This paper looks at both the prepayment risks of housing mortgage loan credit default swaps (LCDS) as well as the fuzziness and hesitation of investors as regards prepayments by borrowers. It further discusses the first default pricing of a basket of LCDS in a fuzzy environment by using stochastic analysis and triangular intuition-based fuzzy set theory. Through the 'fuzzification' of the sensitivity coefficient in the prepayment intensity, this paper describes the dynamic features of mortgage housing values using the One-factor copula function and concludes with a formula for 'fuzzy' pricing the first default of a basket of LCDS. Using analog simulation to analyze the sensitivity of hesitation, we derive a model that considers what the LCDS fair premium is in a fuzzy environment, including a pure random environment. In addition, the model also shows that a suitable pricing range will give investors more flexible choices and make the predictions of the model closer to real market values.