For "open-minded":
* Receptive
* Tolerant
* Liberal
* Broad-minded
* Flexible
* Understanding
For "strong-minded":
* Determined
* Resolute
* Willful
* Independent
* Self-assured
* Headstrong
For other uses of "minded":
* Interested (e.g., "He's art-minded.")
* Inclined (e.g., "She's business-minded.")
* Focused (e.g., "He's career-minded.")
It's always best to consider the specific context and choose the word that best fits the meaning you want to convey.