diff --git a/pandas/_libs/interval.pyi b/pandas/_libs/interval.pyi
index 3bd5dd2042e69..ba0a339fa93dd 100644
--- a/pandas/_libs/interval.pyi
+++ b/pandas/_libs/interval.pyi
@@ -12,7 +12,7 @@ import numpy.typing as npt
 
 from pandas._libs import lib
 from pandas._typing import (
-    IntervalClosedType,
+    IntervalInclusiveType,
     Timedelta,
     Timestamp,
 )
@@ -56,7 +56,7 @@ class IntervalMixin:
 
 def _warning_interval(
     inclusive, closed
-) -> tuple[IntervalClosedType, lib.NoDefault]: ...
+) -> tuple[IntervalInclusiveType, lib.NoDefault]: ...
 
 class Interval(IntervalMixin, Generic[_OrderableT]):
     @property
@@ -64,17 +64,17 @@ class Interval(IntervalMixin, Generic[_OrderableT]):
     @property
     def right(self: Interval[_OrderableT]) -> _OrderableT: ...
     @property
-    def inclusive(self) -> IntervalClosedType: ...
+    def inclusive(self) -> IntervalInclusiveType: ...
     @property
-    def closed(self) -> IntervalClosedType: ...
+    def closed(self) -> IntervalInclusiveType: ...
     mid: _MidDescriptor
     length: _LengthDescriptor
     def __init__(
         self,
         left: _OrderableT,
         right: _OrderableT,
-        inclusive: IntervalClosedType = ...,
-        closed: IntervalClosedType = ...,
+        inclusive: IntervalInclusiveType = ...,
+        closed: IntervalInclusiveType = ...,
     ) -> None: ...
     def __hash__(self) -> int: ...
     @overload
@@ -151,14 +151,14 @@ class Interval(IntervalMixin, Generic[_OrderableT]):
 
 def intervals_to_interval_bounds(
     intervals: np.ndarray, validate_closed: bool = ...
-) -> tuple[np.ndarray, np.ndarray, str]: ...
+) -> tuple[np.ndarray, np.ndarray, IntervalInclusiveType]: ...
 
 class IntervalTree(IntervalMixin):
     def __init__(
         self,
         left: np.ndarray,
         right: np.ndarray,
-        inclusive: IntervalClosedType = ...,
+        inclusive: IntervalInclusiveType = ...,
         leaf_size: int = ...,
     ) -> None: ...
     @property
diff --git a/pandas/_typing.py b/pandas/_typing.py
index ac1237f8841be..4bc5f75400455 100644
--- a/pandas/_typing.py
+++ b/pandas/_typing.py
@@ -314,7 +314,7 @@ def closed(self) -> bool:
 
 # Interval closed type
 IntervalLeftRight = Literal["left", "right"]
-IntervalClosedType = Union[IntervalLeftRight, Literal["both", "neither"]]
+IntervalInclusiveType = Union[IntervalLeftRight, Literal["both", "neither"]]
 
 # datetime and NaTType
 DatetimeNaTType = Union[datetime, "NaTType"]
diff --git a/pandas/core/arrays/arrow/_arrow_utils.py b/pandas/core/arrays/arrow/_arrow_utils.py
index 5893ca77193c4..5ed10661e8983 100644
--- a/pandas/core/arrays/arrow/_arrow_utils.py
+++ b/pandas/core/arrays/arrow/_arrow_utils.py
@@ -6,6 +6,7 @@
 import numpy as np
 import pyarrow
 
+from pandas._typing import IntervalInclusiveType
 from pandas.errors import PerformanceWarning
 from pandas.util._decorators import deprecate_kwarg
 from pandas.util._exceptions import find_stack_level
@@ -107,11 +108,11 @@ def to_pandas_dtype(self):
 
 class ArrowIntervalType(pyarrow.ExtensionType):
     @deprecate_kwarg(old_arg_name="closed", new_arg_name="inclusive")
-    def __init__(self, subtype, inclusive: str) -> None:
+    def __init__(self, subtype, inclusive: IntervalInclusiveType) -> None:
         # attributes need to be set first before calling
         # super init (as that calls serialize)
         assert inclusive in VALID_CLOSED
-        self._closed = inclusive
+        self._closed: IntervalInclusiveType = inclusive
         if not isinstance(subtype, pyarrow.DataType):
             subtype = pyarrow.type_for_alias(str(subtype))
         self._subtype = subtype
@@ -124,11 +125,11 @@ def subtype(self):
         return self._subtype
 
