A defuzzification-free hierarchical fuzzy system (DF-HFS): Rock mass rating prediction

When the use of a single fuzzy system becomes inapplicable due to the increase in the number of input parameters, hierarchical fuzzy systems are commonly used for the solution. This inapplicability arises from both computational cost and the challenging process of fuzzy rule creation. The conventional application of hierarchical fuzzy systems performs the steps from fuzzification to defuzzification one by one in each subsystem, and the provided crisp result is transferred to the higher layer. The major drawback of this process is that the defuzzification steps performed in the inner layers degenerate the fuzziness level of information. This drawback leads to two outcomes: the output of the hierarchical system and single fuzzy system may be highly different from each other, and the output of the hierarchical system can change according to its hierarchical structure. As a result, the preservation of fuzziness during the hierarchical inference flow should be considered to employ hierarchical approaches to the problems. In this study, the defuzzification-free hierarchical fuzzy inference system (DF-HFS) is proposed in which the misleading defuzzification steps are eliminated from the hierarchical inference flow, and the fuzziness is propagated up to the highest layer without being exposed to any degeneration. To test the accuracy of data transmission, experiments are performed on two different problems: the modeling of the logical XOR and rock mass rating. The obtained experimental results indicate that the proposed hierarchical flow achieves more successful data transmission than its counterparts and that it provides the closest outputs to the corresponding single fuzzy system.