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E-fuzzy groups
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DOI：10.1016/j.fss.2015.03.011.png)
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Abstract
En 中文
An E-fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one - denoted by E. The classical group-like properties are formulated as appropriate fuzzy identities - special lattice-theoretic formulas. We prove basic features of E-fuzzy groups: properties of the unit and inverses, cancellability, solvability of equations, subgroup properties and others. We also prove that for every cut of an E-fuzzy group, which is a classical subalgebra of the underlying algebra, the quotient structure over the corresponding cut of the fuzzy equality is a classical group. (C) 2015 Elsevier B.V. All rights reserved.
Keywords:
Fuzzy algebra
Fuzzy group
Fuzzy identity
Fuzzy congruence
Fuzzy equality
Complete lattice
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