Can wood-decaying urban macrofungi be identified by using fuzzy interference system? An example in Central European Ganoderma species

Ganoderma is a cosmopolitan genus of wood-decaying basidiomycetous macrofungi that can rot the roots and/or lower trunk. Among the standing trees, their presence often indicates that a hazard assessment may be necessary. These bracket fungi are commonly known for the crust-like upper surfaces of their basidiocarps and formation of white rot. Six species occur in central European urban habitats. Several of them, such as Ganoderma adspersum, G. applanatum, G. resinaceum and G. pfeifferi, are most hazardous fungi causing extensive horizontal stem decay in urban trees. Therefore, their early identification is crucial for correct management of trees. In this paper, a fast technique is tested for the determination of phytopathologically important urban macrofungi using fuzzy interference system of Sugeno type based on 13 selected traits of 72 basidiocarps of six Ganoderma species and compared to the ITS sequence based determination. Basidiocarps features were processed for the following situations: At first, the FIS of Sugeno 2 type (without basidiospore sizes) was used and 57 Ganoderma basidiocarps (79.17%) were correctly determined. Determination success increased to 96.61% after selecting basidiocarps with critical values (15 basidiocarps). These undeterminable basidiocarps must be analyzed by molecular methods. In a case, that basidiospore sizes of some basidiocarps were known, a combination of Sugeno 1 (31 basidiocarps with known basidiospore size) and Sugeno 2 (41 basidiocarps with unknown basidiospore size) was used. 84.72% of Ganoderma basidiocarps were correctly identified. Determination success increased to 96.83% after selecting basidiocarps with critical values (11 basidiocarps).

www.nature.com/scientificreports/ Several Ganoderma species are however difficult to distinguish based solely on morphological features and recently, molecular data have been used for Ganoderma spp. identification 16 . Molecular identification of fungal species relies mainly on DNA sequencing of ITS (internal transcribed spacer) region that is widely accepted as the "gold standard" by fungal taxonomists 17 . Schmidt et al. 18 identified G. applanatum and G. australe at first from fruit-bodies grown on urban trees in Germany by ITS sequencing and subsequently also from the neighbouring rotten wood. Thus, an advantage of ITS sequencing is its ability to identify fungal species also if only mycelium or even only rotten wood are available. However, molecular methods tend to require expensive, stationary equipment that requires specialized skills to operate and fungi identification can be time-consuming 19 .
The aim of the present study is to develop a fast and reliable method for determining Ganoderma species based on selected qualitative and quantitative characters of the basidiocarps. Mathematical processing via fuzzy interference system of these characters can be done within 1 day.
From the mathematical point of view, the determination of some elements into some special classes is a problem of cluster analysis and classification. There are two main ways how to divide elements into clusters [20][21][22][23] . The first one is the use of hierarchical cluster analysis, which is based on statistical data processing. In the current big data era, where it is time-consuming or impossible to calculate all common character properties, the second one, non-hierarchical cluster analysis, is often used. Some of the non-hierarchical cluster analyses use soft computing tools as fuzzy sets or neural networks 24,25 . These systems and their combinations have been used to solve different biological problems [26][27][28][29][30][31] . The advantages of these methods can be viewed in the fast obtaining of the results. Moreover, they provide us with information about the existence of such elements which belong simultaneously to different clusters with certain degree (membership degree). This could help researchers to find the problematic/atypical items (usually when the membership degrees for more clusters are the same).
In this study, the non-statistical access by using fuzzy sets was chosen. Fuzzy sets are special mathematical structures that were developed for computing not just with the numbers but also with the words, which are used in everyday life. Since selected basidiocarp traits could be easily described using fuzzy sets, we focused on building a fuzzy inference system of the Sugeno type (Sugeno-type FIS) with constant output 32,33 , so that if specific trait values are defined as inputs, the species of Ganoderma will be generated as output by the Sugeno-type FIS.
The FIS of the Sugeno type with constant output consist of the rules which have the following form In this form R represent the rule, i represent the rules order, X 1 , X 2 , . . . , X n represent input linguistic variables, A 1i , A 2i , . . . , A ni are the values of input linguistic variables defined by the fuzzy sets, n represent the number of input linguistic variables, Y represent an output linguistic variable and b i is the value of output linguistic variable defined by the constant. Let's have the particular numerical values of the characters, x = (x 1 , x 2 , . . . , x n ) and let the system consist of k rules. For each rule R i and each particular numerical values of the characters x the weight of the rule w i is computed by the formula Moreover, there is a possibility to decide for each rule the power of the rule for the produced system. Denote this power weight by − w i . Since each rule R i had assigned the constant output b i , then the final output for the specific numerical values of the character x is computed by the formula 33
The aim of this study was to create the FIS of the Sugeno type with constant output in such a way that the given values of the characters are defined as inputs, the particular Ganoderma species will be generated as output by the FIS. In the first step the input and output variables with their parameters need to be defined. The selected traits of the basidiocarps were described by 13 characters (n = 13) designated as X 1 to X 13 Table 1. Each of these characters was designated as one linguistic variable input and the values of linguistic variables were assigned according to the real situation. The values of input linguistic variables were defined by the fuzzy sets. Each fuzzy set was exactly defined by its membership function. The data were processed in the program MATLAB 34 . For easily processing of the characters, the software application was developed in the program MATLAB Runtime  Table 2. X 1 , X 2 characters: light microscopic analysis of basidiospores was performed on fertile basidiocarps. The basidiospores were mounted in 5% KOH with cotton blue. Their size, without exosporium and without expanded vesicular apex, was measured with maximum magnification (with immerse objective 100×) of a MOTIC light microscope (MOTIC Company, Germany). The width and length of 30 basidiospores from each fertile basidiocarp were measured. The individual value indicates the arithmetic mean of 30 replications. X 3 , …, X 8 morphological characters of basidiocarps were described according to standard anatomo-morphological data 2,3,6,7,37 and our characters of 72 basidiocarps. X 9 , …, X 13 colour characters of basidiocarps were measured using the List of RAL colours (RAL 840-HR) 38 . Y: All Ganoderma basidiocarps were identified by the above-mentioned standard anatomo-morphological and molecular data. The total genomic DNA was isolated from basidiocarps, their ITS regions were amplified by PCR and sequenced in both directions at SEQme s.r.o. (Dobříš, Czech Republic). Obtained sequences have been deposited in GenBank database 39 .
As the output variables, one of the six Ganoderma species was expected. Since FIS of the Sugeno type with constant output allows to define each output variable as a constant, this type of FIS was used. The constants need to be defined on some interval and they have to be defined as the numbers. In this study, the universe U = [0, 1] was chosen. It is well known that several Ganoderma species have very similar characters, therefore the labelling of the species as it is mentioned in Table 3 was suggested.
Since the parameters of input and output linguistic variables were designed, the fuzzy rules could be created. In the first step, the combinations of characters which are typical for each species need to be extracted. These combinations were extracted from both characters as they were defined in Table 1 2,3,6 . Since they are typical for each Ganoderma species, these types of rules were assigned the specific power weight which equals 1 in proposed FIS. In Example 1, there is indicated one of the used rules in such a form as it was defined in program MATLAB.

