An interval-valued fuzzy distance measure between two interval-valued fuzzy numbers

Abstract

Interval-valued fuzzy numbers have found remarkable importance in various real-world applications. Such cases often require an evaluation of the distance measure between two interval-valued fuzzy numbers to solve the problems in the intended application. In this regard, an interval-valued fuzzy distance measure is provided in this study. For this purpose, an exact distance measure was first suggested and some of its main properties were investigated via some theorems and lemmas and compared with the results obtained by other studies. Then the proposed exact distance measure was extended in space of interval-valued fuzzy numbers and its axiomatic properties, such as triangular and robustness properties, were also investigated. Two numerical evaluations were presented to illustrate the calculation of the distance between two interval-valued fuzzy numbers as an interval-valued fuzzy number, as well.