Because of their outstanding advantages of high power, high efficiency, multi-wavelength, tunable, narrow linewidth, and variable bandwidth, fiber lasers based on random distributed feedback have a broad development prospect in the exploration of new light sources. Random fiber lasers based on Rayleigh scattering distributed feedback are widely studied and discussed by scholars. As a result, they can overcome the disadvantages of traditional distributed feedback random lasers such as a complex structure, large cavity loss, low output laser efficiency, spectral instability, and low practicality. In recent years, several research reports on random fiber lasers have widely applied the combination of Stimulated Brillouin Scattering(SBS), Stimulated Raman Scattering(SRS), and Rayleigh Scattering(RS) to achieve multi-wavelength cascaded output. A single multi-wavelength Brillouin-Raman random fiber laser with tunable frequency spacing is innovative and worthy of further exploration, considering the lack of flexibility and limited applications of multi-wavelength output at a fixed frequency interval. In this paper, the cavity loss is controlled by tuning the attenuator in the reflection ring, which makes the laser cavity structure switch between a semi-open cavity and a full-open cavity. What's more, the frequency interval of multi-wavelength output can also be switched by this way. Compared to other multi-wavelength fiber lasers with switchable frequency intervals, this structure is more simple and has a wider output bandwidth.In the current laser configuration, the multi-wavelength cascade output is the result of a combination of SBS, RS, and SRS at high Raman Pumping (RP) power. The RP produces a distributed Raman gain in the DCF and then amplifies the BP. When the BP power satisfies the SBS threshold, a back-propagating first-order Brillouin Stokes Light (BSL) is generated. Similarly, the first-order BSL is also amplified by the distributed Raman gain and acts as a new pump source to generate a second-order BSL that propagates backwards with respect to the first-order BSL. Thus, the lower-order BSLs act as a pump source to generate more higher-order BSLs, and such a cascade process will continue until the overall gain is insufficient to offset its losses. The switchable frequency interval of multi-wavelength output is achieved by tuning the attenuator in the reflective ring 2, which can precisely control the power of the reflected signal entering the cavity. When the attenuation is small, the multi-wavelength output has a single-frequency interval, and when the attenuation is large, the multi-wavelength output has a double-frequency interval.The influence of changing the attenuation in reflection ring 2 on the Peak Power Difference (PPD) between adjacent Stokes lines is discussed in the experiment. When the attenuation is small, most of the even-order BSLs propagating to the right are reflected into the fiber through the reflective ring 2, and then combine with the odd-order BSLs propagating to the left. As a result, the laser produces Stokes lines with a single-frequency interval, at which time the spectral flatness is less than 3 dB, satisfying the condition of producing BSLs with a frequency interval of ~10 GHz. Continuing to increase the attenuation, the frequency interval of adjacent Stokes lines is in the transition from ~10 GHz to ~20 GHz, while the PPD is also changing in the range of 3 dB to 20 dB. When the even-order BSLs propagating to the right are almost all attenuated, the laser produces Stokes lines with a double-frequency interval, and only the even-order Rayleigh components propagate together with the odd-order BSLs. Under this circumstance, the PPD is more than 20 dB and almost constant, which satisfies the condition of producing BSLs with a frequency interval of 20 GHz. The influence of BP wavelength and power on the multi-wavelength output is further discussed in the experiment. The best result is obtained under the optimal experimental conditions, at which multi-wavelength outputs with a single-frequency interval (~10 GHz) in wavelength range of 39 nm (1 532 ~1 571 nm) and multi-wavelength output with a double-frequency interval (~20 GHz) in wavelength range of 39.5 nm (1 532 ~1 571.5 nm) are obtained.A frequency interval switchable multi-wavelength Brillouin-Raman random fiber laser based on cavity loss modulation is proposed and demonstrated. The random fiber laser based on the random distributed feedback is formed by RS combined with nonlinear effects such as SBS and SRS to achieve multi-wavelength cascaded output. Further by controlling the attenuation of the tunable attenuator in the reflective ring 2, the cavity structure is switched between a semi-open cavity and a full-open cavity, which makes the frequency interval and optical signal-to-noise ratio of the multi-wavelength output switchable. The experimental results show that when the attenuation is -2 dB, the multi-wavelength output with a single-frequency interval (10.48 GHz) in a wavelength range of 39 nm (1 532 ~1 571 nm) can be obtained, and the optical signal-to-noise ratio is 17.2 dB at this time. When the attenuation is -30 dB, the multi-wavelength output with a double-frequency interval (20.96 GHz) in a wavelength range of 39.5 nm (1 532 ~1 571.5 nm) can be obtained, and the optical signal-to-noise ratio is 25.2 dB at this time. Compared to other multi-wavelength fiber lasers with switchable frequency intervals, this structure is simpler and has a wider output bandwidth.