Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this pape...Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.展开更多
基金Yibin University Pre-research Project,Research on the coupling and coordinated development ofmanufacturing and logistics industry under the background of intelligentmanufacturing,(2022YY001)Sichuan ProvincialDepartment of EducationWater Transport EconomicResearch Center,Research on the Development Path and Countermeasures of the Advanced Manufacturing Industry in the Sanjiang New District of Yibin under a“dual circulation”development pattern(SYJJ2020A06).
文摘Recently,fuzzy multi-sets have come to the forefront of scientists’interest and have been used in algebraic structures such asmulti-groups,multirings,anti-fuzzy multigroup and(α,γ)-anti-fuzzy subgroups.In this paper,we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as(α,γ)-anti-multi-fuzzy subgroups.In a way,the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group.The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group.The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view.Therefore,in this paper,we define(α,γ)-antimulti-fuzzy subgroups,(α,γ)-anti-multi-fuzzy normal subgroups,(α,γ)-antimulti-fuzzy homomorphism on(α,γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures.Then,we introduce the concept(α,γ)-anti-multi-fuzzy subgroups and(α,γ)-anti-multi-fuzzy normal subgroups and of their properties.This new concept of homomorphism as a bridge among set theory,fuzzy set theory,anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure.Certain results that discuss the(α,γ)cuts of anti-fuzzy multigroup are explored.
