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An Algebra of Fuzzy (*m*, *n*)-Semihyperrings

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We propose a new class of algebraic structure named as (*m*, *n*)*-*semihyperring which is a generalization of usual *semihyperring*. We define the basic properties of (*m*, *n*)-semihyperring like identity elements, weak distributive (*m*, *n*)-semihyperring, zero sum free, additively idempotent, hyperideals, homomorphism, inclusion homomorphism, congruence relation, quotient (*m*, *n*)-semihyperring etc. We propose some lemmas and theorems on homomorphism, congruence relation, quotient (*m*, *n*)-semihyperring, etc. and prove these theorems. We further extend it to introduce the relationship between fuzzy sets and (*m*, *n*)-semihyperrings and propose fuzzy hyperideals and homomorphism theorems on fuzzy (*m*, *n*)-semihyperrings and the relationship between fuzzy (*m*, *n*)-semihyperrings and the usual (*m*, *n*)-semihyper-rings.

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*m*,

*n*)-Semihyperrings,"

*American Journal of Computational Mathematics*, Vol. 3 No. 1, 2013, pp. 73-79. doi: 10.4236/ajcm.2013.31012.

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