     @property
-    def inclusive(self) -> str:
+    def inclusive(self) -> IntervalInclusiveType:
         return self._closed
 
     @property
-    def closed(self):
+    def closed(self) -> IntervalInclusiveType:
         warnings.warn(
             "Attribute `closed` is deprecated in favor of `inclusive`.",
             FutureWarning,
diff --git a/pandas/core/arrays/interval.py b/pandas/core/arrays/interval.py
index 4320c862fbc41..ea0e7a769c25e 100644
--- a/pandas/core/arrays/interval.py
+++ b/pandas/core/arrays/interval.py
@@ -32,7 +32,7 @@
 from pandas._typing import (
     ArrayLike,
     Dtype,
-    IntervalClosedType,
+    IntervalInclusiveType,
     NpDtype,
     PositionalIndexer,
     ScalarIndexer,
@@ -230,7 +230,7 @@ def ndim(self) -> Literal[1]:
     def __new__(
         cls: type[IntervalArrayT],
         data,
-        inclusive: str | None = None,
+        inclusive: IntervalInclusiveType | None = None,
         dtype: Dtype | None = None,
         copy: bool = False,
         verify_integrity: bool = True,
@@ -277,7 +277,7 @@ def _simple_new(
         cls: type[IntervalArrayT],
         left,
         right,
-        inclusive=None,
+        inclusive: IntervalInclusiveType | None = None,
         copy: bool = False,
         dtype: Dtype | None = None,
         verify_integrity: bool = True,
@@ -431,7 +431,7 @@ def _from_factorized(
     def from_breaks(
         cls: type[IntervalArrayT],
         breaks,
-        inclusive: IntervalClosedType | None = None,
+        inclusive: IntervalInclusiveType | None = None,
         copy: bool = False,
         dtype: Dtype | None = None,
     ) -> IntervalArrayT:
@@ -513,7 +513,7 @@ def from_arrays(
         cls: type[IntervalArrayT],
         left,
         right,
-        inclusive: IntervalClosedType | None = None,
+        inclusive: IntervalInclusiveType | None = None,
         copy: bool = False,
         dtype: Dtype | None = None,
     ) -> IntervalArrayT:
@@ -586,7 +586,7 @@ def from_arrays(
     def from_tuples(
         cls: type[IntervalArrayT],
         data,
-        inclusive=None,
+        inclusive: IntervalInclusiveType | None = None,
         copy: bool = False,
         dtype: Dtype | None = None,
     ) -> IntervalArrayT:
@@ -1364,7 +1364,7 @@ def overlaps(self, other):
     # ---------------------------------------------------------------------
 
     @property
-    def inclusive(self) -> IntervalClosedType:
+    def inclusive(self) -> IntervalInclusiveType:
         """
         Whether the intervals are closed on the left-side, right-side, both or
         neither.
@@ -1372,7 +1372,7 @@ def inclusive(self) -> IntervalClosedType:
         return self.dtype.inclusive
 