Example 1
Example of the one of the used rules. www.nature.com/scientificreports/ If (Basidiospore length without exosporium is Middle) and (Basidiospore width without exosporium is Middle) and (Basidiocarp without stem) and (Pileus surface is crusty) and (Pileus surface without resinous crust) and (Pileus shape is ungulate) and (Pileus surface colour/surface pattern is fawn brown/buff/clay brown/green brown/olive brown) and (Stem colour none) and (Tube layer colour is nut brown/chestnut brown/clay brown) and (Context colour is orange brown/ochre brown) and (Basidiocarp weight is not very light in weight) then (Species is Ganoderma adspersum) (power weight 1).
In our collection of 72 basidiocarps, there were visible also combinations of characters, mostly the shade of colours, in another form as it was mentioned in literature. We have also used the rules with these characters. Since these combinations of characters were not mentioned in the literature, these rules got power weight less than 1 (usually 0.75, 0.5, 0.25). The value of power weight depended on the number of variables in which the characters did not match the literature. Table 2. List of the used parameters of input linguistic variables.

Studied parameters (= input linguistic variables)-used definition scope
Used values of input variables (= the names of the fuzzy sets) Parameters of the used fuzzy sets   www.nature.com/scientificreports/ All the obtained rules were processed by program MATLAB in the Fuzzy Logic Designer Toolbox. Finally, FIS of the Sugeno type with constant output was created. It consisted of 243 fuzzy rules, which described the whole system and it was named as Sugeno1.
If someone wants to use a developed system, he/she needs to assign each of 13 characters to the particular values following the values mentioned in Table 1 (see Example 2). Example 2 One item from collection and its input values. Table 4 represents the input values of one item from the collection. Therefore, for the vector of input values it hold After the completing of particular numerical values of the characters x 1 , x 2 , …, x 13 into the FIS, the system computes the output by the process, which was mentioned above. The output of the FIS was particular value from interval [0, 1]. There exist more approaches how to assign specific Ganoderma species considering the calculated value. The greatest problem is, when the output value is one of the values 0.9, 0.7, 0.5, 0.3 and 0.1 (critical values). For these output values, the system is not able to decide between two closely related Ganoderma species. We have decided to group them into a specific category: unrecognised. It could help us to find the critical individuals. According to the output values (except for critical values), we are able to decide upon a specific Ganoderma species. The insertion of Ganoderma species to particular output value is listed in Table 5.

