The Suitable Two Kinds of Interval-valued Fuzzy Metric Spaces for Interval-valued Fuzzy Reasoning

Abstract

In this paper, a new definition of distance of interval-valued fuzzy sets is presented. Four interval-valued fuzzy metric spaces respectively induced by four specific interval-valued implication operators are established. By discussing and comparing the structures of four specific interval-valued fuzzy metric spaces, it can be concluded that interval-valued fuzzy metric spaces induced by interval-valued Åukasiewicz implication and interval-valued Goguen implication respectively are suitable for interval-valued fuzzy reasoning.