A note on distributivity of the lattice of L-ideals of a ring

Many studies have investigated the lattice of fuzzy substructures of algebraic structures such as groups and rings. In this study, we prove that the lattice of L-ideals of a ring is distributive if and only if the lattice of its ideals is distributive, for an infinitely ?- distributive lattice L. © 2019 Hacettepe University. All rights reserved

Aggregating fuzzy subgroups and T-vague groups

Fuzzy subgroups and T-vague groups are interesting fuzzy algebraic structures that have been widely studied. While fuzzy subgroups fuzzify the concept of crisp subgroup, T-vague groups can be identified with quotient groups of a group by a normal fuzzy subgroup and there is a close relation between both structures and T-indistinguishability operators (fuzzy equivalence relations). In this paper the functions that aggregate fuzzy subgroups and T-vague groups will be studied. The functions aggregating T-indistinguishability operators have been characterized [9] and the main result of this paper is that the functions aggregating T-indistinguishability operators coincide with the ones that aggregate fuzzy subgroups and T-vague groups. In particular, quasi-arithmetic means and some OWA operators aggregate them if the t-norm is continuous Archimedean.Peer ReviewedPostprint (author's final draft

Smarandache near-rings

The main concern of this book is the study of Smarandache analogue properties of near-rings and Smarandache near-rings; so it does not promise to cover all concepts or the proofs of all results