Comparison of Takuti-Titan and Atanasov Intuitive Fuzzy Regions

Document Type : Original Article

20.1001.1.27174409.1399.3.2.5.2/DOR

Abstract

Two distinct but identical types of Atanasov's set theory and intuitive fuzzy logic and Takotti-Titanian set theory and intuitive fuzzy logic are introduced. Atanasov believes that he has turned the theory of sets and fuzzy logic into the theory of sets and intuitive logic by defining two functions of membership (correctness) and non-membership (correctness), the sum of which does not necessarily become one. They have developed two values ​​into set theory and logic that can infer fuzzy data. Atanasov's condition on the set of functions reinforces the idea of ​​eliminating the principle of the exclusion of the third clause, and Takotti and Titan rely on theorems that construct intuitive theories using a set of valuations that is a perfect Heat algebra. In this paper, these two types of intuitive fuzzy logic are reviewed in terms of some properties, and their relationship with intuitive, fuzzy and classical regions. The focus of this study is on three important issues: the principle of double contradiction, generalized regions, and the philosophy of intuitionism. Then, from the terminological and content point of view, they compare the properties of fuzzy logic and the properties of intuitive logic, and in the end, the non-intuition of Athanasov's theory and the non-fuzzy nature of Takoti-Titanian theory are concluded.

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References

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History

  • Receive Date: 04 February 2021
  • Revise Date: 25 March 2021
  • Accept Date: 26 April 2021

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