A Unified Distance Approach for Ranking Fuzzy Numbers and Its Comparative Reviews
Abstract
Even though a large number of research studies have been presented in recent years for ranking and comparing fuzzy numbers, the majority of existing techniques suffer from plenty of shortcomings. These shortcomings include counterintuitiveness, the inability to distinguish the fuzzy number and its partnered image, and the inconsistent ability to distinguish symmetric fuzzy numbers and fuzzy numbers that represent the compensation of areas. To overcome the cited drawbacks, this paper suggests a unified distance that multiplies the centroid value (weighted mean value) of the fuzzy number on the horizontal axis and a linear sum of the
distances of the centroid points of the left and right fuzziness areas from the original
point through an indicator. The indicator reflects the attitude of the left and
right fuzziness of the fuzzy number, we can call it the indicator of fuzziness. To use
this technique, the membership functions of the fuzzy numbers need not be linear.
That is the proposed approach can also rank the fuzzy numbers with non-linear
membership functions. The suggested technique is highly convenient and reliable to
discriminate the symmetric fuzzy numbers and the fuzzy numbers having compensation
of areas. The advantages of the proposed approach are illustrated through
examples that are common for a wide range of numerical studies and comparisons
with several representative approaches, that existed in the literature.
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