Combining Spatial Data Layers using Fuzzy Inference Systems:

Application to an Agronomic Case Study

Serge Guillaume

1 a

, Terry Bates

2 b

, Jean-Luc Labl

, Thom Betts

and James Taylor

1 c

ITAP, Univ Montpellier, INRAE, Montpellier SupAgro, Montpellier, France

Cornell Lake Erie Research and Extension Laboratory, Cornell University, New-York, U.S.A.

Betts Vineyard LLC, New-York, U.S.A.

Keywords:

Fusion, Multicriteria, Preference, Decision.

Abstract:

This paper presents an application of Fuzzy Logic, well known for its linguistic modeling ability, in a multi-

criteria decision making framework applied to spatial data sets. The Fuzzy Logic is integrated in two different

ways. First, fuzzy sets are used to model an expert preference relation for each of the individual spatial infor-

mation sources to turn raw data into satisfaction degrees. Second, fuzzy rules are used to model the interaction

between sources to aggregate the individual degrees into a global score. The whole framework is implemented

in an open source software called GeoFIS. The potential of the method is illustrated using a typical farm-

ing decision: the design of a nitrogen fertilization map within a vineyard. The vineyard is a Concord (Vitis

labrusca) juice grape vineyard in the Lake Erie region of New York state. The vineyard manager and a lo-

cal research/extension viticulturist both used the tool to generate a prescription nitrogen map based on their

knowledge and spatial crop and soil information. The process captured different preferences between the two

users (industry vs. research) and generated different prescription maps that reﬂected their differing objectives,

knowledge and risk perception in vine management. Although applied to vineyard data, this decision tool has

a wide potential application to agri-environmental (and other) spatial data sets.

1 INTRODUCTION

Complex systems, such as agricultural production

systems, are characterized by several interrelated di-

mensions, for instance agronomic, social and eco-

nomic. The production process includes different

steps performed systematically, from initial selection

of the product type right the way through to product

marketing. Decisions are made at each step of this

process that may degrade or support the sustainability

of the production system.

Decision making often involves several, poten-

tially conﬂicting, attributes. Multicriteria decision

analysis (MCDA) has been indicated as an appropri-

ate set of tools. In a recent paper (Cinelli et al., 2014)

ﬁve MCDA methods were evaluated for their abil-

ity to handle sustainability problems using ten com-

parison criteria. The methods were from three main

families: i) utility-based theory: Multi-Attribute Util-

https://orcid.org/0000-0002-3546-5276

https://orcid.org/0000-0002-6719-9435

https://orcid.org/0000-0001-9709-8689

ity Theory (MAUT) and Analytical Hierarchy Process

(AHP), ii) outranking relation theory: elimination and

choice expressing the reality (ELECTRE) and pref-

erence ranking organization method for enrichment

of evaluations (PROMETHEE) and, iii) the sets of

decision rules theory: Dominance-based Rough Set

Approach (DRSA). The latter uses crisp “if . . . then”

rules where the satisfaction degree for each criterion

is compared to a deﬁned threshold and the conclusion

is a category or a set of categories.

In this work, a generic methodology, implemented

as an open source software is introduced. The pro-

posed framework ﬁrst converts raw data into satis-

faction degrees according to the decision to be made

and then aggregates these degrees to compute a global

score. The ﬁrst step is carried out using fuzzy sets:

they are used to model the expert preference relation

for each individual information source. The second

step usually involves numerical operators of aggrega-

tion, including the well known Weighted Arithmetic

Mean (WAM), as well as the Ordered Weighted Aver-

age (OWA). An introduction to these operators can be

found in (Bloch, 1996; Dujmovi

c et al., 2009). Few

Guillaume, S., Bates, T., Lablée, J., Betts, T. and Taylor, J.

Combining Spatial Data Layers using Fuzzy Inference Systems: Application to an Agronomic Case Study.

DOI: 10.5220/0009356000620071

In Proceedings of the 6th International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM 2020), pages 62-71

ISBN: 978-989-758-425-1

20 25 30

(x)

Medium

Figure 1: A Trapezoidal Shaped Fuzzy Set.

papers from the GIS community have utilized these

kind of operators (Shorabeh et al., 2019), and the most

popular technique for multicriteria decision making

remains the AHP (El Jazouli et al., 2019; Seyedmo-

hammadi et al., 2019; Graff et al., 2019; Konstantinos

et al., 2019; Giamalaki and Tsoutsos, 2019).

