated, and finally decision point comparison matrix will be prepared by considering modified importance value scale.

In other words, it is sufficient for the expert to identify important factors at model running (http://portal.netcad.com.tr/pages/viewpage.action?pageId=113803523). The details of the mentioned algorithm/tool (M-AHP) with an example on snow avalanche can be found in Nefeslioglu et al. (2013).

3.4. Mamdani fuzzy logic

The fuzzy set theory was first introduced by Zadeh (1965), and it is one of the tools used to handle complex problems. Fuzzy sets theory is a mathematical method used to characterize and propagate uncertainty and imprecision in data and functional relationships (Kurtener & Badenko 2000). The mentioned theory has been commonly used in different scientific studies and disciplines (Juang et al. 1992; Alvarez Grima & Babuska 1999; Ercanoglu & Gokceoglu 2002; Nefeslioglu et al. 2006; Saboya et al. 2006; Gokceoglu et al. 2009; Yagiz & Gokceoglu 2010; Akgun et al. 2012; Pourghasemi et al. 2012b; Osna et al. 2014). In the fuzzy set theory, membership can take on any value between 0 and 1, reflecting the degree of certainty of membership (Zadeh 1965; Pradhan 2011). A membership value was chosen arbitrary according to subjective judgement about the relative importance of the maps and their various states (Bonham-Carter 1994). A number of different types of membership functions (MFs) have been proposed for fuzzy inference system. These MFs are triangular, trapezoidal, sigmoidal, bell, Gaussian combination, and π-shaped (Pradhan 2013; Osna et al. 2014).

Meanwhile, in the literature, different fuzzy inference systems (FIS) have been proposed (Mamdani, Sugeno, and Tsukamoto), but the Mamdani fuzzy is one of the most interesting methods applied in engineering geology problems (Alvarez Grima 2000; Akgun et al. 2012).

In the Mamdani fuzzy model, if–then rules replace the usual set of equations used to characterize a system (Yager & Filev 1994). The Mamdani fuzzy model takes the following form: (3) where k is the number of rules, are input variables, y is the output variables, and A_ij and B_i are linguistic terms.

In Mamdani model, each rule is a fuzzy relation which is calculated using the following equation: (4) where the operator I can be either a fuzzy implication or a conjunction operator (t-norm) (Jager 1995).

There are four inference steps in Mamdani fuzzy inference system such as fuzzification, rule assessment, aggregation, and defuzzification steps (Mamdani & Assilian 1975); they are presented in equations (5)–(7).

Step 1: compute the degree of fulfillment α_i of the antecedent for each rule i: (5)

Step 2: for each rule, drive the output fuzzy set using the minimum t-norm: (6)

Step 3: Aggregate the output fuzzy sets by taking the maximum method (Eq. 8): (7)

Finally, in this study, due to defuzzification process (Step 4) was used of the centroid method because of its simplicity and producing consistent results (Jager 1995). The details of the mentioned algorithm can be found in Alvarez Grima (2000).

As a result, the fuzzy logic allows more flexible combinations of weighted maps and could be readily implemented in GIS modelling language (Pradhan 2010a, 2010b).

For applying of the mentioned models (M-AHP and MFL) were used of a laptop computer by a hardware configuration such as CORE i7 processor, 64-bit CPU and 6GB RAM, the inference process completes in approximately 7 hours. But the computer output in the M-AHP model can be obtained in a less time, almost at 10 min.

