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Paper Information

Journal:   IRANIAN JOURNAL OF FUZZY SYSTEMS   February 2019 , Volume 16 , Number 1 ; Page(s) 159 To 172.
 
Paper: 

Generalized states on EQ-algebras

 
 
Author(s):  Xin X.L.*, Khan M., JUN Y.B.
 
* School of Mathematics, Northwest University, Xi’an, 710127, China
 
Abstract: 
In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) states on EQ-algebras. Moreover we discuss the relations between generalized states on EQ-algebras and internal states on other algebras, respectively. We obtain the following results: (1) Every state-morphism on a good EQ-algebra E is a G-state from E to the EQ-algebra E0 = ([0; 1]; ^0; ⊙ 0;  0; 1). (2) Every state operator  satisfying  (x) ⊙  (y) 2  (E) on a good EQ-algebra E is a GI-state on E. (3) Every state operator  on a residuated lattice (L; ^; _; ⊙ ; !; 0; 1) can be seen a GI-state on the EQ-algebra (L; ^; ⊙ ;  ; 1), where x  y: = (x! y) ^ (y! x). (4) Every GI-state  on a good EQ-algebra (L; ^; ⊙ ;  ; 1) is a internal state on equality algebra (L; ^;  ; 1). (5) Every GI-state  on a good EQ-algebra (L; ^; ⊙ ;  ; 1) is a left state operator on BCK-algebra (L; ^; !; 1), where x! y = x  x ^ y.
 
Keyword(s): EQ-algebra,generalized state,internal state,residuated lattice,equality algebra,BCK-algebra
 
 
References: 
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Citations: 
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+ Click to Cite.
APA: Copy

Xin, X., & KHAN, M., & JUN, Y. (2019). Generalized states on EQ-algebras. IRANIAN JOURNAL OF FUZZY SYSTEMS, 16(1 ), 159-172. https://www.sid.ir/en/journal/ViewPaper.aspx?id=697512



Vancouver: Copy

Xin X.L., KHAN M., JUN Y.B.. Generalized states on EQ-algebras. IRANIAN JOURNAL OF FUZZY SYSTEMS. 2019 [cited 2021October20];16(1 ):159-172. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=697512



IEEE: Copy

Xin, X., KHAN, M., JUN, Y., 2019. Generalized states on EQ-algebras. IRANIAN JOURNAL OF FUZZY SYSTEMS, [online] 16(1 ), pp.159-172. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=697512.



 
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