Assume that there is a fixed collection O of objects and that there are m attributes of the objects. Assume that for attribute i (with 1 ≤ i ≤ m), there is a function fi that assigns a score fi(x) to each object x in O. Typically we have 0 ≤ fi(x) ≤ 1. Intuitively, fi(x) tells the extent to which object x has attribute i. For example, if attribute i represents “redness” (telling how red an object is), then a redness score fi(x) near 1 means that object x is very red and a redness score fi(x) near 0 means that object x is far from being red.
We assume that there is a scoring function (or aggregation function) F with m arguments, so that F (f1(x), …, fm(x)) gives the overall score of object i (the result of aggregating the scores of object x over all of the attributes). It is natural to assume that F is monotone, in the sense that if yi ≤ zi, for 1 ≤ i ≤ m, then F (y1, …, ym) ≤ F (z1, …, zm). Typical scoring functions are the min, which is used in fuzzy logic  to represent the...