Keywords

1 Introduction

This investigation aims to formulate a procedure for selecting crops that would be suitable for cultivation under vertical irrigation systems. Advances in neurogenetic models and fuzzy logic are used to identify and predict the suitability of crops for the considered conditions.

The recent demand for land by burgeoning populations and requirements to ensure food security for those populations make the system of vertical crop cultivation the easiest and most useful solution to the current crisis of land availability. The scarcity of land has forced farmers to encroach on forest land and even riverbeds to satisfy the rising demand for food.

To prevent such land use, the cultivation of crops under vertical irrigations systems to maintain the food supply has been found to be the easiest and most reliable solution. But the problem with such a system is that not all crops support vertical irrigation systems. The following factors must be considered for the cultivation of crops under vertical irrigation methods:

  1. 1.

    Length of roots (L R)

  2. 2.

    Spread of roots (R S)

  3. 3.

    Nutrient absorption (N)

  4. 4.

    Temperature tolerance (T)

  5. 5.

    Water tolerance (W)

  6. 6.

    Parasite tolerance (Pa)

  7. 7.

    Space requirements (A)

  8. 8.

    Profitability compared with conventional agricultural practices (P)

Short crops whose roots do not spread out very much can absorb nutrients from water and do not depend on the soil for their daily nutrient requirements, and crops that are temperature tolerant and do not attract parasites or other pests can be used for cultivation under vertical irrigation systems.

Because the cultivation will be performed in vertical systems, the weight of the crop is a major factor when selecting crops for such systems. The crops must not be highly water intensive because excess water will increase the weight requirement. That is why drip or sprinkler irrigation is used in such irrigation methods, where water is channelized from a reservoir situated on a roof. A proper drainage system must also be used so that water is not stored anywhere within the irrigation system. Because soil increases the weight requirement and can attract different hazardous species, hydrophilic plants are generally preferred. But plants with minimum requirements for soil or that can be cultivated in sandy soil also are harvested under vertical irrigation systems. Plants must also be odorless and not attract insects or other parasites because this can create disturbances to other residents of the vertical dwelling. Generally fruits like tomatoes, vegetables like lettuce, cabbage, and brinjal, and crops like rice and maize are popular species known to be cultivated under vertical methods of irrigation.

The success of a vertical irrigation system thus mainly depends on the capacity of the crop to tolerate a controlled and closed environment and the efficiency of the farmer in meeting the daily requirements of the crop. Proper selection of crop species also reduces maintenance requirements.

Not only the environment, but the profitability of crops raised in a vertical irrigation system compared to those raised in conventional irrigation systems must also be considered. Only if profit is maximized or loss minimized compared to old irrigation systems can a species of plant be cultured in a vertical irrigation process.

That is why the present investigation uses neuro-fuzzy techniques to estimate the nonlinear interrelationships that exist in the prediction of crop suitability under such specialized irrigation systems.

1.1 Brief Methodology

Fuzzy logic, a recent innovation in searching for optimal solutions to complex problems, is used to determine the weighting of each variable according to its importance in determining the suitability of a crop being cultivated under a vertical irrigation systems.

The weighting was used to determine the weighted average of the variables, which is directly related to the suitability of a particular plant species for cultivation under a nonconventional irrigation system.

The weighted average and value of all the input variables are categorized such that each category represents the level of suitability of the crop due to the quantitative or qualitative situation of the variable. For example, the length of the root can be encoded into nine categories from Extremely Small to Extremely Large. The category Extremely Small will have the highest level of suitability with respect to other categories of the variable. Again, for the variable parasite tolerance, Extremely High will represent the higher suitability of the crop compared to the other categories for cultivation in a vertical irrigation system.

The categorized data of the variables will help to create a combinatorial data matrix considering each possible combination that may exist among the input and output variables. Each of the categories was rated according to its impact on the selection mechanism. The rankings were then used to determine the weighted average. This weighted average was also categorized in such a way that Extremely High represents greater suitability of the crop than other categories and Extremely Small represents the opposite characteristic of the sample species.

A neurogenetic model was then used to formulate the relationship between input and output variables in such a way that if the category of the input variables is given, the model predicts the level of suitability of the plant species for cultivation under a vertical irrigation system. Because the neurogenetic model will be trained by the combinatorial data matrix, the model can predict the suitability of any combination of input variables. The model is validated by performance metrics like precision, sensitivity, specificity (CEBM 2012), and kappa index of agreement (GANFYD 2012).

