Abstract
Fuzzy subgroups of finite groups have been treated recently using the concept of pinned‐flags. In this paper, we consider the operations of intersection, sum, product, and quotient of fuzzy subgroups of finite abelian groups in general, in terms of pinned‐flags. We develop algorithms to construct pinned‐flags of fuzzy subgroups corresponding to these operations and prove their validity. We illustrate some applications of such algorithms.
Highlights
Some of the past studies of fuzzy subgroups relied heavily on the usual definitions of intersection, union, sum of two fuzzy subgroups by exploiting the lattice properties of membership values in a simplistic way
We develop algorithms to describe the pinnedflags of the intersection, sum, product, and quotient of fuzzy subgroups and prove their validity
It is clear from a close look at Algorithms 4.1 and 4.4 that their constructions were based directly on the definitions of various operations on fuzzy subsgroups
Summary
Some of the past studies of fuzzy subgroups relied heavily on the usual definitions of intersection, union, sum of two fuzzy subgroups by exploiting the lattice properties of membership values in a simplistic way. One can study the operations on fuzzy subgroups by means of pinned-flags, enriching some properties of fuzzy subgroups. It was observed in [6] that the pinnedflag resulting from operations of intersection and direct sum of fuzzy subgroups does not form any particular pattern. We develop algorithms to describe the pinnedflags of the intersection, sum, product, and quotient of fuzzy subgroups and prove their validity.
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