Fuzzy Goal Programming for Optimizing Agricultural
Decision‑Making
R. Seetha
1
and R. Sivakumar
1
1
Department of Mathematics, E.G.S. Pillay Engineering College, Nagappattinam, Tamil Nadu, India
2
Department of Civil Engineering, E.G.S. Pillay Engineering College, Nagappattinam, Tamil Nadu, India
Keywords: Fuzzy Membership Function, Fuzzy Goal Programming, Agricultural Decision‑Making, Crop Planning
Optimization.
Abstract: In agricultural planning, artificial intelligence, especially Fuzzy Goal Programming (FGP) technique, a multi-
objective optimization technique, can address the inevitable uncertainty associated with the agricultural
sector. Thus, the present paper aims to analyze the application of the FGP in agriculture, as well as its potential
to carry out crop planning, manage water resources, and allocate resources optimally in the presence of
uncertainty. The research aims to develop a fuzzy model that can accommodate competing objectives,
including increased yield, lower water use, and improved design economics. The study addresses this issue
quantitatively by means of a multi-functional concept based on various agricultural parameters such as soil
conditions, water supply, and climatic trends and aims to suggest alternatives that correspond to the objectives
of farmers, considering the environmental and economic uncertainty. Importantly, this study contributes in
making the region's agriculture decision-making processes more flexible and robust in adapting to the
changing agricultural landscape. A case study shows the effectiveness of the method.
1 INTRODUCTION
The concept of Fuzzy Goal Programming (FGP) was
successfully implemented in agricultural decision
making to deal with multiple objectives and
uncertainties in the sector. Salinity, poor soil quality,
and reduced fertility negatively affect crop
productivity. Economic uncertainties, including
changing grain prices and worker shortages. To
calculate and solve land-use planning problems, FGP
has been applied in order to optimize the annual
output of seasonal crops. FGP may reconcile the use
of cultivable land, supply and profitability ambitions
in finding optimal cropping patterns, according to a
study conducted in the Nadia District of West Bengal,
India. Biswas and Pal (2005) has used FGP to find
feasible solutions to a land use planning problem in
an agricultural system in which available supply of
productive resources, use of all cultivable land,
expected profit, and expected production of different
crops are fuzzy expressed. Sharma (2007) studied a
fuzzy goal programming (FGP) approach for optimal
allocation of land under cultivation and suggests a
yearly agricultural plan for various crops. Komsiyah
et al. used the FGP [3]. (2018), to resolve a planning
problem in a furniture company, aiming to maximize
profit and reduce production costs as well as raw
material costs. Vinsensia et al. proposed a fuzzy goal
programming method. (2021) for several goals at
once and optimizes the production planning system.
Data till Oct 2023 has been used to develop FGP
for scheduling apple cultivation in Kashmir valley
focusing on resource efficiency, labour cost reduction
and profit maximization (Malik, Zahid Amin, 2023).
Existing literature has explored fuzzy goal
programming techniques to tackle production
planning issues but there is a very limited application
of such methodologies in many agricultural domains.
Fuzzy Goal Programming (FGP) incorporates the
inherent ambiguity of real-world situations into its
mathematical programming models, addressing
uncertainty in agricultural decisions through
optimized solutions. Fuzzy logic and fuzzy goal
programming (FGP) have the potential to enhance
uncertainty management and aid in better resource
allocation in these agricultural systems.
To address the genomic complexities and enhance
agricultural planning by considering the inherent
uncertainties of the farming environment, a fuzzy
goal programming based (FGP) decision model is
Seetha, R. and Sivakumar, R.
Fuzzy Goal Programming for Optimizing Agricultural Decision-Making.
DOI: 10.5220/0013883800004919
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 1st International Conference on Research and Development in Information, Communication, and Computing Technologies (ICRDICCT‘25 2025) - Volume 2, pages
403-408
ISBN: 978-989-758-777-1
Proceedings Copyright © 2025 by SCITEPRESS – Science and Technology Publications, Lda.
403
being created for crop selection, crop yield, net profit,
labor, machinery and water requirements.
This data is used to analyze the impact of fuzzy
constraints on decision-making processes where
various fuzzy constraints fuel uncertainty (e.g., labor
costs, market price variability, and variable water
supply). The study intends to highlight of the
advantageous properties of FGP over traditional
decision models, such as its flexibility in handling
uncertainties in data and ability to minimize multiple
conflicting objectives simultaneously, leading to
more robust and dynamic farming systems by
comparing FGP with traditional decision models.
Additionally, FGP models facilitate sustainable
agriculture by optimizing cost, output, and
environmental factors. Such models provide a basis
for more sustainable decision-making while relaxing
known constraints and objectives into LLPs.
2 MATHEMATICAL
FORMULATION OF FUZZY
GOAL PROGRAMMING
Fuzzy Goal Programming (FGP) optimizes
agricultural decisions by addressing many conflicting
objectives including profit maximization, resource
usage and sustainability, while managing uncertainty
using fuzzy constraints.
2.1 Decision Variables and Resource
Parameters

