A modification of Dempster's and Pawlak's constructs forms a new foundation for the identification of upper and lower sets formulas. Also, in this modified Dempster-Pawlak construct we require that subsets of the power set be restricted to the well-known information granules of the power set. An aggregation of upper information granules amongst each other and lower information granules amongst each other determine upper and lower set formulas for both crisp and fuzzy sets. The results are equivalent...

The aim of this work is to investigate when a weighted sum, or in other words, a linear combination, of two or more aggregation operators leads to a new aggregation operator. For weights belonging to the real unit interval, we obtain a convex combination and the answer is known to be always positive. However, we will show that also other weights can be used, depending upon the aggregation operators involved. A first set of suitable weights is obtained by a general method based on the variation of...