Fuzzy Euclidean Distance for Fuzzy Data

Fuzzy numbers and more generally linguistic values are approximate assessments, given by experts and accepted by decision-makers whenobtaining value that is more accurate is impossibleor unnecessary. Distance between two fuzzy numbers plays an important role in linguistic decision-making. Itis reasonable to define a fuzzy distance between fuzzy objects. To achieve this aim, the researcher first describe the concepts of positive fuzzy number, negativefuzzy number, fuzzy zero and fuzzy absolute of a fuzzy number. Then these concepts are utilized to produce afuzzy distance between two fuzzy numbers. The fuzzydistance is presented as a trapezoidal fuzzy number. It is shown that the fuzzy distance is a fuzzy metric. Themetric properties are also studied. The advantage is the calculation of the proposed method is far simple than previous approaches. Finally, two examples illustrate the presented method as well as comparing it with other various ones.

کلیدواژه ها:

Fuzzy distance ، Fuzzy metric ، Ordering ، Trapezoidal Fuzzy numbers