Philosophical and axiomatic grounding of fuzzy theory

Zaman zaman, yeni araştırma yönleri aramak, keşfetmek ve temel varsayımlara yeni bir ışık tutmak için, Bulanık Teorinin felsefi ve belitlere dayanan temellerini tekrarlamak önemlidir. Bu gaye nedeniyle, önce, Pierce ve Zadeh'nin görüş açılarının belirli ve belirsizlik yönlerini yeniden incelemek gerekir. İkinci olarak teorik sorgulama perspektifinden, Klasik ve Bulanık teorilerin yaratılış ve bilgi kuramı temellerine kısaca işaret ediyoruz. Üçüncü olarak, Aralık-Değerli Tip II bulanık teorinin temel desteklerini ortaya çıkaran 1) klasik küme ve mantık teorileri, 2)bulanık küme ve iki-değerli mantık teorileri, Tip I bulanık teori ve 3) Dil-Bilim Ötesi Belitlerin bulanık yorumunu tetkik ediyoruz.

Bulanık teorinin belitlere dayalı felsefik temelleri

At times, it is essential to re-affirm the philosophical and axiomatic foundations of Fuzzy Theory in order to search and discover new avenues of research and to shed a new light onto basic assumptions. For such a purpose, first, the perspectives of Pierce and Zadeh are reviewed with regards to determinacy and indeterminacy. Secondly, the ontological and epistemological foundations of both the Classical and Fuzzy theories are briefly noted from the perspective of a theoretical inquiry. Thirdly, axiomatic positions are re-stated for: 1) classical set and logic theories, 2) fuzzy set and twovalued logic theories,i.e., Type I fuzzy theory, and then 3) a fuzzy interpretation of Meta-Linguistic Axioms are investigated to reveal part of the foundational underpinnings of Interval-Valued Type II fuzzy theory.

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  • 1. Brock, J.E. 1979. Principal Themes in Peirce’s Logic of Vagueness, in K.L. Ketner and J.M. Ransdell (eds) Studies in Peirce’s Semiotic, Institute for Studies in Pragmaticism.
  • 2. Hoopes, J. (ed). 1991. Peirce on Signs: Writings on Semiotics, Chapel Hill and London, University of North Carolina Press.
  • 3. Peirce, C. S. 1867. “Upon the Logic of Mathematics.” Proceedings of the American Academy of Arts and Sciences 7, 402-412.
  • 4. Resconi, G., I.B. Türkşen. 2001. “Canonical Forms of Fuzzy Truthoods by Meta-Theory Based Upon Modal Logic,” Information Sciences, 131, 157-194.
  • 5. Türkşen I.B. 1986. “Interval-Valued Fuzzy Sets based on Normal Forms,” Fuzzy Sets and Systems, 191-210.
  • 6. Türkşen, I.B. 1989. “Four Methods of Approximate Reasoning with Interval-Valued Fuzzy Sets”, Internet. J. Approx. Reasoning, 3, 121-142.
  • 7. Türkşen, I.B. 1992. “Interval Valued Fuzzy Sets and ‘Compensatory AND’,” Fuzzy Sets and Systems, 51, 295-307.
  • 8. Türkşen, I.B. 1994a, “Fuzzy Normal Forms,” Fuzzy Sets and Systems, 253-266.
  • 9. Türkşen, I.B. 1994b. Interval-Valued Fuzzy Sets and Compensatory AND,” FSS, 87-100.
  • 10. Türkşen, I.B. 1994c. “Interval-Valued Fuzzy Sets and ‘Compensatory AND’,” FSS, 295-307.
  • 11. Türkşen, I.B. 1995. “Fuzzy Normal Forms,” Fuzzy Sets and Systems, 69, 319-346.
  • 12. Türkşen, I.B. 1996. “Non-specificity and Interval Valued Fuzzy Sets,” Fuzzy Sets and Systems (Invited Special Issue), 87-100.
  • 13. Türkşen, I.B. 2001. “Computing with Descriptive and Veristic Words: Knowledge Representation and Reasoning,” in: Computing With Words, P.P. Wang(ed.), Chapter 10, Wiley, New York, 297-328.
  • 14. Türkşen, I.B. 2002. “Upper and Lower Set Formulas: Restriction and Modification of Dempster-Pawlak Formalism,” Special Issue of the International Journal of Applied Mathematics and Computer Science, V.12, No.3,101-111.
  • 15. Türkşen, I.B., A. Kandel, Y-Q. Zhang. 1999. “Normal Forms of Fuzzy Middle and Fuzzy Contradiction,” IEEESMC, 29-2, Part B, Cybernetics, 237-253.
  • 16. Türkşen, I.B., T, Bilgiç. 1993. Interval Valued Strict Preference, in Proceedings of the First European Congress on Fuzzy and Intelligent Technologies (September 1993), 593-599. EUFIT ‘93 Aachen, Germany.
  • 17. Zadeh, L.A. 1965. “Fuzzy Sets,” Information and Control Systems, Vol.8, 338-353.
  • 18. Zadeh, L.A. 1996. “Fuzzy Logic = Computing With Words,” IEEETransactions on Fuzzy Systems, 4, 2, 103-111.
  • 19. Zadeh, L.A. 1997. “Toward a Theory of Fuzzy Information Granulation and its Centrality in Human Reasoning and Fuzzy Logic,” Fuzzy Sets and Systems, 90, 111-127.
  • 20. Zadeh, L.A. 1999. “From Computing with Numbers to- Computing with Words-From Manipulation of Measurements to Manipulation of Perceptions”, IEEE-Trans on Curciuts and Systems, 45, 105-119.
  • 21. Zadeh, L.A. 2000a. Computing With Perceptions, Keynote Address, IEEE- Fuzzy Theory Conference, San Antonio, May 7-10.
  • 22. Zadeh, L.A. 2000b. “Toward a Perception-Based Theory of Probabilistic Reasoning,” Key note address; Fourth International Conference on Applications of Fuzzy Systems and Soft Computing, June 27-29, Siegen, Germany.
  • 23. Zadeh, L.A. 2001. “From Computing with Numbers to Computing with Words - From Manipulation of Measurements to Manipulation of Perceptions,” in: P.P. Wang(ed.) Computing With Words, Wiley Series on Intelligent Systems, Wiley and Sons, New York, 35-68.
  • 24. Zimmermann, H.J., P. Zysno. 1980. “Latent Connectives in Human Decision Making,” Fuzzy Sets and Systems, 4,37-51.