An alternative to numerical operators is proposed

here to aggregate the satisfaction degrees: a set of

fuzzy rules within a fuzzy inference system. Fuzzy

rules are suitable, and easy to deﬁne, to model the in-

teractions between individual variables.

The potential of the method is illustrated using an

agronomic case study: how much nitrogen fertilizer

should be applied according to the production target,

the expert knowledge and the data?

The paper is organized as follows. The basics

of fuzzy logic and linguistic modeling are recalled

in Section 2. The different steps and options of the

multicriteria methodology are introduced in Section

3. Section 4 describes the agronomic case study and

discusses the results. Finally, the main conclusions

are summarized in Section 5.

2 LINGUISTIC MODELING

Fuzzy logic is widely used as an interface between

symbolic and numerical spaces, allowing the imple-

mentation of human reasoning in computers. Fuzzy

sets are used to implement approximate concepts, e.g.

Medium. They are deﬁned using a function that as-

signs to any value, x, in the universe of the variable,

e.g. Temperature, a membership degree, 0 ≤ µ(x) ≤ 1,

as shown in Figure 1. Therefore, in this example,

these degrees would be interpreted as the level to

which x should be considered as a Medium Temper-

ature.

The core of the fuzzy system, Figure 2, is a set of

fuzzy “if . . . then” rules in the form: If Temperature is

Medium then. . . When several variables are involved

in the rule description, the membership degrees can

be combined using an ‘AND’ operator (the most com-

mon are the minimum and the product) to weight

the rule conclusion. The inferred output results from

the aggeregation of all rule conclusions. The rule

base may include expert rules and rules learned from

data, making fuzzy inference systems a suitable en-

vironment for cooperation between expert knowledge

and data mining/learning techniques (Guillaume and

Charnomordic, 2012). As a consequence of overlap

in the fuzzy partition, several rules are likely to be

called by the same input data. The inferred output

is the result of the combination of all these weighted

conclusions.

3 DATA FUSION AND

MULTICRITERIA DECISION

MAKING

The objective here is to ensure that the process of data

fusion for decision making is driven by expert knowl-

edge. Information fusion is done with a speciﬁc goal,

for instance risk level evaluation or variable rate ap-

plication in agriculture. The selection of the relevant

and available information sources is done by the de-

cision maker. The next step is to evaluate the possible

level of decision, e.g. risk or rate, according to each of

the sources for a given entity deﬁned by its spatial co-

ordinates. The ﬁnal step comes down to aggregating

these partial levels, or degrees, to make the ﬁnal deci-

sion. The aggregation function models the decision-

maker’s preferences: Are some attributes more im-

portant than others? How to combine conﬂicting in-

formation sources?

The whole framework can be illustrated as fol-

lows:

, .. . , a

) , (b

, . . . , b

)

−→ f(a) , f(b)

↑ c ↓

, . . . , x

) , (y

, . . . , y

) ≺

∼

(a, b)

There are two steps to formalize expert knowledge

and preferences in the decision process. The ﬁrst

deals with each individual variable, or information

source. The second addresses the interaction between

sources.

The ﬁrst step aims to turn raw data into satisfac-

tion degrees. This is done by deﬁning a preference

relation for the considered attribute: What are the pre-

ferred values for the decision for this variable? Do

some of these values have a similar meaning for the

decision to be made? Once the values are commen-

surable, i.e. they have the same scale with the same

meaning, they can be aggregated in a second step to

compute a global score. Items can be compared ac-

cording to their score. These two steps are now de-

Combining Spatial Data Layers using Fuzzy Inference Systems: Application to an Agronomic Case Study

output

If...Then

inputinput

base

Fuzzy rule

Defuzzification

crisp fuzzy crisp

Inference engineFuzzification

fuzzy

High

(x)

Low Med

Figure 2: A Fuzzy Inference System.

i j Pests

Degree

Figure 3: A Membership Function Indicating the Number

of Plant Pests Present and the Corresponding Degree of

Plant Health.

tailed.

