### 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)^{ε}k(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 language | English |
---|---|

Pages (from-to) | 159-167 |

Number of pages | 9 |

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

Volume | 9 |

Issue number | 2 |

Publication status | Published - ápr. 2001 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Control and Systems Engineering

### Cite this

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

*9*(2), 159-167.

**Pseudo-integral based on non-associative and non-commutative pseudo-addition and pseudo-multiplication.** / Pap, E.; Štajner-Papuga, Ivana.

Research output: Article

*International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems*, vol. 9, no. 2, pp. 159-167.

}

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

UR - http://www.scopus.com/inward/record.url?scp=0012660675&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012660675&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0012660675

VL - 9

SP - 159

EP - 167

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

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

SN - 0218-4885

IS - 2

ER -