Directional Models of Granular Communication

Abstract

In the previous chapter, we introduced a model of collaboration between granular worlds. This model was quite general and showed how such collaboration was accomplished in the framework of fuzzy sets by being directly associated with the granular descriptors realized in the form of fuzzy clusters (fuzzy relations). In the proposed mechanisms of collaboration, we have made two assumptions that were consistently kept throughout the entire flow of investigations. First, the collaborative nature of the communication implies that all granular environments are treated in the same manner and there is no particular role being attached to any of them. Second, in virtue of the character of the collaboration, we considered the same number of information granules across all worlds. While these two assumptions are legitimate and apply to a broad range of cases, they can be augmented in several possible ways. The number of the information granules that can exist in each granular world needs not be the same; it is quite evident that the assumption we have made with this regard looks quite restrictive. Furthermore in the collaborative communication we may envision that there are some mappings between some granular worlds and this sense a set of information granules in one space (granular world) may impact the formation of the granules in some other space. The nature of the collaboration is then more directional as one of the granular worlds attempts to accommodate some “advice” coming from other environments; the advice is conveyed via some logic-based mapping expressed at the level of information granules.