3.1 From Raw Data to Satisfaction

Degrees

A common scale with a common meaning is required

by the aggregation process. This step is thus manda-

tory to aggregate information sources with different

scales and different units. It is carried out by asso-

ciating a preference relation to a variable to deﬁne

a criterion. The preference depends on the decision

to be made and on the attribute used in the decision-

making. For example, if crop health is evaluated us-

ing the number of plant pests present, then the lower

the number of pests the better the health state. In this

work, the scale is the unit interval, [0, 1] with zero

meaning the criterion is not satisﬁed and that it is fully

satisﬁed with one. The preference relation can be

modeled, or implemented, using a fuzzy set as shown

in Figure 3 for this example.

The degrees are computed for any x ∈ [0, +∞[ ac-

cording to Equation 1.

deg(x) =







1 i f x ≤ i

j−x

j−i

i f i ≤ x ≤ j

0 i f x ≥ j

(1)

This is another way of using the fuzzy set concept.

The transformation function includes the part of the

expert knowledge related to each individual variable,

without considering its interaction with the other vari-

ables.

3.2 Numerical Operators

The most popular techniques to aggregate commensu-

rable degrees are numerical operators. The two main

families of such operators, with suitable properties,

are the Weighted Arithmetic Mean (WAM) and Or-

dered Weighted Average (OWA).

The WAM aggregation is recalled in Equation 2.

WAM(a

, . . . , a

) =

∑

i=1

(2)

with w

∈ [0, 1] and

∑

i=1

= 1. The weights are as-

signed to the sources of information. Unfortunately,

WAM cannot model compromise as shown in this ex-

ample. Let’s consider three items described by two

attributes with the following satisfaction degrees:

It 1 0.7 0.7

It 2 0.4 1

It 3 1 0.4

Item 1 is preferred to the other two. This leads to

the two conditions for the weights to fulﬁll:

• Score(It1) > score(It2) =⇒ w

> w

• Score(It1) > score(It3) =⇒ w

> w

These two conditions are contradictory, and there is

no combination (w

, w

) that can model the decision

maker preference.

The OWA (Yager, 1988) is computed as shown in

Equation 3.

OWA(a

, . . . , a

) =

∑

i=1

(i)

(3)

where (.) is a permutation such as a

(1)

≤ · ·· ≤ a

(n)

In this case, the degrees are ordered and the

weights are assigned to the locations in the distribu-

tion, from the minimum to the maximum, whatever

GISTAM 2020 - 6th International Conference on Geographical Information Systems Theory, Applications and Management

High

Low

0.2

0.8

Degree1

Figure 4: A Regular Fuzzy Partition with Two Linguistic

Labels.

the information sources. Using the OWA, the two

contradictory conditions above can be solved. WAM

and OWA can be combined in the Weighted OWA op-

erator, WOWA (Torra, 1996).

These operators are easy to use, the number of

parameters is the number of information sources to

aggregate, but their modeling ability is limited. The

Choquet integral (Choquet, 1954) proved to be use-

ful in multi-criteria decision making (Grabisch and

Labreuche, 2008). It is computed according to Equa-

tion 4.

C(a

, . . . , a

) =

∑

i=1

(i)

− a

(i−1)

)w(A

) (4)

where (.) is a the permutation previously deﬁned with

(0)

= 0 and A

= {(i), . . . , (n)}, meaning the set of

sources with a degree a ≥ a

(i)

The weights are not only deﬁned for each of the

information sources but for all their possible combi-

nations. Speciﬁc conﬁgurations include WAM and

OWA modeling. In the general case, the aggrega-

tion of n information sources requires 2

coefﬁcients.

These are usually set by learning algorithms (Murillo

et al., 2013).

3.3 Fuzzy Inference Systems

A fuzzy inference system usually requires more pa-

rameters than the former numerical aggregators but,

in this particular case of data fusion, the design can

be simpliﬁed as all the input variables are satisfaction

degrees that share the same scale, unit interval, and

the same meaning. Strong fuzzy partitions with reg-

ular grids are used to ensure semantic integrity. The

unique parameter left to the user is the number of lin-

guistic terms for each input variable. In this work it

was set at 2, Low and High, for each variable. The au-

tomatically generated input fuzzy partition is shown

in Figure 4. Thus, any degree 0 < x < 1 partially be-

longs to the two sets with a complementary level.

With two linguistic labels per variable, the num-

ber of rules is 2

, i.e. the equivalent number of co-

Table 1: Functions to Turn Raw Data into Satisfaction De-

grees.

