Should you compare a new offer to your current salary or to the market rate?
How do you deal with offers that are only slightly above your current salary but on the high end according to the market rates?
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Whichever is more
Do the interviews. If they like you, want to hire you, and still give you a salary based on your previous salary, then the org is going to be full of disgruntled employees with compensation issues.
Clearing the interviews is step 1. Worse case you can show them competing offers for negotiation. Worst case you just reject them and act on a red flag.
you should try for market rates, but wrt a company's offer, you should target at least 75th percentile for that role if not the highest. EOD, they can give you what they can offer.
Rationality suggests that you compare to the market rates, but the way human minds work is it takes a lot of conscious effort to ignore the relative change.