Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by ⊕ and ⊗, where a⊕ b = max{a,b}, a⊗ b = min{a,b}. Fuzzy discrete dynamic systems can be introduced by fuzzy matrices and are useful for describing knowledge engineering, scheduling, cluster analysis, fuzzy logic programs, diagnosis of technical devices or medical diagnosis. The paper deals with...

‎in this paper‎, ‎the type-{rm ii} matrices on (negative) latin square graphs are considered and it is proved that‎, ‎under‎ ‎certain conditions‎, ‎the nomura algebras of such type-{rm ii} matrices are trivial‎. ‎in addition‎, ‎we construct type-{rm ii} matrices‎ ‎on doubly regular tournaments and show that the nomura algebras of such matrices are also trivial‎.

Let k, l,m, n, and μ be positive integers. A Zμ-scheme of valency (k, l) and order (m,n) is an m × n array (Sij) of subsets Sij ⊆ Zμ such that for each row and column one has ∑n j=1 |Sij | = k and ∑m i=1 |Sij | = l, respectively. Any such scheme is an algebraic equivalent of a (k, l)-semiregular bipartite voltage graph with n and m vertices in the bipartition sets and voltages coming from the c...

This paper introduce two types of edge degrees (line degree and near line degree) total (total an in a fuzzy semigraph, where semigraph is defined as (V, σ, μ, η) on G* which σ : V → [0, 1], μ VxV 1] η X satisfy the conditions that for all vertices u, v vertex set, μ(u, v) ≤ σ(u) ᴧ σ(v) η(e) = μ(u1, u2) μ(u2, u3) … μ(un-1, un) σ(u1) σ(un), if e (u1, u2, …, un), n ≥ 2 G*, pair sets X) set non - ...

Transitivity of generalized fuzzy matrices over a special type of semiring is considered. The semiring is called incline algebra which generalizes Boolean algebra, fuzzy algebra, and distributive lattice. This paper studies the transitive incline matrices in detail. The transitive closure of an incline matrix is studied, and the convergence for powers of transitive incline matrices is considere...