Name Shape Preference

Semi Trapezoidal Inferior : low values

Semi Trapezoidal Superior : high values

Trapezoidal : an interval

Triangular : a value

In 2

In 1

In 3

Out 1

Out 2

Figure 5: A Hierarchical Structure to Decision-Making

Where the Scaled Output from the First Decision (S1) Is

an Input for the Second Decision (S2).

efﬁcients required by the Choquet integral. A rule

describes a local context that the domain expert, the

decision maker, is able to understand. In this way, the

rule conclusions are easier to deﬁne than the Choquet

integral coefﬁcients.

3.4 Implementation

The fusion module is implemented as an open source

software in the GeoFIS program. The data must be

co-located, i.e. a record includes the spatial coordi-

nates, from a point to a zone, and the corresponding

attributes.

The available functions to turn raw data into de-

grees are summarized in Table 1.

Three aggregation operators are currently avail-

able: WAM, OWA and a fuzzy inference system (FIS)

that can use linguistic rules.

For WAM and OWA the weights can be learned

provided a co-located target is available. Rule con-

clusion can also be learned using the FisPro software

(Guillaume and Charnomordic, 2011).

Rule conclusion can be either a linguistic term,

fuzzy output, or a real value, crisp output. Using a

fuzzy output, it would be necessary to deﬁne as many

labels as there are different suitable rule conclusions.

As a crisp conclusion may take any value in the output

range, it allows for more versatility.

The output should also range in the unit interval.

This constraint ensures that the output can feed a fur-

ther step of the process as shown in Figure 5.

In this way, the intermediate systems can be kept

small, making their design and interpretation easier.

The GeoFIS program includes a distance function

based on a fuzzy partition that allows for integrat-

Combining Spatial Data Layers using Fuzzy Inference Systems: Application to an Agronomic Case Study

ing expert knowledge into distance calculations (Guil-

laume et al., 2013) as well other functionalities, such

as a zone delineation algorithm (Pedroso et al., 2010).

An illustration of its potential use in Precision Agri-

culture can be found in (Leroux et al., 2018).

4 CASE STUDY

In this section a short case study is presented of the

spatial decision support model. It is not possible to

provide an exhaustive case study within the restric-

tions of a conference paper. It is therefore primarily il-

lustrative in nature but based on a typical farming de-

cision, the application of nitrogen within a vineyard.

The vineyard is a Concord (Vitis labrusca) juice grape

vineyard in the Lake Erie region of New York state.

The decision process followed by both a grower and

an academic are presented to illustrate how the dif-

ferent knowledge bases and risk perceptions are cap-

tured in the process. For this illustration, only the FIS

approach is considered and the OWA and WAM op-

erators are not used. Although a relatively simple ex-

ample, the following case study utilizes three differ-

ent types membership functions to derive satisfaction

degrees (both inferior and superior semi-trapezoidal

functions and a trapezoidal function, Table 1). The

degrees are aggregated using a fuzzy rule base.

4.1 The Decision

How much nitrogen fertilizer should be applied to the

vineyard and should this be site-speciﬁc?

The amount of fertilizer applied will be dependent

on the intended vine size management and the pro-

duction target, which is likely to differ between grow-

ers. In general terms, larger vines should be more pro-

ductive and ripen more grapes. Management, includ-

ing nutrition, should aim to enable crop maturity and

to maintain vine size. Smaller vines risk being over-

stressed with a large fruit load and will have lower

long-term productivity. They are also more suscep-

tible to cold and disease damage. The intent with

smaller vines is to manage the fruit load and nutrition

so that the vine can put more effort into vegetative de-

velopment in the short-term to increase its size and so

become more productive in the longer-term.

Information was available on soil variability in the

form of an apparent soil electrical conductivity (EC

)

map that is a surrogate for soil texture and to some

extent soil fertility. Crop information was available

as vine size (measured as pruning mass) and Crop

Load (the ratio of the mass of fruit to pruning mass).

These data were obtained from various sensors (see

Table 2: Membership Functions Deﬁned by a and B to

Standardize the Input Variables into a [0, 1] Range and to

Identify What Constitutes a Good (1) and Bad (0) Score.

The Soil EC

Variable Was Deﬁned Jointly by the Two

Decision-Makers and Is Constant. The Pruning Mass and

Crop Load Were Deﬁned Independently and Illustrate a Dif-

ference in Opinion between the Two on What Is the Mini-

mum Value for a Good Vine Size and a Bad Crop Load.

