Irrigation Planning Under Uncertainty—A Multi Objective Fuzzy Linear Programming Approach
TL;DR: Multi Objective Fuzzy Linear Programming (MOFLP) irrigation planning model is formulated for deriving the optimal cropping pattern plan for the case study of Jayakwadi project in the Godavari river sub basin in Maharashtra State, India.
Abstract: The problem of irrigation planning becomes more complex by considering an uncertainty. The uncertainties can be tackled by formulating the problem of irrigation planning as Fuzzy Linear Programming (FLP). FLP models can incorporate the scenario of real world problem. In the present study, Multi Objective Fuzzy Linear Programming (MOFLP) irrigation planning model is formulated for deriving the optimal cropping pattern plan for the case study of Jayakwadi project in the Godavari river sub basin in Maharashtra State, India. Four conflicting objectives are considered such as Net Benefits (NB), Crop/Yield Production (CP), Employment Generation/Labour Requirement (EG) and Manure Utilization (MU). Four different cases are considered to incorporate the uncertainty in MOFLP model. To include the uncertainty in irrigation planning problem only objectives are taken as fuzzy and constraints are crisp in nature in Case-I. To consider the uncertainty involved in availability of resources, in Case-II the stipulations are fuzzy. The technological coefficients are fuzzy in Case-III. The Case-IV includes both technological coefficients and stipulations fuzzy. The level of satisfaction (λ) works out to be 0.58, 0.50, 0.50 and 0.28 respectively for Case-I to IV. The results obtained in Case-IV are more realistic and promising as it involves the uncertainty in technological coefficients and stipulations simultaneously.
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Book•
01 Jan 1995TL;DR: Fuzzy Sets and Fuzzy Logic is a true magnum opus; it addresses practically every significant topic in the broad expanse of the union of fuzzy set theory and fuzzy logic.
Abstract: Fuzzy Sets and Fuzzy Logic is a true magnum opus. An enlargement of Fuzzy Sets, Uncertainty,
and Information—an earlier work of Professor Klir and Tina Folger—Fuzzy Sets and Fuzzy Logic
addresses practically every significant topic in the broad expanse of the union of fuzzy set theory
and fuzzy logic. To me Fuzzy Sets and Fuzzy Logic is a remarkable achievement; it covers its vast
territory with impeccable authority, deep insight and a meticulous attention to detail.
To view Fuzzy Sets and Fuzzy Logic in a proper perspective, it is necessary to clarify a point
of semantics which relates to the meanings of fuzzy sets and fuzzy logic.
A frequent source of misunderstanding fias to do with the interpretation of fuzzy logic. The
problem is that the term fuzzy logic has two different meanings. More specifically, in a narrow
sense, fuzzy logic, FLn, is a logical system which may be viewed as an extension and generalization
of classical multivalued logics. But in a wider sense, fuzzy logic, FL^ is almost synonymous
with the theory of fuzzy sets. In this context, what is important to recognize is that: (a) FLW is much
broader than FLn and subsumes FLn as one of its branches; (b) the agenda of FLn is very different
from the agendas of classical multivalued logics; and (c) at this juncture, the term fuzzy logic is
usually used in its wide rather than narrow sense, effectively equating fuzzy logic with FLW
In Fuzzy Sets and Fuzzy Logic, fuzzy logic is interpreted in a sense that is close to FLW. However,
to avoid misunderstanding, the title refers to both fuzzy sets and fuzzy logic.
Underlying the organization of Fuzzy Sets and Fuzzy Logic is a fundamental fact, namely,
that any field X and any theory Y can be fuzzified by replacing the concept of a crisp set in X and Y
by that of a fuzzy set. In application to basic fields such as arithmetic, topology, graph theory, probability
theory and logic, fuzzification leads to fuzzy arithmetic, fuzzy topology, fuzzy graph theory,
fuzzy probability theory and FLn. Similarly, hi application to applied fields such as neural network
theory, stability theory, pattern recognition and mathematical programming, fuzzification leads to
fuzzy neural network theory, fuzzy stability theory, fuzzy pattern recognition and fuzzy mathematical
programming. What is gained through fuzzification is greater generality, higher expressive
power, an enhanced ability to model real-world problems and, most importantly, a methodology for
exploiting the tolerance for imprecision—a methodology which serves to achieve tractability,
7,131 citations
"Irrigation Planning Under Uncertain..." refers methods in this paper
...Case II: The Fuzzy Linear Programming Problem, with Fuzzy Right-Hand Side Numbers ( ˜ bi) ( Klir and Yuan 2007 )...
