The fuzzy set theory is applied in the Geological strength index (GSI) determination following the Mamdani fuzzy algorithm. The fundamental parameters (block volume and joint condition factor) which were used in Cai's quantitative GSI chart (Cai et al., 2004) are used as two input membership functions in the determination of GSI after setting 22 "if-then" rules.

Beforehand, the joint condition factor was determined by the first fuzzy algorithm using total 210 "if-then" rules from three input functions namely joint waviness, small-scale smoothness and joint alteration factors proposed by Palmstrom, 1995.

GSI for sedimentary rock masses in Singapore was determined by Mamdani fuzzy algorithm, and it was observed that the results are comparable with quantitative GSI (Cai's 2004 approach) and field-assessed qualitative GSI (Hoek et al., 1995).

Fuzzy inference algorithm

The first step in the fuzzy modeling process is the fuzzification in which the numeric values are converted into the fuzzy values after applying appropriate membership functions. The most commonly used is the linear type, trapezoidal and triangular (den Hartog et al., 1996; Alvarez Grima, 2000). In the second step of the fuzzy modeling process, the fuzzy conditional rules are to be formulated. Those conditional rules describe the input-output relationship. A fuzzy conditional rule is generally composed of a statement and a consequent (IF statement, THEN consequent). For example, "if x is good then y is valuable" in which the terms good and valuable can be represented by fuzzy sets or more specifically by membership functions. The third step in the fuzzy modeling process is to adopt a representative fuzzy inference system (FIS) to aggregate "if-then" rules (Zadeh 1973). The FIS process is to extract the end results from the applied rules used with input parameters and their membership functions. In the final step, the required output of numerical (crisp) value is to be obtained from a fuzzy set. The process is termed as "Defuzzification." Among several defuzzification methods for instance centroid of area (COA), mean of the maximum and smallest of maximum, the COA is applied in this study as it is the most commonly used method (Alvarez Grima, 2000).

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