     @property
-    def closed(self) -> IntervalClosedType:
+    def closed(self) -> IntervalInclusiveType:
         """
         Whether the intervals are closed on the left-side, right-side, both or
         neither.
@@ -1426,7 +1426,9 @@ def closed(self) -> IntervalClosedType:
             ),
         }
     )
-    def set_closed(self: IntervalArrayT, closed: IntervalClosedType) -> IntervalArrayT:
+    def set_closed(
+        self: IntervalArrayT, closed: IntervalInclusiveType
+    ) -> IntervalArrayT:
         warnings.warn(
             "set_closed is deprecated and will be removed in a future version. "
             "Use set_inclusive instead.",
@@ -1478,7 +1480,7 @@ def set_closed(self: IntervalArrayT, closed: IntervalClosedType) -> IntervalArra
         }
     )
     def set_inclusive(
-        self: IntervalArrayT, inclusive: IntervalClosedType
+        self: IntervalArrayT, inclusive: IntervalInclusiveType
     ) -> IntervalArrayT:
         if inclusive not in VALID_CLOSED:
             msg = f"invalid option for 'inclusive': {inclusive}"
diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index 16e7559e4d153..78096d836f5b0 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -38,6 +38,7 @@
 from pandas._typing import (
     Dtype,
     DtypeObj,
+    IntervalInclusiveType,
     Ordered,
     npt,
     type_t,
@@ -1091,7 +1092,7 @@ class IntervalDtype(PandasExtensionDtype):
     def __new__(
         cls,
         subtype=None,
-        inclusive: str_type | None = None,
+        inclusive: IntervalInclusiveType | None = None,
         closed: None | lib.NoDefault = lib.no_default,
     ):
         from pandas.core.dtypes.common import (
@@ -1140,7 +1141,11 @@ def __new__(
                                     "'inclusive' keyword does not match value "
                                     "specified in dtype string"
                                 )
-                        inclusive = gd["inclusive"]
+                        # Incompatible types in assignment (expression has type
+                        # "Union[str, Any]", variable has type
+                        # "Optional[Union[Literal['left', 'right'],
+                        # Literal['both', 'neither']]]")
+                        inclusive = gd["inclusive"]  # type: ignore[assignment]
 
             try:
                 subtype = pandas_dtype(subtype)
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 8089fc58db07d..e2f4574abe5a0 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -48,7 +48,7 @@
     IgnoreRaise,
     IndexKeyFunc,
     IndexLabel,
-    IntervalClosedType,
+    IntervalInclusiveType,
     JSONSerializable,
     Level,
     Manager,
@@ -8066,7 +8066,7 @@ def between_time(
         end_time,
         include_start: bool_t | lib.NoDefault = lib.no_default,
         include_end: bool_t | lib.NoDefault = lib.no_default,
-        inclusive: IntervalClosedType | None = None,
+        inclusive: IntervalInclusiveType | None = None,
         axis=None,
     ) -> NDFrameT:
         """
@@ -8172,7 +8172,7 @@ def between_time(
             left = True if include_start is lib.no_default else include_start
             right = True if include_end is lib.no_default else include_end
 
-            inc_dict: dict[tuple[bool_t, bool_t], IntervalClosedType] = {
+            inc_dict: dict[tuple[bool_t, bool_t], IntervalInclusiveType] = {
                 (True, True): "both",
                 (True, False): "left",
                 (False, True): "right",
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 18c0d56abbeb4..6aa2ff91ba933 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -35,7 +35,7 @@
 from pandas._typing import (
     Dtype,
     DtypeObj,
-    IntervalClosedType,
+    IntervalInclusiveType,
     IntervalLeftRight,
     npt,
 )
@@ -920,7 +920,7 @@ def date_range(
     normalize: bool = False,
     name: Hashable = None,
     closed: Literal["left", "right"] | None | lib.NoDefault = lib.no_default,
-    inclusive: IntervalClosedType | None = None,
+    inclusive: IntervalInclusiveType | None = None,
     **kwargs,
 ) -> DatetimeIndex:
     """
@@ -1126,7 +1126,7 @@ def bdate_range(
     weekmask=None,
     holidays=None,
     closed: IntervalLeftRight | lib.NoDefault | None = lib.no_default,
-    inclusive: IntervalClosedType | None = None,
+    inclusive: IntervalInclusiveType | None = None,
     **kwargs,
 ) -> DatetimeIndex:
     """
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index b1f839daa694d..ced675fe9a3cf 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -30,7 +30,7 @@
 from pandas._typing import (
     Dtype,
     DtypeObj,
-    IntervalClosedType,
+    IntervalInclusiveType,
     npt,
 )
 from pandas.errors import InvalidIndexError
@@ -198,7 +198,7 @@ class IntervalIndex(ExtensionIndex):
     _typ = "intervalindex"
 
