Some new classes of fuzzy contraction defined by means of fuzzy negations and related fixed point theorems

Using the notion of fuzzy negation functions which naturally arises in the theory and applications of fuzzy logic, we enlarge the class of fuzzy ψ-contractions of (ϵ,λ) type as well as the class of fuzzy k−♢ contractions and generalize corresponding fixed point theorems. We show that strict negations, strong negations and Archimedean t-norms play a central role in the aforesaid fixed point theorems. Appropriate examples that illustrate the exposed theory are provided. In the process, we obtain a new type of topology (as well as convergence and completeness) for the fuzzy metric spaces that suggesting a potential new research avenue to explore the subject.