Abstract:
The author introduces a term called total belongingness
indicator of an element by adding the partial belongingness
of the element to a number of sets. When the universal set is
constructed by obtaining the union of disjoints sets, it is justified
that the total belongingness indicator of an element to all the
disjoint sets is equal to one. The author proves that this condition
only satisfies for the multiplication rule and not for the minimum
rule irrespective of the application. Hence it can be concluded
that for the intersection of two fuzzy sets, the multiplication rule
is more accurate and appropriate whereas the minimum rule is
only an approximation. An example is illustrated to show that
the multiplication rule is more appropriate than the minimum
rule by defining the same problem in slightly different ways. In
addition, a method is proposed in calculating the union of two
sets when the multiplication rule is applied as the intersection of
two fuzzy sets.
Citation:
V. Palitha and C. Dassanayake, "Which is the Better Rule? The Multiplication Rule or The Minimum Rule for Fuzzy Set Intersection," 2018 3rd International Conference on Information Technology Research (ICITR), 2018, pp. 1-4, doi: 10.1109/ICITR.2018.8736140.