     # annotate properties pinned via inherit_names
-    inclusive: IntervalClosedType
+    inclusive: IntervalInclusiveType
     is_non_overlapping_monotonic: bool
     closed_left: bool
     closed_right: bool
@@ -217,7 +217,7 @@ class IntervalIndex(ExtensionIndex):
     def __new__(
         cls,
         data,
-        inclusive=None,
+        inclusive: IntervalInclusiveType | None = None,
         dtype: Dtype | None = None,
         copy: bool = False,
         name: Hashable = None,
@@ -266,7 +266,7 @@ def closed(self):
     def from_breaks(
         cls,
         breaks,
-        inclusive=None,
+        inclusive: IntervalInclusiveType | None = None,
         name: Hashable = None,
         copy: bool = False,
         dtype: Dtype | None = None,
@@ -302,7 +302,7 @@ def from_arrays(
         cls,
         left,
         right,
-        inclusive=None,
+        inclusive: IntervalInclusiveType | None = None,
         name: Hashable = None,
         copy: bool = False,
         dtype: Dtype | None = None,
@@ -337,7 +337,7 @@ def from_arrays(
     def from_tuples(
         cls,
         data,
-        inclusive=None,
+        inclusive: IntervalInclusiveType | None = None,
         name: Hashable = None,
         copy: bool = False,
         dtype: Dtype | None = None,
@@ -989,7 +989,7 @@ def interval_range(
     periods=None,
     freq=None,
     name: Hashable = None,
-    inclusive: IntervalClosedType | None = None,
+    inclusive: IntervalInclusiveType | None = None,
 ) -> IntervalIndex:
     """
     Return a fixed frequency IntervalIndex.
diff --git a/pandas/io/formats/style.py b/pandas/io/formats/style.py
index 10b607da45ca8..0461fbfc6faa8 100644
--- a/pandas/io/formats/style.py
+++ b/pandas/io/formats/style.py
@@ -25,6 +25,7 @@
     Axis,
     FilePath,
     IndexLabel,
+    IntervalInclusiveType,
     Level,
     QuantileInterpolation,
     Scalar,
@@ -3479,7 +3480,7 @@ def highlight_between(
         axis: Axis | None = 0,
         left: Scalar | Sequence | None = None,
         right: Scalar | Sequence | None = None,
-        inclusive: str = "both",
+        inclusive: IntervalInclusiveType = "both",
         props: str | None = None,
     ) -> Styler:
         """
@@ -3584,7 +3585,7 @@ def highlight_quantile(
         q_left: float = 0.0,
         q_right: float = 1.0,
         interpolation: QuantileInterpolation = "linear",
-        inclusive: str = "both",
+        inclusive: IntervalInclusiveType = "both",
         props: str | None = None,
     ) -> Styler:
         """
@@ -3969,7 +3970,7 @@ def _highlight_between(
     props: str,
     left: Scalar | Sequence | np.ndarray | NDFrame | None = None,
     right: Scalar | Sequence | np.ndarray | NDFrame | None = None,
-    inclusive: bool | str = True,
+    inclusive: bool | IntervalInclusiveType = True,
 ) -> np.ndarray:
     """
     Return an array of css props based on condition of data values within given range.
diff --git a/pandas/util/_validators.py b/pandas/util/_validators.py
index caa191dc78493..3676e6eb0091e 100644
--- a/pandas/util/_validators.py
+++ b/pandas/util/_validators.py
@@ -14,6 +14,7 @@
 
 import numpy as np
 
+from pandas._typing import IntervalInclusiveType
 from pandas.util._exceptions import find_stack_level
 
 from pandas.core.dtypes.common import (
@@ -487,7 +488,7 @@ def validate_endpoints(closed: str | None) -> tuple[bool, bool]:
     return left_closed, right_closed
 
 
-def validate_inclusive(inclusive: str | None) -> tuple[bool, bool]:
+def validate_inclusive(inclusive: IntervalInclusiveType | None) -> tuple[bool, bool]:
     """
     Check that the `inclusive` argument is among {"both", "neither", "left", "right"}.