Building granular fuzzy decision support systems

In various scenarios of fuzzy decision-making we encounter a collection of sources of knowledge - local models describing decision pursuits undertaken by individual decision-makers. These sources have to be agreed upon. The reconciliation mechanisms are present quite vividly in any collective pursuit including distributed modeling, time series characterization and classification. There is an interesting and practically pertinent task of reconciling decisions coming from the decision models and construct a decision of a holistic character. In this study, we introduce a concept of a granular fuzzy decision built on a basis of decisions formed by individual decision models. Here the term "granular" pertains to a wealth of possible realizations of such decision thus giving rise to fuzzy fuzzy (namely, fuzzy²), interval-valued, probabilistic-fuzzy and rough-fuzzy representations of information granules. Information granularity plays a pivotal role in reconciling differences among existing decisions, quantifying their diversity and associating it with the overall fuzzy decision. We exploit a principle of justifiable granularity to develop and articulate a granular fuzzy decision of a holistic nature. Along with the passive way of forming the granular fuzzy decisions, we introduce an active form of design in which established is a feedback loop using which on a basis of the holistic view adjusted are the individual decisions. Detailed optimization schemes are discussed along with compelling examples of forming type-2 and type-3 fuzzy sets.