α-Interval Valued Fuzzy Sets and α-Interval Valued Fuzzy Subgroups

α-interval valued sets are studied in the paper. The members of these sets are sub-closed intervals that include α of unit interval. Basic characteristics are researched. The definition of order relation and negation function on these sets are given. α-interval valued fuzzy sets that the degree of membership is sub-closed interval of unit interval including α, are given. The basis algebraic features are viewed. The connection between classical sets and defined sets in the paper is studied. α-interval valued fuzzy subgroups is defined. Typical properties of groups are studied. Main definition and propositions about that structure are examined.