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How to Relate Fuzzy and OWA Estimates

By Tanja Magoc and Vladik Kreinovich


Abstract—In many practical situations, we have several estimates x1,..., xn of the same quantity x, i.e., estimates for which x1 ≈ x, x2 ≈ x,..., and xn ≈ x. It is desirable to combine (fuse) these estimates into a single estimate for x. From the fuzzy viewpoint, a natural way to combine these estimates is: (1) to describe, for each x and for each i, the degree µ≈(xi−x) to which x is close to xi, (2) to use a t-norm (“and”-operation) to combine these degrees into a degree to which x is consistent with all n estimates, and then (3) find the estimate x for which this degree is the largest. Alternatively, we can use computationally simpler OWA (Ordered Weighted Average) to combine the estimates xi. To get better fusion, we must appropriately select the membership function µ≈(x), the t-norm (in the fuzzy case) and the weights (in the OWA case). Since both approaches – when applied properly – lead t

Year: 2011
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