4. Results

4.1. Statistical index (SI)

The spatial relationship between forest fire occurrences and the conditioning factors using the SI model is presented in table 3. According to the relationship between forest fire occurrence and altitude, forest fire numbers or frequency is highest at elevations higher than 500 m. Thus, the probability of occurrence of fire in these altitudes is higher. Chuvieco and Congalton (1989) and Adab et al. (2013) reported that fire behaviour trends are less severe at higher altitudes because of higher rainfall. The SI value between forest fire occurrence and slope aspect shows that forest fires are most common on east (SI = 0.89), south-west (SI = 0.38), and west (SI = 0.21) facing slopes, respectively, and the flat (SI = −0.5) and north-west (SI = −0.36) facing slopes have the lowest incidence. The analysis of SI for the relationship between forest fire occurrence and slope degree indicates that slope degree class >30° and <5° has the highest and lowest values of SI (0.64 and −0.75), respectively. The results showed that the SI values decreased with the slope degree addition in the study area. Assessment of annual temperature showed that the temperature of 16–17 °C has high correlation with forest fire occurrence (SI = 0.55). The result of wind effect indicates that class >1.14 is considered to be susceptible to fire with an SI value of 0.47. In the case of land use, it can be inferred that 99.06% of forest fire falls on dense forest area with value of 0.51, indicating that the probability of occurrence of forest fire in this land use type is very high. The NDVI factor indicates that the range between 0.1 and 0.5 and >0.5 have the highest frequency for forest fire occurrence (26.42% and 72.64%). On the other hand, the remaining classes are lowest susceptible or non-susceptible to forest fire occurrence.

Table 3. Spatial relationship between conditioning factors and forest fire locations using statistical index (SI) model.

Factor	Class	No. of pixels in domain (Pij)	% Pixels in domain	No. of forest fires (FFij)	% forest fires	SI
Altitude (m)	<500	464,718	27.32	6	5.66	−1.57
	500–1000	534,642	31.43	44	41.51	0.28
	1000–1500	521,829	30.67	43	40.57	0.28
	1500–2000	169,287	9.95	11	10.38	0.04
	<2500	10,809	0.64	2	1.89	1.08
Slope aspect	Flat	316,740	18.62	12	11.32	−0.50
	North	209,679	12.32	15	14.15	0.14
	North-east	139,591	8.21	9	8.49	0.03
	East	92,104	5.41	14	13.21	0.89
	South-east	100,549	5.91	5	4.72	−0.22
	South	134,018	7.88	7	6.60	−0.18
	South-west	143,326	8.43	13	12.26	0.38
	West	195,660	11.50	15	14.15	0.21
	North-west	369,618	21.73	16	15.09	−0.36
Slope angle (degree)	<5°	544,326	32.00	16	15.09	−0.75
	5–15°	400,683	23.55	25	23.58	0.001
	15–30°	621,420	36.53	49	46.23	0.24
	>30°	134,856	7.93	16	15.09	0.64
Annual temperature (mm)	<15	40,017	2.35	1	0.94	−0.92
	15–16	393,766	23.15	13	12.26	−0.64
	16–17	647,991	38.09	70	66.04	0.55
	17–18	485,269	28.52	22	20.75	−0.32
	>18	134,242	7.89	0	0.00	0
Wind effect	0.75–0.95	721,245	42.39	41	38.68	−0.09
	0.95–1.14	629,205	36.98	30	28.3	−0.27
	>1.14	350,835	20.62	35	33.02	0.47
Land use*	IR	199,564	11.73	0	0	0
	DF	1,012,790	59.53	105	99.06	0.51
	LF	22,381	1.32	1	0.94	−0.34
	IRMF	95,828	5.63	0	0	0
	RF	347,307	20.41	0	0	0
	GR	267	0.02	0	0	0
	MR	1345	0.08	0	0	0
	MF	12,649	0.74	0	0	0
	WS	634	0.04	0	0	0
	U	8520	0.50	0	0	0
NDVI	<−0.001	453	0.03	0	0	0
	−0.001 to 0.00	302	0.02	0	0	0
	0.00–0.05	1527	0.09	0	0	0
	0.05–0.1	7280	0.43	1	0.94	0.78
	0.1–0.5	1,005,442	59.10	28	26.42	−0.81
	>0.5	686,281	40.34	77	72.64	0.59

*IF = irrigation farming, DF = dense forest, LF = low forest, IRMF = irrigated and rain-fed mixed farming, RF = rain-fed farming, GR = good range, MR = moderate range, MF = moderate forest, WS = woodlands and shrubbery, U = urban (residential).

