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

E. Pap, Ivana Štajner-Papuga

Research output: Article

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
Publication statusPublished - ápr. 2001

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Convolution

ASJC Scopus subject areas

  • Artificial Intelligence
  • Control and Systems Engineering

Cite this

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title = "Pseudo-integral based on non-associative and non-commutative pseudo-addition and pseudo-multiplication",
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.",
keywords = "Generalized pseudo-operations, Pseudo-convolution, Pseudo-integral, Pseudo-measure",
author = "E. Pap and Ivana Štajner-Papuga",
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language = "English",
volume = "9",
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journal = "International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems",
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TY - JOUR

T1 - Pseudo-integral based on non-associative and non-commutative pseudo-addition and pseudo-multiplication

AU - Pap, E.

AU - Štajner-Papuga, Ivana

PY - 2001/4

Y1 - 2001/4

N2 - 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.

AB - 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.

KW - Generalized pseudo-operations

KW - Pseudo-convolution

KW - Pseudo-integral

KW - Pseudo-measure

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VL - 9

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EP - 167

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JF - International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems

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