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• 作者：Asghar Khan (1) azhar4set@yahoo.com
  Young Bae Jun (2) skywine@gmail.com
  Muhammad Zaheer Abbas (1)
• 关键词：Fuzzy subsets &#8211 ; Fuzzy interior ideals &#8211 ; (∈ ; ∈ ; ∨ ; q) ; fuzzy interior ideals &#8211 ; (∈ ; ∈ ; ∨ ; q) ; fuzzy ideals &#8211 ; Regular (resp. intra ; regular ; simple and semisimple) ordered semigroups &#8211 ; Implication oper
• 刊名：Neural Computing & Applications
• 出版时间：April 2012
• 出版年：2012
• 期刊代码：113_0941-0643
• 类别：cp
• 卷：21
• 期：3
• 页码：433-440
• 数据来源：sp

摘要

In this paper, we give characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals (resp. (∈, ∈ ∨q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨q)-fuzzy ideals and (∈, ∈ ∨q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy ideals (resp. (∈, ∈ ∨q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.