Application of the Inverse Weibull Distribution to Agricultural Data Based on Intuitionistic Fuzzy Sets

Abstract

The inverse Weibull distribution (IWD) is a frequently used model in dependability analysis that finds widespread use in a variety of scientific domains. This work examines the intuitionistic fuzzy lifespan data-based dependability estimation of the IWD. Prior to deriving the ideas of intuitionistic fuzzy conditional expectation, intuitionistic fuzzy probability function, and intuitionistic fuzzy conditional density, the associated concepts of fuzzy set theory are examined. In conventional estimations, the maximum likelihood estimators for reliability and parameters are obtained. The maximum likelihood estimates are obtained using the EM algorithm because of the nonlinearity. The gamma prior is chosen in the Bayesian estimation process, and the symmetric entropy and scale square error loss functions, respectively, are used to estimate the parameters and reliability. The Lindley approximation is used to approximate the Bayesian estimates due to the complexity of the integrals. According to the simulation results, the maximum likelihood estimate is not as appropriate for reliability estimation as the Bayesian estimation. Ultimately, the efficacy of these suggested techniques is demonstrated using a collection of agriculture production data. These techniques yield an accurate evaluation of the intuitive fuzzy life data's reliability, serving as a crucial point of reference for reliability analysis in the scientific community. Using intuitionistic fuzzy values for real-time data, the present work investigated the Reliability Estimation, cumulative density function, and probability density function of the inverse Weibull distribution. We examined Andra agricultural output in 2019 in this analysis. The comparison thus showed that the estimation of fuzziness values is better than the real-time data.