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- W3210294279 abstract "Calculating the difference between fuzzy numbers is often seen as a complicated operation, mainly because of the semi-linear nature of the space of fuzzy numbers. In addition, in this space a universally acceptable method of total ordering does not yet exist. An efficient solution for these problems is to consider a suitable metric. The proposed metrics are distances defined on the space of fuzzy sets. On the other hand, some of these distances have served as defuzzification operators and/or ranking operators. Properties of such metrics are appealing to investigate. In this chapter, we give a chronological review of some known distances and some of their properties. We finally expose a new L2 metric based on the so-called signed distance, paving the way to the construction of an updated version of it. This new version, called the “generalized signed distance,” preserves the directionality of the original signed distance. We finally highlight that we will consider the case of a one-dimensional setting only, in other words, a given fuzzy component (tilde {X}) is associated with a single dimension x with the corresponding α-level set." @default.
- W3210294279 created "2021-11-08" @default.
- W3210294279 creator A5021005957 @default.
- W3210294279 date "2021-01-01" @default.
- W3210294279 modified "2023-09-24" @default.
- W3210294279 title "Distances Between Fuzzy Sets" @default.
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- W3210294279 doi "https://doi.org/10.1007/978-3-030-76916-1_4" @default.
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