Pseudo-integral based on non-associative and non-commutative pseudo-addition and pseudo-multiplication

Endre Pap, Ivana Štajner-Papuga

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7 Citations (Scopus)

Abstract

We shall consider non-associative and non-commutative pseudo-addition and pseudo-multiplication, i.e., generalized pseudo-operations. More precise, we shall consider special class of generalized pseudo-operations that have the following form: x⊕y = k-1(εk(x)+ k(y)), x ⊙ y = k-1(k(x)εk(y)), where ε is arbitrary fixed positive real number and k is a positive strictly monotone function. Using previous pseudo-operations, corresponding pseudo-measure and pseudo-integral will be introduced. Pseudo-convolution based on pseudo-measure and pseudo-integral will be constructed.

Original languageEnglish
Pages (from-to)159-167
Number of pages9
JournalInternational Journal of Uncertainty, Fuzziness and Knowlege-Based Systems
Volume9
Issue number2
DOIs
Publication statusPublished - Apr 2001

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Keywords

  • Generalized pseudo-operations
  • Pseudo-convolution
  • Pseudo-integral
  • Pseudo-measure

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Information Systems
  • Artificial Intelligence

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