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Fortified Transposition Hypergroups appeared during the study of the theory of Formal Languages and Automata from the point of view of the hypercompositional structures theory. This paper studies the subhypergroups of these hypergroups and presents properties of their closed, symmetric, normal and reflexive subhypergroups. [ABSTRACT FROM AUTHOR]

This paper deals with the enumeration of the different classes of 2-element fuzzy hypergroups and with the construction of some classes of 2-element mimic fuzzy hypergroups. It also introduces the notion of the pseudo-mimic fuzzy hypergroup. [ABSTRACT FROM AUTHOR]

M. Krasner introduced the notions of the hypefield and the hyperring in 1956. Much later, he constructed the quotient hyperfield/hyperrring, using a field/ring and a subgroup of its multiplicative group/semigroup. The existence of non-quotient hyperfields and hyperrings was an essential question for the self-sufficiency of the theory of hyperfields and hyperrings vis-à-vis that of fields and rings. The momogene hyperfield, which was introduced by the author, is a hyperfield H having the property x - x = H for all x ∊ H with x ≠ 0. The existence of non-quotient monogene hyperfields is a hitherto open question. The answer to this question is directly connected with the answer to the question which fields can be expressed as a difference of a subgroup of their multiplicative group from itself and which these subgroups are. These issues, as well as some relevant theorems are presented in this paper. [ABSTRACT FROM AUTHOR]

In the hypecompositional structures, unlike the classical ones, there exist several types of identities. This paper deals with two main types of identities, the scalar and strong ones and with the hypergroups in which they appear. Certain such hypergroups e.g. the fortified join hypergroup and the join polysymmetric hypergroup derived from the theory of formal languages and automata. [ABSTRACT FROM AUTHOR]