| This paper mainly includes three parts. Part I is Chapter3. In this part, we study the (∈,∈∨q)-fuzzyideals and the fuzzy homomorphism properties of ordered semigroups. Part II is Chapter4. In this part,we consider the concept of fuzzy point in studying all kinds of prime (∈,∈∨q)-ideals of an orderedseimigroup and their properties. Part III is Chapter5. In this part, we consider the characterizationtheorems of ordered semigroups in terms of (∈,∈∨q)-fuzzy ideals.In Chapter1, a general survey of the topic is provided.In Chapter2, some concepts and results which will be used in this paper are given.In Chapter3, by using a new ordering relation, called inclusion or quasi-coincidence relation on theset of all fuzzy subsets in an ordered somigroup, the concepts of (∈,∈∨q) fuzzy left ideals (rightideals, ideals, bi-ideals, interior ideals, quasi-ideals) of an ordered seimigroup are provided and therelationships among them are given. Several characterizations of these (∈,∈∨q) fuzzy ideals arepresented. Some fuzzy homomorphism properties of ordered simgiroups are developed.In Chapter4, by uising the concept of fuzzy point, the concepts of prime (completely prime,completely weak prime, semiprime, completely semiprime)(∈,∈∨q)-ideals of an ordered seimigroupare provided and the relationships among them are given.In Chapter5, several characterizations of ordered semigroups that are regular, left(right)regular, leftregular and left duo, regular and duo, intra-regular, regular and intra-regular, left(right) quasi-regular,left quasi-regular and intra-regular, or semisimple are derived in terms of (∈,∈∨q) fuzzy left ideals(right ideals,ideals,bi-ideals,interior ideals quasi-ideals) of ordered semigroups.In Chapter6, the main work of this paper is summarized, and the future work is given. |
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