COMMUTATIVE FUNDAMENTAL RELATION IN FUZZY HYPERSEMIGROUPS
We introduce and study the construction of commutative fundamental relation in fuzzy hypersemigroups and investigate its basic properties. We will determine some necessary and sufficient conditions so that this relation is transitive in fuzzy hypersemigroups. Also we show that this relation is transitive in every fuzzy hypergroup.
Applications of Left Almost Subhypersemigroups to Fuzzy Subsets
N 2008, Sen et al. [19] introduced the notion of fuzzy hypersemigroup, fuzzy hypergroup, fuzzy hyperideal, homomorphism, fuzzy homomorphism, hyper congruence, fuzzy hypercongruence. In 2009, Fotea and Davvaz [10] defined the concept of fuzzy hyperrings. In 2010, Yin et al. [22] introduced and studied the L -fuzzy hypermodules over an L -fuzzy hyperring. The idea of fuzzy join n -ary spaces and fuzzy canonical n -ary hypergroups first introduced by Fotea in 2010 [9], as a generalization of join spaces and canonical hypergroups. In 2011, Ameri and Nozari [4] formulated and studied the notion of fuzzy regular (fuzzy strongly regular) relations of hyperalgebras. Corsini et al. [7] introduced the notion of prime (semiprime) hyperideals and prime (semiprime) fuzzy hyperideals in semihypergroups and studied basic properties of them. Yin et al. [20] defined the concept of (weak) L -fuzzy polygroups. The concepts of hypercongruence on hyperlattices and the fuzzy (strong) hypercongruence on fuzzy hyperlattice were introduced and discussed by He and Xin [11]. The idea of fuzzy hypervector spaces first introduced by Ameri and Motameni [3], as a generalization of fuzzy vector spaces. In 2013, Ameri and Sadeghi [5] introduced and studied the fuzzy R hypermodules. In 2016, Motameni et al. [15] studied this structure under the name of prime fuzzy hyperideals and maximal fuzzy hyperideals in fuzzy hyperrings. Ameri and Nozari [16] formulated and studied the notion of commutative
Congruence relations of multialgebras
Abstract A concept of congruence relation and homomorphism for multialgebras is developed such that a subdirect decomposition theorem can be proved and varieties of multialgebras can be described by implications of a certain kind.