Adjusting the Core and/or the Support of a Fuzzy Set - A New Approach to Fuzzy Modifiers

A label semantics approach to linguistic hedges

“…0 otherwise [2,8] both ground their approaches in the idea of looking at the elements near a fuzzy set in order to contract or dilate the set. The two approaches are similar, so we restrict ourselves to that of [2].…”

“…Consider a fuzzy set F and a proximity relation E Z which is approximate equality, parametrised by a fuzzy set Z. As described in [2]…”

“…For example, suppose we start with a set F described in trapezoidal notation as F = (A, B, C, D) = (2,4,6,8), and an approximate equality function parametrised by Z = (−z−a, −z, z, z+a) = (−1, −0.5, 0.5, 1). The dilation of the set F using T-norm min is then:…”

“…Figure 2: Illustration of the expansion and contraction modifiers proposed in [2]. The original set F can be described in trapezoidal set notation as (2,4,6,8). The approximate equality function is parametrised by a set Z = (−1, −0.5, 0.5, 1).…”

“…The approximate equality function is parametrised by a set Z = (−1, −0.5, 0.5, 1). Dilating the set as described in [2] gives the set E Z (F ) = (1, 3.5, 6. 5,9).…”