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Conversion based fuzzy fractal dimension integrating self-similarity and porosity, via DFS and FIS (Mamdani and Sugeno systems)

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  • Sarkheil, Hamid
  • Rahbari, Shahrokh
  • Rayegani, Behzad

Abstract

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 FIS11fuzzy inference system 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 IP22Image Processing 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.

Suggested Citation

  • Sarkheil, Hamid & Rahbari, Shahrokh & Rayegani, Behzad, 2020. "Conversion based fuzzy fractal dimension integrating self-similarity and porosity, via DFS and FIS (Mamdani and Sugeno systems)," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305798
    DOI: 10.1016/j.chaos.2020.110183
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    1. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    1. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).

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