4.2. Forest fire susceptibility mapping (FFSM) by M-AHP model

For FFSM, a tool was developed in Netcad GIS 6 as M-AHP. At first, seven forest fire conditioning factors were classified based on literature review and expert knowledge. Then, the score of their classes (condition factor classes) was determined according to expert knowledge (table 4) and, subsequently, maximum score factors were extracted. In the mentioned table, for the altitude, the maximum score is 7 for classes >2000 m. Hernandez-Leal et al. (2006) reported that humidity and temperature have higher influence on fire at higher altitude areas than lower ones. In the case of slope aspect, maximum scores referred to south-facing slopes by value of 6. It is noticed that south-facing slopes received more sunlight, higher temperatures, stronger winds, low humidity, and low fuel moistures than those facing the north pole. Thus, vegetation is generally drier and less dense on south-facing slopes than north-facing ones (Anderson 1982; Prasad et al. 2008), and drier fuels are more prone to ignition (Noonan 2003; Iwan et al. 2004). For the slope degree, the maximum score is 7 for slopes >30°. Kushla and Ripple (1997) stated that fire can move more quickly up the slope and less quickly down the slope. On the other hand, flames being angled closer to the ground surface, thus, fire spread rate may rise on steeper slopes, and the process of heat convection can be enhanced by wind effects due to fire behaviour (Whelan 1995; DeBano et al. 1998; Adab et al. 2013). The maximum score for annual temperature showed that higher temperature caused dry combustion (Artsybashev 1983; Antoninetti et al. 1993) and the resulting classes >18 °C have the highest maximum value (score = 7). In the case of wind effect and according to the expert knowledge scores, when wind effect increases, the probability of forest fire increases. In other words, the rate of burning is increased with increasing of wind effect. (Rawat 2003). So, classes of >1.14 have a highest score (score = 5). Another important factor for forest fire occurrence is land use type. The relationships between forest fire locations and land use types show that 99.06% of forest fire falls on dense forest area with value of 0.51, indicating that the probability of occurrence of forest fire in this land use type is very high. Thus, for M-AHP model, the maximum score (score = 5) corresponded to dense forest land use type. In the case of NDVI, maximum score was 7. In the range of greater than 0.5, the study area is generally covered by dense vegetation and tropical rainforest, so it is susceptible to fire occurrence.

Table 4. The conditioning factor scores given by expert and maximum scores.

Factor	Class	Score	Maximum score
Altitude (m)	<500	1	7
	500–1000	2
	1000–1500	3
	1500–2000	5
	>2000	7
Slope aspect	Flat	1	6
	North	2
	North-east	2
	East	3
	South-east	4
	South	6
	South-west	5
	West	4
	North-west	3
Slope angle (degree)	0–5	1	7
	5–15	3
	15–30	5
	>30	7
Annual temperature (°C)	<15	1	7
	15–16	2
	16–17	3
	17–18	5
	>18	7
Wind effect	0.75–0.95	1	5
	0.95–1.14	3
	>1.14	5
Land use	IR	1	5
	DF	5
	LF	3
	IRMF	1
	RF	1
	GR	1
	MF	1
	WS	1
	U	1
	IR	1
NDVI	<−0.001	1	7
	−0.001–0.00	1
	0.00–0.05	1
	0.05–0.1	3
	0.1–0.5	4
	>0.5	7

Another important problem in calculation of M-AHP is instant factor scores. During application of the model, for any terrain mapping unit in the field, instant factor scores should also be defined by the expert or relevant user (Nefeslioglu et al. 2013). But, one of the attributes of Netcad GIS 6 is that the instant scores will be obtained from the region basin (study area basin) automatically. In other words, they are computed from the raster maps used in this study. For running the M-AHP model, one key point is determination of decision points. In the current research, the decision points for the FFSM is grouped into four classes as low, moderate, high, and very high (figure 7(a)).

Figure 7. Forest fire susceptibility map (FFSM) produced by M-AHP (a) and MFL (b) models. Modified from Pourtaghi et al. (2014).

Finally, the FFSM prepared from the M-AHP method, which covered 29.66% of the total area, was designated to be a low FFSM class; 20.78, 33.17, and 16.39% of the total area are related to moderate, high, and very high FFSM zones, respectively (figure 7(a)).

4.3. Forest fire susceptibility mapping (FFSM) by Mamdani fuzzy logic

To produce FFSM using Mamdani fuzzy inference system (FIS), at first, conditioning factors were created in raster format with a 30 m × 30 m pixel size in GIS environment. After the inputs were loaded to Netcad GIS 6, the user can select a fuzzy existing model or build a new one based on the input numbers in the Architect page. In the next step, membership functions were defined for input and output layers. The input layers are the same as considered in the previous models.

