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 distrib...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.展开更多
In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups ...In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups play an essential role in studying the structure,especially the decomposition,of semigroups.The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory.As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals.We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on S is idempotent.展开更多
文摘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.
文摘In this article,a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup.It is well known that the intra-regular semigroups play an essential role in studying the structure,especially the decomposition,of semigroups.The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory.As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals.We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on S is idempotent.
