PRODUCT T-NORM ARTIHMETIC OF SUBNORMAL TRIANGULARFUZZY NUMBERS

Soylu G.

1st BILSEL INTERNATIONAL ASPENDOS SCIENTIFIC RESEARCH CONGRESS, Antalya, Türkiye, 24 Şubat 2024

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Antalya
  • Basıldığı Ülke: Türkiye
  • Akdeniz Üniversitesi Adresli: Evet

Özet

Arithmetic with fuzzy numbers is  widely applied in many different directions such as in engineering and decision making. This high potential of applications of fuzzy arithmetic in different disciplines is attracting a huge amount of interest of researchers. Most of these applications use the minimum t-norm as the join in the well-known Zadeh's extension formula. For this type of arithmetic the alpha-level method is easy to employ because of the monotonicity of arithmetic operators. Nevertheless, arithmetic with other types of t-norms still plays an important role in applications. However, fuzzy arithmetic with different type of t-norms, which actually is a generalization of Zadeh's extension by replacing the minimum with a general t-norm, is facing much complexity in practical applications. These difficulties with product-arithmetic have to be overcome since there is a necessity for it in certain fields of applications. For example it is proven that the product t-norm is the only t-norm for which fuzzy constrained optimization problems are scale-invariant. Another example could be the successful employment of product t-norms in fuzzy controllers. On the other hand we observe that in the literature the majority of papers deal with normal fuzzy numbers. Arithmetic taking into account subnormal fuzzy numbers is however needed for more appropriate modeling of real life problems. One comes across subnormal fuzzy numbers in applications like fuzzy risk analysis, fuzzy decision making and fuzzy linear programming.

 The objective of this work is to provide a particular response to the requirements mentioned above. Namely, the paper deals with the product t-norm arithmetic of subnormal triangular fuzzy numbers which will be called generalized triangular fuzzy numbers hereafter. The work expands the authors former study about product arithmetic with normal fuzzy numbers, so in the same way the extension principle is followed.