Example 3
In the Example 2 input values of basidiocarp with collection code MS137 were mentioned. After insertion of these values into FIS, the system gave the result 1.0. This value belongs to the interval mentioned in the first row of the Table 5 therefore this basidiocarp is recognized as G. adspersum.

Example 4
If the FIS output value of some basidiocarp reach, for example the value 0.9, then the basidiocarp will not be assigned to any Ganoderma species.
The insertion of each of 72 basidiocarps of this study is presented in the section "Results and discussion".   www.nature.com/scientificreports/ However, only 31 fertile basidiocarps have been observed at the time of our collection, while the rest of the basidiocarps were sterile. Therefore, there was not possibility to determine the first two characters "Basidiospore length" and "Basidiospore width" in proposed FIS Sugeno1 for all basidiocarps. For this reason, another FIS of the Sugeno type with constant output (named Sugeno2) was created. System Sugeno2 consists of 11 input linguistic variables, except "Basidiospore length" and "Basidiospore width". All other characters from FIS Sugeno1 were used. The 41 sterile basidiocarps were processed by this system. The second system had also 243 rules. The process of calculation of the output values was the same as in the FIS Sugeno1, the only one difference was, that in the FIS Sugeno2, the user need to enter just 11 numerical values of the characters x 3 , x 4 , . . . , x 13 into the FIS. Subsequently, system calculates one specific value from interval [0, 1]. To assign the particular Ganoderma species considering to calculated output value, the values from Table 5 were used.
Let's look at the created systems from the informatics point of view. FIS Sugeno1 and FIS Sugeno2, which were created in program MATLAB, allows user to process characters of more basidiocarps at the same time. The user needs to prepare data as a matrix of characters in the right order. Each character need to be evaluated by a number, as it was mentioned in Table 1 and showed in Example 2.
The proposed system was developed on the basis of requirements of biological sciences. Since the filling of the character values as they were mentioned in Example 2 into the program MATLAB was not very meaningful from the biological point of view, also the software application was created. Proposed application consists of buttons, popup-menus and strings. They consist the characters in the natural form (as they were mentioned in Table 1, what means that user choose from the items expressed by the words (for example for "pileus surface colour-surface pattern" one of the possibilities is "beige-grey-brown beige-grey beige-grey brown").
The characters, for which it is enough to decide between few "short" possibilities (yes/no, crusty/shiny) were defined by buttons. The characters, for which it is need to choose one "long" possibility (for "pileus surface colour-surface pattern" one of the possibilities "beige-grey-brown beige-grey beige-grey brown") the popupmenus were used. The first button was designed as special button. It consists of the question if the scientist knows the measurements of the basidiospores without exosporium. If the answer is yes, then two strings are showed to user, to add the values of basidiospore length and width without exosporium, and the numeric values of them could be filled. If the answer is no, then the application consists just of the buttons and popup-menus. After the filling of all characters, the characters are transferred by the application to the numerical values mentioned in the Table 1 and processed by the designed FIS. Of course, the processing of the characters is also divided considering to known/unknown basidiospore measurements. If the scientist known these measurements, then the system uses FIS Sugeno1, if scientist didn´t know them, then the FIS Sugeno2 is used.
After the filling of all characters, user just need to push the confirmation button and got as the result the classified Ganoderma species (for example "Ganoderma adspersum"). When the value of result is not assigned to one specific Ganoderma species (it reach critical value), then the information "It is not possible to be exactly classified this basidiocarp" is displayed.
The application was developed such way that user did not need to have program MATLAB in the computer. It is enough to install MATLAB Runtime Library, which is free of charge. The application is suitable to classify the basidiocarps just one by one.

