Triangular norm-based iterative compensatory operators.

*(English)*Zbl 0931.68123Summary: Aggregation operators based on a fixed t-norm and on suitable transformations of processed data are introduced. A special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic, geometric and harmonic means. Several properties of introduced operators are studied, e.g., the symmetry, the associativity, the idempotency, the annihilation, etc. Several examples are given, including continuous idempotent bisymmetric iterative compensatory operators with zero annihilator.

##### MSC:

68T35 | Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence |

03E72 | Theory of fuzzy sets, etc. |

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\textit{A. Kolesárová} and \textit{M. Komorníková}, Fuzzy Sets Syst. 104, No. 1, 109--120 (1999; Zbl 0931.68123)

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##### References:

[1] | Dombi, J., Basic concepts for a theory of evaluation: the aggregative operator, European J. oper. res., 10, 282-293, (1982) · Zbl 0488.90003 |

[2] | Klement, E.P., Some mathematical aspects of fuzzy sets: triangular norms, fuzzy logics and generalized measures, Fuzzy sets and systems, 90, 133-140, (1997) · Zbl 0922.03032 |

[3] | Klement, E.P.; Mesiar, R., Triangular norms, Tatra mount. math. publ., 13, 169-194, (1997) · Zbl 0915.04002 |

[4] | E.P. Klement, R. Mesiar, E. Pap, Triangular Norms, Monograph, in preparation. |

[5] | Klement, E.P.; Mesiar, R.; Pap, E., On the relationship of associative compensatory operators to triangular norms and conorms, J. uncertainty, fuzziness knowledge-based systems, 4, 129-144, (1996) · Zbl 1232.03041 |

[6] | Klir, G.J.; Yuan, B., Fuzzy sets and applications, (1995), Prentice-Hall Upper Saddle River, New York |

[7] | Ling, C.M., Representation of associative functions, Publ. math. debrecen, 12, 189-212, (1965) · Zbl 0137.26401 |

[8] | Luhandjula, M.K., Compensatory operators in fuzzy linear programming with multiple objectives, Fuzzy sets and systems, 8, 245-252, (1982) · Zbl 0492.90076 |

[9] | Mesiar, R., Compensatory operators based on triangular norms and conorms, (), 131-135 |

[10] | Mesiar, R.; Komorníková, M., Triangular norm-based aggregation of evidence under fuzzinness, (), 11-35 |

[11] | Mesiar, R.; Komorníková, M., Aggregation operators, (), 193-211 · Zbl 0960.03045 |

[12] | Moser, B.; Tsiporkova, E.; Klement, E.P., Convex combinations in terms of triangular norms: a characterization of idempotent, bisymmetrical and self-dual compensatory operators, Fuzzy sets and systems, 104, (1999) · Zbl 0928.03063 |

[13] | Turksen, I.B., Interval-valued fuzzy sets and ‘compensatory AND’, Fuzzy sets and systems, 51, 295-307, (1992) |

[14] | Yager, R.R., On ordered averaging aggregation operators in multi-criteria decision making, IEEE trans. systems man cybernet., 18, 183-190, (1988) · Zbl 0637.90057 |

[15] | Yager, R.R., Aggregation operators and fuzzy systems modelling, Fuzzy sets and systems, 67, 129-146, (1994) · Zbl 0845.93047 |

[16] | Zimmermann, H.J.; Zysno, P., Latent connectives in human decision making, Fuzzy sets and systems, 4, 37-51, (1980) · Zbl 0435.90009 |

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