Due to definition of membership function for categorical factors such as slope aspect and land use, the forest fire density and spatial relationship between these factors and forest fire locations (table 1) were considered in the current research. To minimize the uncertainty, a 50% overlap is applied between the fuzzy sets for each input parameter, and triangular membership functions are used for each fuzzy set (Akgun et al. 2012). On the other hand, output set as FFSM and its membership function draw into four classes such as low, moderate, high, and very high. Another important part in Mamdani FIS is definition of the fuzzy if–then rules. In this study, a total 128 if–then rules were used. First, the if–then rules are created automatically and then edited according to expert opinion. For transforming output linguistic variables into crisp values, defuzzification method should be used. Thus, for FFSM, the most common defuzzification method, namely, gravity center, was used (Jager 1995; Babuska 1996; Saboya et al. 2006).

Finally, the FFSM produced from the MFL method, which covered 23.17% of the total area, was designated to be a low FFSM class; 24.41, 38.97, and 13.45% of the total area are related to moderate, high, and very high FFSM zones, respectively (figure 7(b)).

4.4. Validation of forest fire susceptibility maps

In general, the validation of predicted results is the crucial step in the modelling process, so that the results can provide a meaningful interpretation (Fabbri & Chung 2001; Chung & Fabbri 2003). To determine the accuracy of the two FFSMs produced using M-AHP and MFL models, the ROC curve (Pradhan et al. 2009; Pradhan 2010a, 2010b, 2011; Akgun et al. 2012; Mohammady et al. 2012; Pourghasemi, Goli Jirandeh, et al. 2013; Osna et al. 2014; Jaafari et al. 2014) was used. ROC curve analysis is a common method used to assess the diagnostic test accuracy (Egan 1975). The ROC curve plots the true positive rate on the Y-axis and the false positive rate on the X-axis. It represents the trade-off between the two rates (Negnevitsky 2002). In the ROC method, the area under the curve (AUC) values range from 0.5 to 1.0 and are used to evaluate the model accuracy (Nandi & Shakoor 2010). If the model does not predict the forest fire occurrences better than the chance, the AUC would equal 0.5. A ROC curve of 1 shows perfect prediction (Yesilnacar 2005). The quantitative–qualitative relationship between AUC and prediction accuracy can be classified as follows: 0.9–1, excellent; 0.8–0.9, very good; 0.7–0.8, good; 0.6–0.7, average; and 0.5–0.6, poor (Yesilnacar 2005). In this study, the forest fire locations that were not used during the model building process were used to verify the FFSMs. The AUC values of the ROC curve for MFL and M-AHP models were found to be 88.20% and 77.72% with a standard error of 0.042 and 0.49, respectively (figures 8 (a) and (b)). Hence, it is concluded that the MFL model employed in this study showed more reasonable results with respect to the M-AHP model in predicting the forest fire susceptibility of study area.

Figure 8. Prediction rate curve for the forest fire susceptibility map by MFL (a) and M-AHP (b) models.

5. Conclusion

The present study attempts to assess FFSMs produced by the M-AHP and MFL models and to compare their performances. The results of this study suggest that FFSMs for the Minudasht Township, Golestan Province, of Iran are viable. Meanwhile, based on the obtained AUC, the MFL model has better prediction performance (88.20%) than the M-AHP (77.72%) model. As a result, the FFSM by M-AHP is easy, because the mentioned model does not use the membership functions and if–then fuzzy rules; thus, it takes a less time for model running. According to Nefeslioglu et al. (2013), another advantage of the M-AHP is that, using this methodology, the consistency ratio value for the comparison matrix and the weights never exceeds 0.10. In contrast, fuzzy algorithm is a powerful tool in modelling of complex natural processes and nonlinear systems. Finally, these maps can be used to early warning, fire suppression resources planning, and allocation works.

Acknowledgements

The authors would like to thank Prof. Candan Gokceoglu, Dr Hakan A. Nefeslioglu, Turgay Osna, and Deniz Celik for their supports in creating and training of spatial analyst in the Netcad GIS 6, especially on M-AHP and MFL modules. Also, the authors would like to thank the three anonymous reviewers for their helpful comments on the previous version of the manuscript.