Trends of Inference Considering Extended Fuzzy Logic (FLe)

The introduction of fuzzy logic in 1965 has been one of the main advancements in the last several decades in different subjects and especially in control theory [1]. Fuzzy logic has given large deals to reasoning, and clearly, shows its applicability in many areas to solve different problems concerning approximate reasoning. However, in large measure what remains unrecognized is that fuzzy logic is itself a precise logic of imprecise reasoning. In fact, the definitions of membership functions and generalized constraints are precise within fuzzy logic [2]. This precision requires the necessary condition of provably validity about achieved results. This condition can be satisfied only in the problems defined in closed world assumption that can be handled by mathematical analysis. In fact, in closed world, we only deal with precisiated information. However, most real world problems cannot satisfy the provable validity condition since they are mostly defined in uncertain, non-stationary, evolving, and imprecise environment and dealt with incomplete information. Therefore, in most cases, the provably-valid solutions cannot be achieved. Zadeh in 2009 introduced extended fuzzy logic (FLe) [2] to deal with the issue of being unprecisiated. As a matter of fact, FLe is a new trend to solve problems by introducing unprecisiated fuzzy logic (FLu) and adding it to fuzzy logic.