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Processing realized in fuzzy rule-based models is associated with matching individual rules with the existing input data and aggregation of the levels of matching and conclusions of the rules. Rules are processed as individual entities. In this study, we introduce an augmentation of fuzzy models by facilitating interaction among the rules leading to more flexible type membership functions of fuzzy sets forming conditions of the rules (thus resulting in substantially advanced topology of the partition of the input space). Different ways of realizing interaction among the rules are studied. In the sequel, we develop a granular fuzzy model implied by the rule-based model showing how granular parameters of the original rule-based model enhance its quality expressed in terms of coverage of experimental data. The two evaluation criteria of the constructed granular model, namely coverage and specificity are studied. Experimental results are reported for a series of publicly available data. [ABSTRACT FROM AUTHOR]