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What’s ‘rough’? Modelling the vague meaning of joint roughness classifiers by means of empirical fuzzy sets
Published in Hans-Peter Rossmanith, Mechanics of Jointed and Faulted Rock, 2018
A general method for the measurement of membership functions μF based on methods of mathematical psychology (e.g. Norwich & Turksen 1984, Hersh & Caramazza 1976), has not been proposed so far (Zimmermann 1991). For engineering practice, however, the most efficient way to establish membership functions seems to be the use the relationship between probability and possibility. By elaborating Zadeh’s general definition of a possibility measure, the following relation between possibility and probability was established by Dubois & Prade (1982, 1983).
Goguen's contributions to fuzzy logic in retrospect
Published in International Journal of General Systems, 2019
Let us conclude this section by mentioning further conceptual issues recognized and discussed by Goguen, namely his recognition of the fundamental importance of a nearness relation on the universe with respect to which the fuzzy sets considered are compatible; his emphasis on the ordinal nature of the set of truth values and its topology; his awareness of measurement theory – an area of mathematical psychology – as a proper conceptual tool for considerations regarding the truth degrees and their assignment; his consideration of context as determining e.g. the right choice of the truth functions of logical connectives; his general and thorough considerations regarding the problem of fuzzification; his recognition of the importance of fuzzy properties of fuzzy relations; his recognition of category theory and categories of fuzzy sets as an important conceptual means of treating foundational problems; his detailed outline of a general theory of fuzzy relations; as well as his considerations regarding higher types of fuzzy sets and interval-valued fuzzy sets. Even though most of these issues have been explored in further developments, some – such as connections to measurement theory and the choice truth functions of logical connectives – yet remain to be explored properly in my view.
Utilising physiological data for augmenting travel choice models: methodological frameworks and directions of future research
Published in Transport Reviews, 2023
Thomas O. Hancock, Charisma F. Choudhury
Overall, key avenues for future research include further direct comparisons of methodologies, enriching choice modelling with concepts of neuropsychology and mathematical psychology, the use of alternative types of physiological sensor data not yet integrated into choice models (e.g. facial expressions) and further utilisation of physiological sensor data to help explain both inter and intra-respondent heterogeneity in real-world contexts. These will undoubtedly advance our understanding of travel behaviour and result in models that are both more valid and more realistic.