Soil conductivity Pruning Mass CropLoad

(mS/m) (lbs/vine) (Ravaz Index)

1 - 2 10 - 18

2, 10, 15, 33 1 - 2.5 10 - 15

(Bates et al., 2018) for further details) and mapped

onto a common grid. The interpolated data are shown

in Figure 6 to illustrate general (and differing) trends

between the variables.

Within this case study, the thought process of two

decision-makers was used to illustrate the ﬂexibility

in the decision systems and the potential to arrive at

different outcomes from identical inputs based on the

speciﬁc objectives of each individual decision-maker.

The ﬁrst decision-maker, denoted “A”, is the vineyard

owner/manager, who routinely makes decisions in the

vineyard to ensure the viability of the production sys-

tem. Their decision-making is strongly inﬂuenced by

the accumulated knowledge of 3 generations of vine-

yard management in the region.

The second decision-maker is a trained viticultur-

ist, denoted “B”, who is involved in research and ex-

tension activities in the district. B is also a vineyard

manager, but their knowledge is strongly informed

from the scientiﬁc literature, rather than a family his-

tory in vineyards.

4.2 The Aggregation System

The ﬁrst step is to allow each decision-maker to im-

pose their knowledge onto the input variables. The

decision is based on managing larger and smaller

vines; but what is a large and small vine? Similarly,

what soil EC

response is considered good or bad

from a nutritional perspective? To deﬁne this, mem-

bership functions were generated (Table 2) to transfer

the decision-makers preferences into the analysis and

also to standardized inputs to a [0,1] range for future

analysis.

There was agreement between A and B on the E C

function so it is common for both decision paths. Note

that in the EC

layer, very low and very high values

are both considered poor for production, and this is

permissible in the analysis. The two decision-makers

GISTAM 2020 - 6th International Conference on Geographical Information Systems Theory, Applications and Management

Figure 6: Images Illustrating the Spatial Patterns of the Three Input Variables - Apparent Soil Electrical Conductivity (Left,

) to a Depth of 1.5 M Using a Dualem 1s (DUALEM, Mississauga, ON, Canada); Pruning Mass (Centre, PM 2014)

from 2014 Predicted from a Calibrated Canopy Sensor ((Taylor et al., 2017) and Crop Load (Ravaz Index) in 2014 Using the

Pruning Mass and Grape Yield Monitoring Data (Yield Data Not Shown).

differed in their interpretation of good vine size (prun-

ing mass) and desired Crop Load. The vineyard man-

ager (A) considered 2 lbs (0.91 kg) vines as a good

vine size, while the researcher (B) deﬁned 2.5 lbs

(1.13 kg) as the minimum for a good vine size. Simi-

larly, A did not consider the vines over-cropped until

a higher Crop Load value was achieved, i.e. A, the

commercial grower, was more content to have more

fruit in the vineyard, effectively pushing the vines

harder than B through this step. This may stem from

a better understanding of what the vineyard can pro-

duce and/or a need to ensure sufﬁcient short-term pro-

duction to remain economically viable.

Following the speciﬁcation of the membership

functions, a fuzzy inference system can be used to

deﬁne the decisions for A and B. For the three in-

puts, 2 levels of operation [High/Low] were deﬁned.

This gave 8 potential linguistic rules (Table 3). Again,

these rules were deﬁned jointly by A and B in agree-

ment with the relative amount of nitrogen fertilizer

needed in each situation. Of course, this may not al-

ways be the case, and producers with differing objec-

tives could generate different “if-then” statements at

this point. However, in this case, the rules were com-

mon for both A and B to simplify the example. Crisp

numerical values were used for the rule conclusions,

Table 3: The Linguistic Rule Base. Abbreviations Refer to

the Variables Presented in Figure 6.

CropLoad EC

PM Nitrogen

1 Low low Low 0.7

2 Low low High 0.5

3 Low High Low 0.5

4 Low High High 0.3

5 High low Low 0.9

6 High low High 0.7

7 High High Low 0.7

8 High High High 0.5

such that Line one (Table 3) reads If CropLoad is Low

AND EC

Deep

is Low AND PM is Low then Nitrogen

is 0.7 (i.e. 70% application). As indicated previously,

linguistic or fuzzy outputs could also be possibly used

here for the rule conclusions.

