GENERALIZED FUZZY POLYGROUPS

نویسندگان

1 Department of Mathematics, Yazd University, Yazd, Iran.

2 Dipartimento Di Matematica E Informatica, Via Delle Scienze 206, 33100 Udin, Italy

doi
10.22111/ijfs.2006.438
چکیده

small Polygroups are multi-valued systems that satisfy group-likeaxioms. Using the notion of “belonging ($\epsilon$)” and “quasi-coincidence (q)” offuzzy points with fuzzy sets, the concept of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy subpolygroups isintroduced. The study of ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy normal subpolygroups of a polygroupare dealt with. Characterization and some of the fundamental properties ofsuch fuzzy subpolygroups are obtained. ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy cosets determined by($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy subpolygroups are discussed. Finally, a fuzzy subpolygroupwith thresholds, which is a generalization of an ordinary fuzzy subpolygroupand an ($\epsilon$, $\epsilon$ $\vee$ q)-fuzzy subpolygroup, is defined and relations between twofuzzy subpolygroups are discussed.