Fuzzy logic via Fractal geometry is a novel mathematical combination. Using Conversion Based Fuzzy Fractal Geometry (cbFFG), researchers can approach to fractal geometry with the utilization of Direct Fuzzy Sets DFS and Fuzzy Inference Systems FIS¹ in their immense fields of studies. It is proposed a new fuzzy fractal dimension FFD using membership functions instead of conventional log-log linear regression processes which needed more time and calculations. The results are derived from IP² by developing the defined FIS via Fuzzy Analyses and/or for the defined direct membership function. As that of FD, the cbFFD range is [0, 3] for solid geometry and is [0, 2] for plane geometry with discrimination that the output results are upon fuzzy inference and so identifiable and interpretable. Here, cbFFDs are computed by two main inputs: 1) Porosity Conversion Based Factor and 2) Self-Similarity Conversion Based Factor. The outputs of the cbFFD process can be both interpreted by linguistic terms and graduated by the fuzzy numbers. The cbFFD makes the geometric dimensioning more understandable. The final values of cbFFDs can accurately be ranged between geometric and arithmetic means of the proposed cbFFDs or logically computed by prepared FISs.

通过分形几何学的模糊逻辑是一种新颖的数学组合。使用基于转换的模糊分形几何（cbFFG），研究人员可以在其大量研究领域中利用直接模糊集DFS和模糊推理系统FIS ¹来处理分形几何。提出了一种新的使用隶属函数的模糊分形维数FFD来代替传统的log-log线性回归过程，该过程需要更多的时间和计算量。结果源自IP ²通过模糊分析和/或定义的直接隶属函数开发定义的FIS。与FD一样，对于实体几何，cbFFD范围为[0，3]，对于平面几何，cbFFD范围为[0，2]，区别在于输出结果是基于模糊推理的，因此可识别和可解释。此处，cbFFD是通过两个主要输入来计算的：1）基于孔隙率转换的因数和2）基于自相似转换的因数。cbFFD过程的输出既可以用语言术语来解释，也可以用模糊数来表示。cbFFD使几何尺寸标注更容易理解。cbFFD的最终值可以准确地在建议的cbFFD的几何和算术平均值之间变化，或通过准备的FIS进行逻辑计算。