In this paper the Mamdani-type inference system model and its possible variations are studied. The modification of the conventional inference procedure aims to reduce the computational complexity of the evaluation, thereby allowing the novel structure to be used in systems that require optimization, adaptive techniques or to be used in real-time, while the advantages of the original Mamdani model are retained. The intuition still can be built into the system, thus its behavior is much closer to human thinking. In order to fulfill the above requirements the authors developed a simplified evaluation structure in which several different fuzzy operators are studied. The operator- dependency of the derivative model and its applicability is proven mathematically furthermore through simulation by the authors. It is also demonstrated which operators can be used to obtain an equivalent simplified evaluation structure and which cannot. The simplified version of the Mamdani-type inference reduces the computational complexity of the evaluation process, while it is equivalent to the conventional Mamdani-type inference system. The interconnectivity of the rule premises using different fuzzy operators was also studied both of the original Mamdani-type system and the derived model, called Mamdani-like structure with discretized output. The usability of the different operators in the interconnectivity is also proven by the authors. The great advantage of both the Mamdani-like structure with discretized output and also the rule-premise interconnectivity is that they make the model applicable in real-time and even in adaptive systems due to the lower computational needs.