Introduction On Some Problems Of Hyperlattices

In this article,we mainly study some problems of hyperlattices.On the one hand,we study hyperideals and hyperfilters in hyperlattices.We give five definitions of hyperideals in meet-hyperlattices and establish relationships between the one definition of a hyperideal with other four definitions,and then we give prime hyperideal theorems of meet-hyperlattices and prime hyperfilter theorems of strong join-hyperlattices.On the other hand,combining fuzzy mathematics with the hyperlattices theory,we introduce notions of fuzzy subhyperlattices of meet-hyperlattices,interval-valued fuzzy subhyperlattices,fuzzy subhyperlattices of complemented hyperlattices and some properties of fuzzy subhyperlattices.In addition,we generalize fuzzy hyperfilters of meet-hyperlattices,give the equivalent characterization of fuzzy hyperfilters and hyperfilters and some properties of fuzzy hyperfilters.Finally,we generalize fuzzy hyperfilters to(?,? ?q)-fuzzy hyperfilters,giving the equivalent characterization of(?,? ?q)-fuzzy hyperfilters and introducing some properties of(?,? ?q)-fuzzy hyperfilters.The details are as follows:In the first chapter,we mainly introduce the research background,research status and significance of hyperlattices and fuzzy hyperlattices.At the same time,the fundation theory and main work of this paper are given.In the second chapter,we introduce five definitions of hyperideals in meet-hyperlattices and investigate relationships between five definitions.Then we give prime hyperideal theorems of meet-hyperlattices and prime hyperfilter theorems of strong join-hyperlattices.In the third chapter,we give the concept of fuzzy subhyperlattices on meet-hyperlattices and their equivalent characterizations.Also investigate interval-valued fuzzy subhyperlattices of meet-hyperlattices,fuzzy subhyperlattices of complemented hyperlattices and some properites of fuzzy subhyperlattices.In the fourth chapter,we introduce the concept and the equivalent characterization of fuzzy hyperfilters on meet-hyperlattices and some properies of hyperfilters.Moreover,we generalize fuzzy hyperfilters to(?,? ?q)-fuzzy hyperfilters,give equivalent characterizations of(?,? ?q)-fuzzy hyperfilters and study some properites of(?,??q)-fuzzy hyperfilters.