What is the test for determining whether a decision of an administrative agency substantially affects a fundamental right?

If, as here, the decision of an agency substantially affects a fundamental vested right, "the trial court, in determining under [Code of Civil Procedure] section 1094.5 whether there has been an abuse of discretion because the findings are not supported by the evidence, must exercise its independent judgment on the evidence and find an abuse of discretion if the findings are not supported by the weight of the evidence." (Strumsky v. San Diego Employees Retirement Assn. (1974) 11 Cal.3d 28, 32.) "In exercising its independent judgment, a trial court must afford a strong presumption of correctness concerning the administrative findings, and the party challenging the administrative decision bears the burden of convincing the court that the administrative findings are contrary to the weight of the evidence." (Fukuda v. City of Angels (1999) 20 Cal.4th 805, 817.)