Fuzzy quantifiers in syllogisms, direct versus inverse computations (Q1111542)

An important issue in approximate reasoning concerns the treatment of propositions involving fuzzy quantifiers such as most, approximately 20\%, a few \dots Zadeh originally introduced several inference schemes with propositions involving fuzzy quantifiers. In this paper one of these inference schemes, the so-called intersection-product syllogism: \[ \begin{aligned} &\varphi_1 \text{ of A's are B's} \\ &\varphi_2 \text{ of (A's are B's) are C's} \\ &\text{\hbox to.3{\strut\hrulefill\strut}} \\ &\varphi \text{ of A's are (B and C)'s} \end{aligned} \] and related schemes are critically examined and improved. Using the methods for solving fuzzy relational equations it is shown that the degree of fuzziness (the degree of specificity) of the quantifier in the conclusion can be reduced (enlarged).