1.2 Fuzzy Logic

Zadeh et al. discovered the benefit of following fuzzy logic in solving practical decision-making problems. Fuzzy logic nowadays is applied in various field such as the selection of a reservoir operating mechanism, watershed management, dam break analysis, and other optimization and clusterization problems.

Fuzzy logic was used in this study to determine the weighting that represents the role of variables in identifying species’ suitability for cultivation under a vertical irrigation system.

1.3 Neurogenetic Models

Neural network models follow the signal-transmission mechanism of the human nervous system. The capability of the human nervous system to identify complex, nonlinear, and uncertain situations is mimicked in solving real-life decision-making problems. Analysis of recent studies shows that neural networks have been applied to various topics in engineering, medicine, science, and the arts (Table 7.1).

Table 7.1 Examples of neural network applications in different fields of science, arts, and engineering
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Such networks were used either separately or coupled with other sophisticated and high-end linear, nonlinear, and metaheuristic algorithms for prediction, clusterization, and function approximation problems (Table 7.2)

Table 7.2 Applications of neural networks in prediction, classification, and regression or functional approximation problems
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The problem independency, data flexibility, and efficiency in mapping complex collinearity has made the neural network one of the most sought-after modeling techniques, and it was thus applied in the present investigation for the assessment of crop suitability.

Neural networks are often referred to as black boxes and, due to the requirements for large amounts of data and computational infrastructure, applications of neural networks are generally limited to problem domains where a satisfactory database is available and supported by high-end computational facilities. The selection of network topology and activation function along with algorithms for updating the weights is made using either a trial-and-error method or by the application of various search algorithms like genetic or swarm or simulated annealing, as shown in Table 7.2. As was correctly pointed out by Duin (2000) and Jain and Nag (1998), no universally accepted methodology is available yet to guide a developer of such models in the selection of the three most important parameters (network topology, activation function, and input weights), which inherently affect the accuracy level of the developed models.

1.4 Genetic Algorithm

A genetic algorithm (GA) is a popular search algorithm that replicates the crossover mechanism of meiotic cell division where traits of the parent are transferred to the new cell. Some traits become dominant, some dormant, but few new traits are formed due to mutation. In practical problem solving, GAs are applied to searching for the optimal solution from among the many available ones. Available solutions are compared with genes that are transferred to the child cell and from the available solution 100 or 1,000 new solutions are randomly generated. Among the newly generated solutions, the five or ten best solutions are selected with the help of fitness functions. The selected optimal sets of solutions are then used in crossing over where traits of one solution are combined with other traits of another solution to generate a new solution. The optimal solution is identified with the help of the same fitness function, but from the new set of generated solutions. The crossover mechanism is not mimicked when optimal solutions are identified with asexual GAs.

Although GAs have been applied with satisfactory results (Park et al. 2012; Pinthong et al. 2009; Reddy and Kumar 2006) in various problem domains where the optimal solution must be found, but due to the randomized nature of the algorithm and the lack of a predetermined methodology, problems are solved using such metaheuristic algorithms when no other solution is available.

2 Methodology

The suitability of crops in vertical irrigation systems was identified using fuzzy logic and neurogenetic models. Fuzzy logic was used to determine the weighting of the input variables, and neurogenetic models were used to predict crop suitability. Crop suitability was estimated based on the characteristics of the input variables represented by different categories, which reflected the different levels of intensity of the input variables.

Table 7.3 presents a step-by-step description of the important phases of the study methodology in identifying the suitability of a species in terms of being cultivated under a vertical irrigation system. Table 7.4 gives the rules that were used to categorize variable data sets and corresponding rankings for encoding the influence of variables in the objective or suitability function, which in turn represents the suitability of a species to be cultured in a vertical irrigation scheme.

Table 7.3 Important steps in identification of suitability of a species for cultivation under vertical irrigation systems
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Table 7.4 Methods of categorization of variables
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Table 7.5 shows the rank and corresponding degree of importance of the same, which were later used to determine the weighting of the variables.

Table 7.5 Degree of importance and corresponding ranks assigned to variables based on their importance compare to other variables (fuzzification)
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The fuzzy categories of the input variables were established using the rule described in Table 7.5. Inference is performed by comparing each variable with the others and assigning the variable to the given fuzzy category according to Table 7.5.