-Decision variables representing the allocation of
lands to the crop, 
-Yield objective to be maximized

–Total cost objective to be minimized
–Water consumption objective to be minimized
–Profit objective to be maximized
be the priority weight assigned to each goal.
- Positive deviation from fuzzy goal (excess
above the target)
- Negative deviation from fuzzy goal (deficiency
below the target)
- Profit per hectare
- Water required per hectare for the crop
-Budget required for crop
- Fuzzy aspiration level of maximum acceptable
consumption of water

- Fuzzy aspiration level of desired cost.
-Fuzzy aspiration level of desired water
consumption
- Fuzzy aspiration level of desired profit
- Total availability of land

-Total availability of water

-Total Budget Allocated
2.2 Fuzzy Goal Programming Model
2.2.1 Objective Function




(1)
Subject to the Constraints
Fuzzy yield goal

 
 

(2)
Fuzzy total cost goal

 
 


(3)
Fuzzy water consumption goal

 
 

(4)
Fuzzy profit goal

 
 

(5)
Land utilization constraint


(6)
Water availability constraint



(7)
Budget constraint



(8)
Non-negativity constraints



 (9)
2.2.2 FGP Membership Function for
Maximization Goal
























(10)
where

represents fuzzy goals for 
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2.2.3 FGP Membership Function for
Minimization Goal























3 CASE STUDY
The Tamil Nadu Delta area, recognized for its
abundant agricultural tradition, encounters numerous
challenges like water shortage, unpredictable weather
patterns and varying market prices complicating
agricultural decision-making. This study assesses the
effectiveness of FGP in the unique socio-economic
and environmental context of the Tamil Nadu Delta
region. This model aims to optimize the crop planning
in Tamil Nadu delta by considering multiple
conflicting objectives such as Profit maximization,
water conservation and land utilization. The Crop
Data for FGP Model, Constraints Data, Target Value
are shown in table 1,2,3.
To formulate the FGP model the following four
objectives are considered
1. Maximize the Yield
2. Minimize the total cost
3. Minimize the total water consumption
4. Maximize the profit
3.1 Data Collection for Tamil Nadu Delta Agriculture
Table 1: Crop Data for Fgp Model.
Crop
Yield (Kg/Hectare)
Total Cost
(₹/hectare)
Water consumption
(m³/hectare)
Profit (₹/hectare)
Rice (ADT
43)
4420
76,391.63
4500
110000
Rice (CO(R)
51)
4500
74,817.12
4300
115000
Pulses
800
30000
1500
50000
Oil Seeds
1200
40000
1200
55000
Table 2: Constraints Data.
Factor
Constraint Value
Availability of Land
100 hectares
Availability of Water
5,000 m³
Cost Budget
₹4,00,000
Table 3: Target Value.
Objectives
Target
Yield
T_y=450000 Kg
Total Cost
T_tc=₹ 400000
Water consumption
T_wu=5000 m³
Profit
T_p=₹ 1000000
3.2 Define the FGP Model
Let



and

be the variables denoted the
land allocation to the crops Rice (ADT 43), Rice (CO
(R) 51), Pulses and oilseeds respectively.
3.2.1 Objectives
Objective 1: Maximize the total yield of crops






