One of the most used renewable energy systems to produce clean and sustainable energy are solar energy photovoltaic (PV) plants. The selection among solar energy PV plant location alternatives requires a multi-criteria decision making approach with several conflicting and linguistic criteria. The assessment process is generally done in a vague and imprecise environment. Fuzzy set theory is often very beneficial for evaluating the subjective judgments of decision makers. The Analytic Hierarchy Process is the most used multi-criteria decision making method in the world because of its simplicity and efficiency. In this paper, we select a location for a solar energy PV plant using a 4-level hierarchy. We consider several criteria and sub-criteria including initial cost, maintenance cost, slope and distance to highways. A Z-fuzzy number is a relatively new concept in fuzzy set theory that enables one to circumvent the limitations of ordinary fuzzy numbers. Z-fuzzy numbers can be viewed as a combination of crisp numbers, intervals, fuzzy numbers and random numbers because of their generality. They give a better representation than ordinary fuzzy numbers. This study solves the multi-criteria solar PV power plant location selection problem with a Z-fuzzy based AHP method. To check the applicability of the method proposed here, a real-life case study from Turkey is presented and solved.