Journal of Statistics and Mathematical Engineering

A Comprehensive Survey of Fuzzy Logic Utilization in Different Agricultural Sectors

Mukesh Kumar Sinha — 2024-03-01

Fuzzy logic (FL) has emerged as a pivotal component within the realm of Expert Systems, demonstrating its efficacy in addressing real-life challenges that had previously eluded resolution. Its versatile applications span a multitude of domains, with this paper specifically delving into the successful utilization of fuzzy logic methods to tackle various agricultural issues. This comprehensive review explores instances where fuzzy logic has been seamlessly integrated into expert systems to provide innovative solutions within the field of agricultural sciences. The examined applications encompass a spectrum of challenges encountered in agriculture, showcasing the adaptability and effectiveness of fuzzy logic in addressing complex issues. This paper serves not only as an insightful examination of existing applications but also as a valuable contribution to the literature survey, laying the groundwork for future research endeavours. Particularly, it provides a foundational reference for those undertaking research aimed at developing expert systems tailored for specific crops in designated regions of our country. As a part of the broader landscape, this study acts as a cornerstone, offering a starting point for further investigations and advancements in the intersection of fuzzy logic and agricultural sciences.

A Statistical Study on Effects of Plastics on Flooding in Salem Western Region

V. Nirmala — 2024-04-24

The escalating issue of plastic pollution has garnered significant attention in recent years due to its detrimental effects on the environment and ecosystems. In this study, we employ R software to investigate the intricate relationship between flooding occurrences and plastic pollution density, considering the influence of land use patterns and precipitation levels. Through rigorous statistical analysis, we uncover compelling insights into how plastic waste density, land use characteristics, and precipitation dynamics collectively impact the frequency of flooding events.

Our findings reveal significant correlations between plastic waste density, land use types, precipitation levels, and the incidence of flooding. Specifically, areas with higher concentrations of plastic waste exhibit heightened susceptibility to flooding, particularly when coupled with specific land use patterns and precipitation regimes. These significant relationships underscore the critical role that plastic pollution plays in exacerbating flood risks in various geographical contexts.

The implications of our research extend beyond academic discourse, as the identified relationships provide valuable guidance for policymakers, legislators, and environmentalists. By pinpointing the locations where plastic pollution intensifies the likelihood of flooding events, our data-driven approach facilitates targeted interventions aimed at mitigating the adverse impacts of plastic on flood susceptibility. This strategic approach empowers stakeholders to prioritize and implement effective measures to curb plastic pollution and safeguard vulnerable communities against the ravages of flooding.

In essence, our study underscores the urgent need for concerted efforts to address the intertwined challenges of plastic pollution and flooding, emphasizing the imperative of informed decision-making and proactive environmental management strategies. By leveraging empirical evidence and advanced statistical techniques, we contribute to the growing body of knowledge aimed at fostering sustainable solutions to mitigate the multifaceted threats posed by plastic pollution and climate change-induced flooding.

On Poisson and Compound Poisson Processes and Some Comparisons

Suman Kalyan Ghosh — 2024-04-29

Poisson and Compound Poisson processes are well known and have been studied and applied extensively. We define the random extrema process generated by the Poisson process and look at the distributional properties of the corresponding random variables. A few results are obtained by comparing Poisson and Compound Poisson processes with respect to stochastic orderings and based on the corresponding rate parameters and/ or the distribution function of summand random variables. We have presented detailed proofs of the results and their converse implications as applicable. We address these questions in this article: As the probability mass function of a Poisson random variable is log-concave, does this imply that the random maxima generated by a Poisson random variable also preserve this property? Whether more arrivals occurring for a Poisson process by a given time when compared to another independent Poisson process? Some illustrations and applications are given along with the computations of the relevant quantities using the properties of the Poisson process.

On Fuzzy G* Algebras

S. Hariharan — 2024-04-30

A matrix with entries that may only have the values 0 or 1 is called a Boolean matrix. A matrix containing members that fall between [0, 1] is called a fuzzy matrix. This study proposes a novel approach to Fuzzy G* algebra (FG*A). A few novel models in the fascinating area of fuzzy algebra have been developed. Because it simply assigns weight to diagonals, other fuzzy algebras have the drawback of not considering the matrix and not being a function of the overall components. To address this lack of thought, this study presents a novel method, the G* algebra of a fuzzy matrix. The unique solution to a particular set of equations can be found using the generalization inverse of a non-singular matrix. Any (potentially rectangular) matrix with complex components has this generalized inverse. Also, this paper demonstrated that Fuzzy G* algebra is always fuzzy dot subalgebra and fuzzy G* Idle algebra.

Utilizing Fuzzy Logic in Precision Agriculture: Techniques for Disease Detection and Management

Mukesh Kumar Sinha — 2024-04-30

The agricultural sector is paramount in meeting global food demands, necessitating research efforts to enhance productivity, improve food quality, and optimize profitability. Central to this endeavour is equipping farmers with efficient and affordable information and control technologies. Plant disease identification is pivotal for effective disease management and enhancing product quality. Various image processing and soft computing methods are employed for the early detection and diagnosis of plant diseases. Fuzzy logic, adept at handling fuzzy image data, is extensively discussed in the paper concerning precision agriculture, highlighting its efficacy in addressing agricultural challenges. Farmers can improve the accuracy and efficiency of disease detection and management by employing fuzzy logic techniques in precision agriculture, leading to higher crop yields, reduced input costs, and sustainable agricultural practices. Utilizing fuzzy logic in precision agriculture for disease detection and management involves leveraging the flexibility and interpretability of fuzzy logic systems to handle the inherent uncertainties and imprecisions in agricultural data. This paper explores applying fuzzy logic techniques in precision agriculture for disease detection and management. We discuss the theoretical foundations of fuzzy logic and its practical implementation in agricultural systems. Various methodologies and strategies are examined, including fuzzy membership functions, rule-based systems, fuzzy inference systems, and data fusion techniques. Case studies and examples are provided to illustrate the effectiveness of fuzzy logic in disease detection and management. These include applications in crop monitoring using remote sensing data, dynamic thresholding for disease risk assessment, and feedback control systems for automated disease management.