On Rough Sets and Hyperlattices

In this paper, we introduce the concepts of upper and lower rough hyper fuzzy ideals (filters) in a hyperlattice and their basic properties are discussed. Let $\theta$ be a hyper congruence relation on $L$. We show that if $\mu$ is a fuzzy subset of $L$, then $\overline{\theta}()=\overline{\theta}()$ and $\overline{\theta}(\mu^*) =\overline{\theta}((\overline{\theta}(\mu))^*)$, where is the least hyper fuzzy ideal of $L$ containing $\mu$ and \mu^*(x) = sup\{\alpha \in [0, 1]: x \in I( \mu_{\alpha} )\}$$ for all $x \in L$. Next, we prove that if $\mu$ is a hyper fuzzy ideal of $L$, then $\mu$ is an upper rough fuzzy ideal. Also, if $\theta$ is a $\wedge-$complete on $L$ and $\mu$ is a hyper fuzzy prime ideal of $L$ such that $\overline{\theta}(\mu)$ is a proper fuzzy subset of $L$, then $\mu$ is an upper rough fuzzy prime ideal. Furthermore, let $\theta$ be a $\vee$-complete congruence relation on $L$. If $\mu$ is a hyper fuzzy ideal, then $\mu$ is a lower rough fuzzy ideal and if $\mu$ is a hyper fuzzy prime ideal such that $\underline{\theta}(\mu)$ is a proper fuzzy subset of $L$, then $\mu$ is a lower rough fuzzy prime ideal

Development of memory-based models for reservoir fluid characterization

The petroleum industry play an important role in supplying required energy all over the world. Effective methods are required to stimulate the process. Petroleum fluids are the mixture of complex hydrocarbons. Several techniques being used to predict reserve estimation, recovery, production, enhanced oil recovery, etc. Despite of modern engineering advancement, still, there are some drawbacks, such as, conventional models, linearized rock-fluid properties models, inaccurate risk assessment, and inappropriate descriptions of thermal effects. In this research, new mathematical models for petroleum fluids (non-Newtonian) regarding various degree of complexities will be developed. The most significant component will be the continuous time function introduced to the rheology. Previous attempts are addressed in this modeling, and those models were limited for some specific cases and fluids. The current proposal will develop a comprehensive model that can be applied to different reservoir fluids irrespective to fluid origin. In addition, the proposed models will also be adjusted for a complex mixture of reservoir fluids. The model equations will be solved numerically and validated using field data and data gathered from experimental tasks available in the literature. The proposed models will be developed focusing light crude oil for reservoir conditions. The role of various factors, such as crude oil density, viscosity, compressibility, surface tension, ambient temperature, and temperature will be included in the predictive models. Model equations will be solved with non-linear solvers, as outlined earlier. This will generate a range of solutions, rather than a line of unique solutions. This analysis will increase an accuracy of the predictive tool and will enable one to assess the uncertainty with greater confidence