ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS

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ZHANG Q.Y.

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2011 | Volume:8 | Issue:5 (SPECIAL ISSUE: FUZZY MATHEMATICS) Page(s): 31-58

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Information Journal Paper

Title

ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS

Author(s)

ZHANG Q.Y. | Issue Writer Certificate

Keywords

COMPLETE RESIDUATED LATTIC

L-FUZZY POSET

CATEGORY

ADJUNCTION

ALGEBRAIC THEORY

POWER SET THEORY

ALGEBRAIC GENERATION

Abstract

In this paper, let L be a COMPLETE RESIDUATED LATTICe, and let Set} denote the CATEGORY of sets and mappings, LF-Pos denote the CATEGORY of LF-posets and LF-monotone mappings, and LF-CSLat (˽), LF-CSLat (̪) denote the CATEGORY of LF-complete lattices and LF-join-preserving mappings and the CATEGORY of LF-complete lattices and LF-meet-preserving mappings, respectively. It is proved that there are ADJUNCTIONs between Set and LF-CSLat (˽), between LF-Pos and LF-CSLat (˽), and between LF-Pos and LF-CSLat (̪), that is, Set LF-CSLat (˽), LF-Posv LF- CSLat (˽), and LF-Pos LF-CSLat (̪), And a usual mapping ¦ generates the traditional Zadeh forward powerset operator ¦®L the fuzzy forward powerset operators ¦~®,¦~®*, ¦~*® defined by the author et al via these ADJUNCTIONs. Moreover, it is also shown that all the fuzzy powerset operators mentioned above can be generated by the underlying algebraic theories.

Cites

MEET-CONTINUITY ONL-DIRECTED COMPLETE POSETS

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APA: Copy

ZHANG, Q.Y.. (2011). ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS. IRANIAN JOURNAL OF FUZZY SYSTEMS, 8(5 (SPECIAL ISSUE: FUZZY MATHEMATICS)), 31-58. SID. https://sid.ir/paper/605700/en

Vancouver: Copy

ZHANG Q.Y.. ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2011;8(5 (SPECIAL ISSUE: FUZZY MATHEMATICS)):31-58. Available from: https://sid.ir/paper/605700/en

IEEE: Copy

Q.Y. ZHANG, “ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET OPERATORS,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 8, no. 5 (SPECIAL ISSUE: FUZZY MATHEMATICS), pp. 31–58, 2011, [Online]. Available: https://sid.ir/paper/605700/en

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