A Note on Extension of Fuzzy Metric Spaces

Abstract

In this note, we prove that for two compatible fuzzy metrics MH and MK on H and K, respectively, there exists a fuzzy metric M on H⋃K such that M|H=MH and M|K=MK under the conditions that t-norm ∗ is positive and fuzzy metrics MH,MK are strong, or t-norm ∗ is positive and t-norm ∗, fuzzy metrics MH,MK satisfy the Lipschitz conditions.

Keywords

• fuzzy metric
• positive
• stationary
• Lipschitz condition