An Algebra of Fuzzy (<i>m</i>, <i>n</i>)-Semihyperrings
- 1 College of Computers and Information Technology, Taif University, Taif, KSA
- 2 College of Computers and Information Technology, Taif University, Taif, KSA
- 3 College of Computers and Information Technology, Taif University, Taif, KSA
Abstract
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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