```ts
merge_overlapping_intervals(intervals: Array<{
    range: [number, number],
    strength: number,
    id: any
}>, threshold: number, precision: number): Array<{
    range: [number, number],
    strength: number,
    id: any
}>
```

Merges overlapping intervals within a given set, accounting for the strength of each interval and a specified threshold.

## Parameters

- `intervals`: An array of objects, each containing a range (as a two-element array), strength, and an identifier.
- `threshold`: A numerical threshold determining the minimum strength required for an interval to be included in the final output.
- `precision`: The precision level for comparing interval boundaries (not explicitly used in the given implementation).

## Returns

- An array of merged intervals that meet or exceed the specified strength threshold.

## Summary

The `merge_overlapping_intervals` function is designed to process a collection of intervals, merging those that overlap based on their range and strength. The function first sorts the intervals by their starting points. It then merges overlapping intervals by calculating weighted averages of their start and end points, accumulating their strengths, and combining their identifiers. The merged intervals are then filtered based on a specified strength threshold, ensuring that only significant intervals are retained. This function is particularly useful in contexts where overlapping data ranges need to be consolidated, such as in event scheduling, resource allocation, or in financial analysis for combining similar price ranges or time periods.

*Note: The function's effectiveness in accurately merging intervals depends on the integrity and format of the input data. Careful consideration of the threshold parameter is important for ensuring meaningful output.*
