The Singapore PR eligibility criteria are different for all the schemes. If you apply under the PTS scheme, you must provide your salary slip and an employer’s letter from your current employer. For other schemes like GIP or Foreign Students scheme, you do not need to provide these documents. ICA may also ask you for these documents if you apply under the Sponsored scheme and are currently employed in Singapore (Spouse or Child of Singapore PR / Citizen Scheme).
If you are a self-employed person, then you can provide the documents as required for this category. Generally it is better to declare yourself fixed monthly salary if you are on self employment. This way you avoid complexity of explaining your situation in the PR application form, as to why you don’t have salary slips.