Results and discussion
All 72 basidiocarps were identified using ITS sequence analysis with high similarity values. In general, 97% similarity cut-off (e.g. 41 ) is applied for species delimitation in ITS analysis. At this level, clear separation of all but Ganoderma carnosum/lucidum species pair was observed. Several recent taxonomic revisions (e.g. 42 ) that this cut-off score is too low for most fungi, and for some of tested Ganoderma species similarity values as high as 98.9% were observed.
Molecular based identification of Ganoderma specimens was then compared to the morphology-based identification using developed the FIS of type Sugeno with constant output. Similar to the molecular data the Ganoderma basidiocarps could be classified into the six classes (species). There are two possibilities how to use this FIS. The first one, directly in the program MATLAB, allows user to process characters of more basidiocarps together. The user needs to prepare data as a matrix of characters in the right order. Each character needs to be evaluated by a number, as it was mentioned in the Table 1. The second one, software application, allows user to process characters of basidiocarps one by one, but in this application the user define the characters of the basidiocarps by words, as they are really biologically specified. Since we had the collection of 72 basidiocarps, we used the application that was developed in program MATLAB.
Since the information of the basidiospore size for some basidiocarps was known and for some of them not, there were used two approaches. One without using of the information of basidiospore size for whole collection of basidiocarps. Second, where the information about basidiospore size was used for those basidiocarps from collection, for which it was known.
Results obtained without using of the information of basidiospore size. In this part the basidiocarps features were used for species identification based just on morphological data. Each of 72 basidiocarps was defined by 11 characters and they were processed by using FIS Sugeno2. As an output system could give any value form the interval [0, 1]. For some basidiocarp the output value reach critical values (values 0.9, 0.7, 0.5, 0.3 and 0.1). The basidiocarps that did not reach critical values were classified into the classes due to intervals mentioned in Table 5. The basidiocarps that reached critical values were not classified into any class. By using this approach 57 basidiocarps were classified correctly Table 6. From 15 incorrectly identified basidiocarps the critical value was assigned to 13 basidiocarps Table 6-bold font). www.nature.com/scientificreports/ From used collection there were 15 incorrectly identified basidiocarps. The most of them were species of G. adspersum (8 basidiocarps) and G. applanatum (3 basidiocarps). From these 11 items for 7 items system gave as a result number 0.9, where 4 items with this value were G. adspersum and 3 items were G. applanatum. As it was mentioned before, the output values for these species were assigned as follows: G. applanatum interval (0.7, 0.9), G. adspersum interval (0.9, 1.0]. This means, that system determined the incorrect classified items between these two species. However, in the field and herbaria, G. applanatum basidiocarps not attacked by larvae of Agathomyia wankowiczii (Diptera) or without both basidiospores and tube layers separated by thin layers of the context are externally almost indistinguishable from those of G. adspersum 39,43 . In addition, it should be noted that G. applanatum basidiocarps attacked by larvae occur irregularly as well as the first year of growth a perennial Ganoderma basidiocarps will have only one tube layer without thin layer of the context. Therefore, these characters could not be included in Table 1. In these cases, molecular studies based on the analysis of the DNA are needed to confirm the species determination and ITS sequence analysis clearly separated these two species with similarity level 90.52 only, significantly lower than required for species discrimination.
From the remaining 3 incorrectly identified items of G. adspersum, 1 item got as a result value 0.8857 which determined it again into the species G. applanatum and 2 of them reached the value 0.5 which determine these items somewhere between G. carnosum and G. lucidum.
Another 3 incorrectly identified items were species of G. carnosum (2 basidiocarps) and G. lucidum s. str. (1 basidiocarps). The situation with the results was similar as before. For all 3 items system gave as an output value number 0.5. The following output values were assigned to mentioned species: G. lucidum s. str. interval (0.3, 0.5), G. carnosum interval (0.5, 0.7). This again means that system determined the items between these two species. Morphologically, mature G. carnosum basidiocarp has dark brown to black upper surface, usually grows on Abies, while G. lucidum s. str. has orange red to bay upper surface, usually grows on hardwoods 6 . However, in the field and herbaria, immature G. carnosum basidiocarps are superficially almost indistinguishable from those of G. lucidum s. str. Also, phylogenetically, sequences data from nuclear internal transcribed spacer regions (ITS) and the translation elongation factor 1-α gene (tef1-α) confirmed that G. lucidum groups together with G. carnosum 39,44 . Similarly, in our experiments similarity value 98.9% was observed between G. carnosum and G. lucidum, making this pair of species the most difficult for correct identification.
From seven basidiocarps of Ganoderma pfeifferi, 6 items got as an output value equal to 0.2 which mean that they were determined correctly and just one output value reached the value 0.5 and was determined incorrectly. No accurate items identification could be caused by untypical flat pileus shape (in this study), or by untypical dull basidiocarps of the otherwise laccate species G. pfeifferi in other studies 43 . The collection contains also 6 basidiocarps of Ganoderma resinaceum. All these items were determined by developed system correctly.
By using this method there were correctly classified 57 basidiocarps from all 72 basidiocarps. It could be calculated that the percentage of accurate classified basidiocarps reach the value 79.17%. It could be seen that this method assigned the critical value to 13 basidiocarps Table 6-bold font). System determines those basidiocarps, which need special attention from researcher. It means that researcher needs to process these items separately by using additional methods. If we omitted these items from the final table, then we could see that system makes mistakes only for 2 items from 59 and the percentage of accurate classified basidiocarps reach the value 96.61%.
Results obtained with using of the information of basidiospore size. Among all basidiocarps tested, for 31 items, the information about basidiospore size was known. Therefore, we could use basidiocarps features for species identification based on morphological and morphometric data. In this step 31 items were processed by FIS Sugeno1 and the rest 41 items we processed by FIS Sugeno2. The basidiocarps that did not reach critical values were classified into the classes due to intervals mentioned in Table 5. The basidiocarps which reached the critical value were labelled as incorrectly identified items. By using this approach 61 basidiocarps www.nature.com/scientificreports/ were classified correctly Table 7. From 11 incorrectly identified basidiocarps the critical value was assigned to 9 basidiocarps Table 7-bold font).
After the processing of basidiocarps by using the second access (combination of FIS Sugeno1 and Sugeno2) we could conclude following results: In the "Results obtained without using of the information of basidiospore size" from mentioned 11 incorrectly identified items of G . adspersum (8 basidiocarps) and G . applanatum (3 basidiocarps) there were 5 of them with the known information about the basidiospore size. The 4 from these 5 items were classified by second approach correctly. By this result we again confirmed the known fact 44 (and others) that the basidiospore length and width are important characters for determination of G . adspersum and G . applanatum . Nevertheless, that the information about the basidiospore size was known for 2 from 3 incorrectly classified items of G . carnosum (2) and G . lucidum s. str. (1), the situation did not improve after using combination of FIS Sugeno1 and Sugeno2. Morphologically, G . carnosum has ellipsoid basidiospores (10-13 × 7-8.5 μm), while G . lucidum s. str. has smaller ellipsoid (7-11 × 6-8 μm) basidiospores 6 . Other achieved results correspond well with the previous analysis of "Results obtained without using of the information of basidiospore size". After this process the percentage increased on the value 84.72% Table 7 .
This method assigned the critical value to 9 basidiocarps. These basidiocarps need to be processed by additional method. If we omitted these 9 items from the final table, then we could see that system makes mistakes only for 2 items from 63 and the percentage of right classified basidiocarps reach the value 96.83%.