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TL;DR: A fuzzy ranking method is used to rank the fuzzy objective values and to deal with the inequality relation on constraints in linear programming problems where all the coefficients are, in general, fuzzy numbers.
544 citations
"Irrigation Planning Under Uncertain..." refers methods in this paper
...Jimenez et al. (2007) developed an interactive method for solving linear programming with fuzzy numbers.Tsakiris and Spiliotis (2006) have developed the goal programming approach using the fuzzyset theory to find out the cropping pattern for Thessaly Plain in Greece....
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TL;DR: In this article, a non-linear programming optimization model with an integrated soil water balance was developed to determine the optimal reservoir release policies, the irrigation allocation to multiple crops and the optimal cropping pattern in irrigated agriculture.
Abstract: This paper develops a non-linear programming optimization model with an integrated soil water balance, to determine the optimal reservoir release policies, the irrigation allocation to multiple crops and the optimal cropping pattern in irrigated agriculture. Decision variables are the cultivated area and the water allocated to each crop. The objective function of the model maximizes the total farm income, which is based on crop–water production functions, production cost and crop prices. The proposed model is solved using the simulated annealing (SA) global optimization stochastic search algorithm in combination with the stochastic gradient descent algorithm. The rainfall, evapotranspiration and inflow are considered to be stochastic and the model is run for expected values of the above parameters corresponding to different probability of exceedence. By combining various probability levels of rainfall, evapotranspiration and inflow, four weather conditions are distinguished. The model takes into account an irrigation time interval in each growth stage and gives the optimal distribution of area, the water to each crop and the total farm income. The outputs of this model were compared with the results obtained from the model in which the only decision variables are cultivated areas. The model was applied on data from a planned reservoir on the Havrias River in Northern Greece, is sufficiently general and has great potential to be applicable as a decision support tool for cropping patterns of an irrigated area and irrigation scheduling.
116 citations
"Irrigation Planning Under Uncertain..." refers background in this paper
...Georgiou and Papamichail (2008) have developed a non-linear programming optimization model with an integrated soil water balance, to determine the optimal reservoir release policies, the irrigation allocation to multiple crops and the optimal cropping pattern in irrigated agriculture....
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TL;DR: In this paper, a model of crop planning with uncertain (stochastic) values is proposed to support decision making of agricultural farms, treating such uncertain elements as the values with the fuzziness and randomness.
100 citations
"Irrigation Planning Under Uncertain..." refers background in this paper
...Itoh et al. (2003) have presented crop planning problem with profit coefficients for agricultural products as discrete random variable....
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TL;DR: In this article, a monitoring study was conducted at the Zanyokwe Irrigation Scheme (ZIS) in the Eastern Cape to identify cropping systems and management practices used by farmers and to determine how these were related to performance.
Abstract: Generally, smallholder irrigation schemes (SIS) in South Africa have performed poorly and have not delivered on their development objectives of increasing crop production and improving rural livelihoods. Limited knowledge of irrigated crop production among farmers has been identified as one of the constraints to improved crop productivity, but research that investigates the relationship between farmer practices and productivity is lacking. A monitoring study was therefore conducted at the Zanyokwe Irrigation Scheme (ZIS) in the Eastern Cape to identify cropping systems and management practices used by farmers and to determine how these were related to performance. Evidence from 2 case studies showed that water management limited crop productivity. Irrigation application and system efficiencies were below the norm and irrigation scheduling did not take crop type and growth stage into account. Monitoring of 20 farmers over a 3-yr period showed that cropping intensity averaged only 48% and that the yields of the 2 main summer crops, grain maize (Zea mays L.) and butternut (Cucurbita moschata) averaged only 2.4 and 6.0 t∙ha-1, respectively. In addition to poor water management, other main constraints to crop productivity were inadequate weed and fertiliser management and low plant populations. The results indicated that a lack of basic technical skills pertaining to irrigated crop production among farmers was a possible cause of inadequate management. In this regard, it is expected that farmers could benefit from ‘back to basics’ training programmes in the areas of crop and irrigation water management. Research needs to focus on labour-saving production technologies, establishing farm-specific fertiliser recommendations, the identification and use of affordable sources of nutrients, as well as strategies to improve plant population in maize by preventing bird damage to newly-planted stands. Keyword s: smallholder irrigation schemes, cropping pattern, constraints to crop productivity, research agenda
89 citations