Some Generalized Forms of Fuzzy Interval Valued Hyperideals in a Hyperring

Some generalized forms of the hyperideals of a hyperring in the paper of Zhan et al. (2008) will be given. As a generalization of the interval valued (α,β)-fuzzy hyperideals of a hyperring with α,β∈{∈,q,∈∧q,∈∨q} and α≠∈∧q, the notion of generalized interval valued (α,β)-fuzzy hyperideals of a hyperring is also introduced. Special attention is concentrated on the interval valued (∈γ~,∈γ~∨qδ~)-fuzzy hyperideals. As a consequence, some characterizations theorems of interval valued (∈γ~,∈γ~∨qδ~)-fuzzy hyperideals will be provided

Interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (\in,\ivq)-fuzzy filters of pseudo $BL$-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo $BL$-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo $BL$-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed

History and new possible research directions of hyperstructures

We present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research

Fuzzy n-ary polygroups related to fuzzy points

AbstractRecently, fuzzy n-ary sub-polygroups were introduced and studied by Davvaz, Corsini and Leoreanu-Fotea [B. Davvaz, P. Corsini, V. Leoreanu-Fotea, Fuzzy n-ary sub-polygroups, Comput. Math. Appl. 57 (2008) 141–152]. Now, in this paper, the concept of (∈,∈∨q)-fuzzy n-ary sub-polygroups, (∈¯,∈¯∨q¯)-fuzzy n-ary sub-polygroups and fuzzy n-ary sub-polygroup with thresholds of an n-ary polygroup are introduced and some characterizations are described. Also, we give the definition of implication-based fuzzy n-ary sub-polygroups in an n-ary polygroup, in particular, the implication operators in Łukasiewicz system of continuous-valued logic are discussed

Discrete Mathematics and Symmetry

Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group