Geometric Approach for Solving First Order Non-Homogenous Fuzzy Difference Equation
Abdul Alamin, Mostafijur Rahaman, Sankar Prasad Mondal
Abstract
Real-life scenario modeling with mathematics is very important nowadays. Depending upon system behavior, it may also model discrete systems in several cases. In discrete system modeling, the difference equation is one of the well-known methodologies. However, if some uncertain factors are involved in the discrete models, then uncertain difference equation concepts come into play. The fuzzy difference equation is one of them. The fuzzy difference equation is significant, as it can represent variances of dependent variables in a discrete frame under uncertainty. In this paper, a first-order non-homogeneous linear difference equation is considered under fuzzy uncertainty, a special kind of fuzzy difference equation. Here, a well-known fuzzy geometric approach is utilized to solve the mentioned first-order non-homogeneous fuzzy difference equation. An application, namely a fuzzy prescription for digoxin based on the fuzzy initial value problem, is also discussed in numerical illustrations as a consequence of the proposed theory.