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Zadeh模糊集合理論的缺陷及其改進:C*-模糊集合理論

Defects and overcoming of Zadeh's fuzzy set theory:C*-fuzzy set theory

  • 摘要: 分析和證明了Zadeh模糊集合理論的三個缺點和兩個錯誤,提出了一個考慮模糊集合之間關系,并且用相關系數來刻畫這種關系的程度的新模糊集合理論(系統)——C*-模糊集合理論(系統).新理論(系統)能克服Zadeh模糊集合理論的三個缺點和兩個錯誤;能正確地描繪客觀世界的全部模糊現象;有補集;隸屬度有統一的計算公式;并且是經典集合系統的特例,能滿足全部經典集合的公式,與正常思維、邏輯和概念一致.

     

    Abstract: Three shortcomings and two errors of Zadeh's fuzzy set theory were analyzed and proved, and a new fuzzy set theory, C*-fuzzy set theory, was proposed. The new C*-fuzzy set considers the relationship between fuzzy sets and represents the relationship with relativity. It overcomes all the errors and shortcomings of Zadeh's fuzzy set theory:it correctly reflects different kinds of fuzzy phenomena in the natural world; set complement exists on it; it has uniform calculating formulas for membership; it satisfies all formulas of the classical set theory and is consistent with classical and normal thinking, logic and concepts.

     

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