We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different ty...

First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra  X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quo...

In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra A with constants 0, 1 is Booolean-like in case for all a ∈ A the congruences θ (a, 0) and θ (a, 1) are compementary factor congruences of A. We also introduced the weaker notion of semi-Boolean-like algebra, showin...

We consider the string, like point particles and branes, to be an irreducible representation of semi-direct product Cartan involution invariant subalgebra [Formula: see text] its vector representation. show that preserves string charges, little algebra, is essentially Borel text]. also known physical states carry a parts this algebra.

In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...