Neutrosophic Sets and Metaheuristic Optimization: A Survey

Abstract

Smarandache presents neutrosophic sets and provides a domain area that is made up of three separate subsets to reflect the various kinds of uncertainty. Neutrosophic sets are defined as the sets where every other element of the universe possesses a degree of truthiness, indeterminacy, and falsity, which range from 0 to 1, and where these degrees are subsets of the neutrosophic sets that are independent of each other. Neutrosophic sets are also known as neutrosophical subsets. In the neutrosophic sets, impreciseness is represented as truth and falsity functions, but the indeterminacy function represents degrees of belongingness and non-belongingness and differentiates between absoluteness and relativeness. Neutrosophic sets can deal with the unpredictability of the system and cut down on the paralysis brought on by conflicting information thanks to this notation. As a result, one might argue that this capacity is the single most significant benefit offered by neutrosophic sets in comparison to the many other forms of fuzzy extensions. By making use of these three functions, neutrosophic sets are able to create a domain area. This area makes it possible for various kinds of mathematical operations to be carried out separately despite the presence of uncertainty. Due to the fact that the behavior of these methodologies is inspired by Nature and its capacity for adapting to issues, in addition to the potential for combining more than one method to reach the best alternatives, metaheuristic algorithms are employed to initiate the finest or the best possible alternatives to a lot of optimization techniques. This is possible because metaheuristic algorithms have the ability to adapt to problems. The fact that numerous academics have utilized these techniques with neutrosophic science to offer several systems in recent years was the impetus for writing this overview study in the first place, which was based on the above rationale.