Granularity and Generalized Inclusion Functions - Their Variants and Contamination

Rough inclusion functions (RIFs) are known by many other names in formal approaches to vagueness, belief, and uncertainty. Their use is often poorly grounded in factual knowledge or involve wild statistical assumptions. The concept of contamination introduced and studied by the present author across a number of her papers, concerns mixing up of information across semantic domains (or domains of discourse). RIFs play a key role in contaminating algorithms and some solutions that seek to replace or avoid them have been proposed and investigated by the present author in some of her earlier papers. The proposals break many algorithms of rough sets in a serious way. In this research, algorithm-friendly granular generalizations of such functions that reduce contamination are proposed and investigated from a mathematically sound perspective. Interesting representation results are proved and a core algebraic strategy for generalizing Skowron-Polkowski style of rough mereology is formulated.