During the conceptual design phase, approximately 70 to 80 percent of a product's life-cycle costs are determined, yet the designer's knowledge of the product's future behavior is incomplete and lacks a known probability distribution—an epistemic condition termed "ignorance" in the decision-making literature, distinct from conventional uncertainty. Conceptual design is inherently multi-actor, with three subsystems—performance, availability, and support—in conflict of interest. To address this gap, this study proposes a standard bi-level optimization model: at the upper level (leader), integrated life-cycle productivity, defined as the ratio of technical-process effectiveness to life-cycle cost, is maximized; at the lower level, the three subsystems reach Nash equilibrium via a non-cooperative game with interval type-2 fuzzy numbers. Fuzzy payoffs are ranked using the interval center-of-gravity method, and Nash equilibrium is solved via the iterated best-response algorithm. The model is implemented on a real case—the world's largest electric taxi fleet (BYD e6 fleet in Shenzhen, China)—with documented parameters. Internal validation is completed through three complementary tests (Nash deviation, boundary-case consistency, and multi-start convergence) and two external checks (parametric anchoring on independent empirical data and retrospective counterfactual analysis of the actual design). Normalized cost sensitivity analysis reveals that to improve expected availability, increasing redundancy is more cost-effective; however, only reducing thermal ignorance narrows the interval width (decision risk)—thus, these two actions are not substitutes but pursue distinct objectives. Furthermore, the equilibrium solution is highly sensitive to the unknown powers of utility functions.