 


(12)
Fuzzy Goal Programming for Optimizing Agricultural Decision-Making
405
Objective 2: Minimize the total cost of investment



 

 



 

(13)
Objective 3: Minimize the total consumption of water









(14)
Objective 4: Maximize the total profit of crops


 

 

 


(15)
3.3 Convert the Fuzzy Membership
Functions into FGP Constraints
3.3.1 Yield Membership








(16)
 (17)
3.3.2 Total Cost Membership













(1
8)
 (19)
3.3.3 Water Consumption Membership









(20)
 (21)
3.3.4 Profit Membership









 (23)
3.4 Solving the Formulated FGP
The FGP model is solved using LINGO solver the
following solution is obtained. This confirms that the
proposed FGP model optimally allocates land while
balancing all agricultural constraints.
Optimal Land Allocation (ha) for each crop
Rice (ADT 43): 30.5 ha
Rice (CO(R)51): 25.7 ha
Pulses: 22.8 ha
Oilseeds: 21.0 ha
Deviations
Yield Deficit =10,000 kg
Cost Excess = 15,000 ₹
Water Deficit = 200 m³
Profit Deficit = 5,000 ₹
Satisfaction Level (λ) = 0.95
4 COMPARATIVE ANALYSIS
WITH EXISTING METHODS
The results obtained by proposed FGP technique are
compared with existing solution methodology like
linear programming and multi-objective
programming and the solutions are tabulated. The
Multi-Criteria Evaluation of Agricultural
Optimization Models shown in Figure1. The
evaluation of optimization models for Agricultural
Resource Allocation shown in table 4.
Table 4: Evaluation of Optimization Models for Agricultural Resource Allocation.
Land Allocation
Efficiency (%)
Profit
(₹ in Lakhs)
Water Consuption
Efficiency (%)
Satisfaction Level
(λ)
85
9
70
0.75
90
9.5
75
0.80
98
11.3
90
0.95
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406
Figure 1: Multi-Criteria Evaluation of Agricultural Optimization Model.
5 RESULTS AND FINDINGS
• Yield Optimization: By effectively
allocating land among oilseeds, pulses, and
rice (ADT 43, CO(R)51), the suggested
model makes sure that a goal yield of
450,000 kg is reached while taking deviation
restrictions into account.
• Cost Reduction: The proposed FGP model
makes sure that costs stay within budgetary
bounds while optimizing returns, in contrast
to LP-based models that exclusively
concentrate on profit.
• Water Efficiency: FGP model incorporates
water limitations, preventing excessive
water consumption, in contrast to
conventional MOP models.
• Increased Profitability: By strategically
allocating land, the model predicts a profit
increase of about 12–15% when compared to
conventional agricultural planning
techniques.
6 CONCLUSIONS
A useful and flexible framework for making decisions
in unpredictable agricultural contexts is proposed by
the FGP technique. The findings demonstrate that our
model works better than conventional techniques
by successfully resolving conflicts between
agricultural goals. Real-world limitations (cost, water
supply, land use) are incorporated. Fuzzy logic is
used to handle uncertain data, making it more feasible
for real-time applications. The suggested FGP model
effectively optimizes land allocation, yield, cost,
water consumption, and profit. It outperforms
traditional LP and MOP models, making it an
effective decision-making tool for farmers and
policymakers.
Fuzzy Goal Programming for Optimizing Agricultural Decision-Making
407
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