Conclusions
The aim of this study was to develop a fast and reliable method for determination of European Ganoderma species based on selected qualitative and quantitative characters. 72 Ganoderma basidiocarps belonging to 6 species were determined using FIS of type Sugeno. At first, the FIS of type Sugeno2 (without basidiospore sizes) was used to identify Ganoderma species and each tested basidiocarp was defined by 11 characters. 57 Ganoderma basidiocarps (79.17%) were correctly determined. Determination success increased to 96.61% after selecting basidiocarps with critical values (15 basidiocarps). These undeterminable basidiocarps must be analyzed by molecular methods.
In a case, that basidiospore sizes of some basidiocarps were known, a combination of Sugeno 1 (31 basidiocarps with known basidiospore size) and Sugeno2 (41 basidiocarps with unknown basidiospore size) was used. 84.72% of Ganoderma basidiocarps were correctly identified. Determination success increased to 96.83% after selecting basidiocarps with critical values (11 basidiocarps). The basidiospore size data slightly increased the determination success of Ganoderma adspersum/applanatum basidiocarps by combining FIS of type Sugeno1 and Sugeno2.
To our knowledge, this is the first application of fuzzy interference system of type Sugeno (Sugeno-type FIS) on the identification of macrofungi. This study confirmed the capabilities of Sugeno-type FIS as an effective practical technique for the determination of phytopathologically important urban macrofungi. At the basis of their features we classify collection of Ganoderma spp. specimens into the 6 classes in accordance with morphological and molecular species identification.

Data availability
The fungal specimens are deposited in the Herbarium of the Department of Biology and Ecology, Faculty of Natural Sciences, Matej Bel University in Banská Bystrica, Slovakia. Nomenclature and authorities are from Index Fungorum (Cooper and Kirk,40) for fungi and The Plant List 35 for woody plants. Molecular identification of fungal species relies mainly on DNA sequencing of ITS (internal transcribed spacer) region that is widely accepted as the "gold standard" by fungal taxonomists 17 .