J4 ›› 2013, Vol. 48 ›› Issue (12): 52-56.

• Articles • Previous Articles     Next Articles

Prime fuzzy ⊙ideals and its topological properties of
regular residuated lattices


LIU Chun-hui1,2   

  1. 1. Office of Academic Affairs,  Chifeng University, Chifeng 024001, Inner Mongolia, China;
    2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Received:2013-07-09 Online:2013-12-20 Published:2014-01-09

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Abstract:

We deeply study the theory of fuzzy ⊙ideals in regular residuated lattices by using the notion of fuzzy set and its operations which proposed by Zadeh. Firstly, the notion of prime fuzzy ⊙ideals is introduced and its properties are studied. And the prime fuzzy ⊙ideals theorem is established. Secondly, a topology T is constructed on the set of all prime fuzzy ⊙ideals PI⊙(L). It is proved that the topology space (PI⊙(L), T) is T0space.

Key words: fuzzy logic; regular residuated lattice; prime fuzzy ⊙ideal; topological space

CLC Number: 

  • O141.1
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[2] MA Li-Na, WANG Guo-Dun. Theory of truth degrees in Lukasiewicz three valued propositional logic [J]. J4, 2009, 44(10): 54-59.
[3] YUAN Pan-Chi, Zhang-Xin-Fang. Study of the conditional probability truth degree of formulas in the Gödel logic system [J]. J4, 2009, 44(9): 70-74.
[4] DUAN Jing-Yao, WANG Guo-Jun. Three types of fuzzy modal logics about K [J]. J4, 2008, 43(12): 31-39.
[5] LIU Chun-hui1,2. Interval valued (∈,∈∨ q)fuzzy subalgebras of Boolean algebras [J]. J4, 2013, 48(10): 94-98.
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