What’s ‘rough’? Modelling the vague meaning of joint roughness classifiers by means of empirical fuzzy sets
We will argue, that the meaning of linguistic geological data is inherently vague in nature. Based on this premise, we will present some results of a demoscopic pilot study on 55 international experts in the fields of engineering geology and rock mechanics. The study was carried out in order to assess empirical fuzzy membership functions for the classifiers VERY SMOOTH, SMOOTH, ROUGH, and VERY ROUGH pertaining to the parameter “joint roughness”. In contrast to probability theory which can only deal with purely statistical (i.e., syntactic) information measures, possibility theory formulated in terms of fuzzy set theory offers a powerful tool for the treatment of semantic imprecision of information. In general, the assessment of realistic membership functions for the linguistic entities in question is the first and crucial step with regard to practical applications of fuzzy set theory. Technically speaking, the transformation of psychological probabilistic data from our pilot study into possibilistic fuzzy sets becomes possible by means of the probability-possibility consistency principle. Dealing with semantic vagueness is necessary for geological purposes, when one considers the influences of the observing embodied subject’s perception and cognition on data structures. In general, the mathematical modelling of linguistic variables should provide a viable interface between geological data sampling and computational models used in geology and rock mechanics.