GENERALIZED FUZZY ALGEBRAIC HYPERSYSTEMS

Abstract

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set, which is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set, is introduced.  Using this new idea, the notion of interval valued (α, β)-fuzzy subalgebraic hypersystems in an algebraic hypersystem, which is a generalization of a fuzzy subalgebraic system, is defined, and related properties are investigated. We also discuss entropy of interval valued (α, β)-fuzzy subalgebraic hypersystems.  In particular, the study of interval valued (∈, ∈ ∨q)-fuzzy subalgebraic hypersystems of an algebraic hypersystem is dealt with.  Finally, we consider the concept of implication-based interval valued fuzzy subalgebraic hypersystems.