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Generalized fuzzy ideals in ordered semirings
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AbstractIn this paper, we introduce the concepts of $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy left (right) ideals and $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy ideals in ordered semirings. Some correspondence between (left, right) ideals and $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy (left, right) ideals of ordered semirings are presented. Moreover, the notion of $$(\kappa ^*,\kappa )$$
(
κ
∗
,
κ
)
-lower part of $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy (left, right) ideals is defined and characterizations of different classes of ordered semirings are given.
Springer Science and Business Media LLC
Title: Generalized fuzzy ideals in ordered semirings
Description:
AbstractIn this paper, we introduce the concepts of $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy left (right) ideals and $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy ideals in ordered semirings.
Some correspondence between (left, right) ideals and $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy (left, right) ideals of ordered semirings are presented.
Moreover, the notion of $$(\kappa ^*,\kappa )$$
(
κ
∗
,
κ
)
-lower part of $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$
(
∈
,
∈
∨
(
κ
∗
,
q
κ
)
)
-fuzzy (left, right) ideals is defined and characterizations of different classes of ordered semirings are given.
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