The rule matrix and corresponding membership function are shown respectively in Tables 7.6 and 7.7. The membership function was determined by dividing the row of the rule matrix by the maximum or worst possible rank assigned for that row.

Table 7.6 Rank of importance assigned to different input variables of proposed model (rule matrix)
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Table 7.7 Weighting assigned to each variable following application of theory of minimization (membership function)
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In the rule matrix, the rank of the importance of the variable with respect to the other variables will be shown in each row. If a variable has a higher importance than the variable with which it is compared, then the cell under the compared variable will have a higher rank (1, 2, …) and vice versa. Thus, when the worst rank received by a row is divided, the lowest value of the operation will be assigned to those variables in comparison to which the present variable has received a high rank and the large value of the result will be for those that are more important than the present variable in the context of the present problem.

Thus, the lowest value of the division will have the highest importance received by the variable and the highest value from the same operation will have the lowest importance assigned to the present variable. The lowest value is inverted to determine the weighting of the given input variable so that the influence due to the importance becomes proportional to the objective of the suitability function.

In the present study, the defuzzification procedure was not required as the authors were interested in predicting a categorized output rather than a numerical one so that the generalization aspect of the modeling platform was not affected.

3 Results and Discussion

The steps described in Table 7.4 were followed to develop a suitability function and a model to predict it with the help of fuzzy logic and a neurogenetic model, respectively. Table 7.6 shows the rank of importance assigned to each of the variables with respect to the others. The importance represented by each rank was already shown in Table 7.5. Table 7.7 presents the value of the weighting assigned to each of the variables according to the theory of maximization rule.

The combinatorial data set was used for training the neurogenetic model so that it could predict any possible unknown combination of the input variables. The parameters of the neurogenetic model and performance as represented by the metrics were shown in Table 7.8.

Table 7.8 Parameters of neurogenetic models and performance metrics used for validation of simulation platform
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The values of the performance metrics (Table 7.8) show the level of accuracy of the model. As the precision, sensitivity, specificity, and kappa of the model prediction compared to the actual categories of the output were respectively 93.93, 98.04, 99.62 and 96.78%, it can be concluded that the model is robust and effective enough to be used to predict the suitability function (Eq. 7.1).

As discussed in the methodology section, the developed model was applied to predict the suitability of rice and maize for cultivation under a vertical irrigation system. Table 7.9 shows the characteristics of rice (Morita and Nemoto 1995; Agrocommerce can be consulted for a thorough description of the cultivation of Oryza sp.) and maize (for an in-depth description of the morphology and cultivation characteristics of maize, FAO manuals can be consulted) represented by the model input. The result of the suitability function is also given in Table 7.9.

Table 7.9 Categories assigned to variables and prediction results from model
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For example, in the case of rice, the lowland variety was chosen, and in the case of maize, the yellow variety was selected for the present investigation.

In terms of climatic variables, only conditions required in the growing season were considered.

According to the prediction results, Oryza sp. had a suitability score of Semi High, whereas that of Zea sp. was predicted to be Very High for vertical irrigation schemes. Although rice has a very short root length and spread compared to maize due to its very high water requirements compare to maize (normal water requirement), the degree of suitability of rice was predicted to be lower than that of maize. Also, maize’s profitability score was higher than rice’s. Both characteristics of the most important input variables (LR and P were assigned the highest weighting among other variables) was found to favor maize, which explains the prediction result from the neurogenetic model.

4 Conclusion

The present investigation proposed a methodology for selecting suitable crop species that could be cultivated under vertical irrigation systems. The features that a crop to be cultivated under such systems should or must have were first identified from various studies and government manuals. Once the features were identified, fuzzy logic was used to determine the weighting of each variable. Once the weighting was determined, a neurogenetic model was prepared to predict suitability through a suitability function. Categorized data considering all possible combinations of the input and output variables were used to train the model, and crop suitability was also predicted in a categorized form so as to maintain the generalized nature of the decision support system. Rice and maize were tested with the modeling platform where the model correctly predicted the lower suitability of rice compared to maize for cultivation under a vertical irrigation scheme. The present study tried to highlight the necessity of evaluating crops in terms of their suitability for vertical farming. The conclusions derived from the model could save both money and energy for a farmer planning to initiate indoor agricultural projects. As a further development of the study, various methods of categorization by objective classification can be experimented.