From interval probability theory to computable fuzzy first-order logic and beyond

摘要

This paper first presents a simple explanation for the min/max bounds which are used in interval probability theory (IPT), possibility theory, fuzzy rough sets, and vague logic. Based on this definition, a computable version of first-order fuzzy logic is defined, where all of the upper bounds for instances of a theorem and its negation are guaranteed to eventually be listed. Based on this fuzzy logic, a complete version of fuzzy Prolog is defined. This fuzzy Prolog is then used to give some examples of fuzzy Prolog definitions of fuzzy concepts such as fuzzy linguistic variables, fuzzy modifiers, fuzzy quantifiers, and various kinds of fuzzy norms and conorms.