4.3 Results and Discussion

The raw output maps are noisy and difﬁcult to directly

interpret (inset of Figure 7). Of course a variable rate

controller may not have difﬁcult in reading and inter-

preting these maps, although the potential levels of

Combining Spatial Data Layers using Fuzzy Inference Systems: Application to an Agronomic Case Study

application may need to be simpliﬁed to account for

the application resolution of the variable rate equip-

ment.

For human intervention, and often for simplic-

ity of application, the data can be aggregated into

zones. In this case they are speciﬁc nitrogen appli-

cation zones. Figure 7 shows the simpliﬁed output for

the decision process of A and B on a common legend.

Note that the legend has yet to be transformed into

actual N values and shows the output (between 0 and

1) from the FIS. The zoning algorithm was performed

using a segmentation approach (Pedroso et al., 2010)

in GeoFIS (Leroux et al., 2018).

In Figure 7 the different satisfaction degrees for

vine size and Crop Load for the two decision makers

have clearly generated some differences in the poten-

tial nitrogen application zones. The inputs were com-

mon, as was the rule set used, so it is not surprising to

see that the pattern of N required is similar in the two

maps. However, seemingly small alterations to the

the idea of a good vine size or an overcropped vine

has clearly affected the ﬁnal zoning. It is not possible

to say which of the maps is preferable, as each was

tailored to the preferences of each decision-maker.

It is important to note that since the output is stan-

dardized, there does exist another potential point of

difference between A and B in their determination of

how much nitrogen equates to a value of 1 and 0 (and

all values in between) in this situation, or rather, how

much N would each user apply in the red zone, the

yellow zone etc. . . There is no need for this amount to

be ﬁxed for a particular output score.

As indicated in Section 3.4, the rule conclusions

can be speciﬁed as a linguistic term (as well as a nu-

merical value. Figure 7 was derived from the numer-

ical rule conclusions in Table 3. However, many pro-

ducers may be more comfortable providing ‘fuzzy’

indications of rates, rather than hard numerical val-

ues. To quickly illustrate this alternative approach,

Table 4 shows the same “if-then” statements as Table

3, but with linguistic rule conclusions. In this case,

the rule conclusions have been speciﬁed simply as ei-

ther a ‘High’, ‘Average’ or ‘Low rate’. The decision

process was then rerun, using the same input layers

and the same satisfaction degrees (membership func-

tions) as before, but with the linguistic rule conclu-

sions (Table 4). These were again common for both

A and B. The zoned outcome, for both A and B, is

shown in Figure 8. The output has been defuzziﬁed

and expressed in numerical form ([0,1]).

The two maps in Figure 8 can be compared to each

other (illustrating again the difference in the determi-

nation of satisfaction degrees for Crop Load and vine

size between A and B), or compared to Figure 7. The

Table 4: The Linguistic Rule Base with ’fuzzy’ Linguistic

Rule Conclusions.

CropLoad EC

PM Nitrogen

1 Low Low Low High

2 Low Low High Average

3 Low High Low Average

4 Low High High Low

5 High Low Low High

6 High Low High High

7 High High Low High

8 High High High Average

difference between Figures 7 and 8 lies in the use of

the numerical or linguistic rule conclusions (Tables 3

and 4 respectively). The patterns again remain simi-

lar, i.e. areas of higher and lower N application, al-

though the size and shape of the zones, and the loca-

tion of boundaries, is changed. The simpler (3-level)

linguistic rule conclusions have generated smoother

zones than the numerical rule conclusions (with 4 lev-

els). Again, there is no perfect answer here. All four

maps present a solution based on slightly differing in-

put knowledge related to the satisfaction degrees or

the FIS rules. The red zone in the eastern part would

receive the same amount of Nitrogen after the output

maps were translated to actual Nitrogen rates.

This case study has shown the steps involved in a

fertilizer decision process using the data-fusion mod-

ule in GeoFIS and the fuzzy logic option. It illustrates

how even a slight change in the process between users

A and B (with only 2 of the 3 membership functions

varying), generated different prescription levels of N

to be spatially applied in the vineyard. Altering the if-

then rules, and possibly also the types of input infor-

mation preferred by different users for the same deci-

sion, will generate even more pronounced differences.

