Generalized states on EQ-algebras

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Xin X.L.; KHAN M.; JUN Y.B.

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Journal: Iranian Journal of Fuzzy Systems Year:2019 | Volume:16 | Issue:1 Page(s): 159-172

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Information Journal Paper

Title

Generalized states on EQ-algebras

Author(s)

Xin X.L. | KHAN M. | JUN Y.B. | Issue Writer Certificate

Keywords

EQ-algebraQ2

generalized stateQ2

internal stateQ2

residuated latticeQ2

equality algebraQ2

BCK-algebraQ2

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.

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APA: Copy

Xin, X.L., KHAN, M., & JUN, Y.B.. (2019). Generalized states on EQ-algebras. IRANIAN JOURNAL OF FUZZY SYSTEMS, 16(1 ), 159-172. SID. https://sid.ir/paper/113240/en

Vancouver: Copy

Xin X.L., KHAN M., JUN Y.B.. Generalized states on EQ-algebras. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2019;16(1 ):159-172. Available from: https://sid.ir/paper/113240/en

IEEE: Copy

X.L. Xin, M. KHAN, and Y.B. JUN, “Generalized states on EQ-algebras,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 16, no. 1 , pp. 159–172, 2019, [Online]. Available: https://sid.ir/paper/113240/en

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