2000
DOI: 10.1155/s0161171200003781
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Positive implicative ordered filters of implicative semigroups

Abstract: Abstract. We introduce the notion of positive implicative ordered filters in implicative semigroups. We show that every positive implicative ordered filter is both an ordered filter and an implicative ordered filter. We give examples that an ordered filter (an implicative ordered filter) may not be a positive implicative ordered filter. We also give equivalent conditions of positive implicative ordered filters. Finally we establish the extension property for positive implicative ordered filters.Keywords and ph… Show more

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Cited by 8 publications
(7 citation statements)
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“…Definisi 2.1. [9] Semigrup terurut parsial secara negatif (A, , •) adalah suatu himpunan yang terdefinisi terurut parsial " " dan terdapat suatu operasi biner " • " pada A sedemikian sehingga untuk semua x, y, z ∈ A berlaku:…”
Section: Pendahuluanunclassified
“…Definisi 2.1. [9] Semigrup terurut parsial secara negatif (A, , •) adalah suatu himpunan yang terdefinisi terurut parsial " " dan terdapat suatu operasi biner " • " pada A sedemikian sehingga untuk semua x, y, z ∈ A berlaku:…”
Section: Pendahuluanunclassified
“…In what follows, let S denote an implicative semigroup unless otherwise specified. Jun and Kim [7] introduced the notion of positive implicative ordered filters in implicative semigroups as follows in the paper.…”
Section: Fuzzy Positive Implicative Ordered Filtersmentioning
confidence: 99%
“…Definition 3.1 (see [7]). A nonempty subset F of S is called a positive implicative ordered filter of S if it satisfies (F3) and for all x, y, z ∈ S,…”
Section: Fuzzy Positive Implicative Ordered Filtersmentioning
confidence: 99%
See 1 more Smart Citation
“…Fuzzy semi-groups were generalized in two folds: fuzzy ordered semi-groups and fuzzy ternary semi-groups. Since ordered semi-groups are useful for computer science, especially in theory of automata and formal language, fuzzy ordered semi-group has been extensively studied (see [1,2,3,5,6]). Interval-valued fuzzy subsets were proposed thirty years ago as a natural extension of fuzzy sets by Zadeh [18].…”
Section: Introductionmentioning
confidence: 99%