It is impossible to identify which solution is best, or

if there is an actual optimal solution, as for each case

the outcome is adapted to the perception, risk and ob-

jectives of the user. While the example here is with

fertilizer application, the decision process can be ap-

plied to any decision, provided relevant input layers

and expert knowledge is available.

Finally, it is important to note that although the

software and decision support tool is capable of us-

ing OWA and WAM operators for aggregation, the

agronomic decision selected here (nitrogen applica-

tion) dictated the use of the FIS approach in this in-

stance. The OWA and WAM approaches require well-

structured and logical decision processes i.e. an ag-

gregation of ‘low’ satisfaction degrees should gener-

ate a ‘low’ output response. Agronomic decisions are

not always so linear or straight-forward. In this case,

both small and large vines could receive high applica-

GISTAM 2020 - 6th International Conference on Geographical Information Systems Theory, Applications and Management

Figure 7: Simpliﬁed Zoned Maps (9 Zones Each) of the Nitrogen Decision Generated by the Two Decision-Makers – a =

Vineyard Manager and B = Research Viticulturist. The Raw Output Is Shown in the Inset Image. The Trends Are Similar for

Both, but Boundaries and Output Levels Do Differ.

tions of nitrogen, for differing reasons (see lines 1 and

6 in Tables 3 and 4). For smaller vines, additional ni-

trogen may be needed to promote vegetative vigor to

grow larger, more sustainable vines, while with larger

vines, additional nitrogen will be needed to maintain

a higher level of production under poorer soil condi-

tions. Therefore, the system has two very different

reasons to arrive at the same nitrogen application rate

decision. This is a limitation for the OWA and WAM

operators and a strength for the FIS approach.

5 CONCLUSIONS

This paper has introduced a novel spatial decision

process and demonstrated it using a typical agronomic

practice. The decision process used satisfaction de-

grees speciﬁed by the user to avoid the requirement

for a large number of parameters to deﬁne input par-

titions and the inference operators. Since all the input

variables in the decision process were satisfaction de-

grees, with a common scale and common meaning,

the automatic setting of the decision rules was possi-

ble using a strong fuzzy partition with linguistic terms

(in this case, Low and High). As a consequence, only

the rule conclusions had to be speciﬁcally deﬁned by

the user. This was a relatively quick and easy activ-

ity, using both numerical and linguistic rule conclu-

sions, to allow the expert knowledge (grower, advi-

sor, etc. . . ) of the variables and their interactions to

be modeled. Fuzzy inference systems, thanks to their

proximity with natural language and expert reasoning,

are a good alternative framework for modeling pref-

erences and for use in multi-criteria decision making

under uncertainty.

Field cropping systems operate under a large

amount of uncertainty and variability imposed by

variable biotic and abiotic stresses and a grower’s risk

and market preferences. As such, no decision is ab-

solute. This simple case study illustrated that a dif-

ference in perception of good and bad vine size and

Crop Load (fruit:leaf ratio) generated a difference in

target nitrogen application. The particular novelty of

this decision system was in its ability to provide a

spatial decision that captured the user’s intentions and

Combining Spatial Data Layers using Fuzzy Inference Systems: Application to an Agronomic Case Study

Figure 8: Alternative Nitrogen Application Zones (9 Zones Each) Derived using the Same Satisfaction Degrees and Inputs as

Figure 7, but with Linguistic Rule Conclusions. It Again Shows the Output for Both Users a and B, Illustrating Differences

between Their Choice of Satisfaction Degrees (Table 2). the Use of ‘less Crisp’ Linguistic Rule Conclusions (and Fewer

Levels) Generates More Regular and Larger Zones Compared with the Equivalent Nitrogen Zone Maps in Figure 7.

knowledge without needing the user to understand all

the local, varying interactions in the multi-variate spa-

tial data. The system modeled and spatially differen-

tiated what a grower would do vs. what an advisor

would recommend.

Under these conditions, aggregation with the

OWA and WAM operators was not possible. This is

a limitation for the OWA and WAM operators and a

strength for the FIS approach.

This framework is implemented as an open source

software called GeoFIS available at: https://www.

geoﬁs.org. This is a strong asset as software support

availability is a key factor for a method to be adopted.

ACKNOWLEDGEMENTS

The work is funded by the USDA-NIFA Specialty

Crop Research Initiative Award No. 2015-51181-

24393.

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