Fuzziness measures for fuzzy rectangles.

*(English)*Zbl 0683.94019Summary: Taking inspiration from the axioms for Shannon entropy and U-uncertainty, we study fuzziness measures such that the fuzziness of a ‘genuine’ rectangular set can be computed from the fuzziness of its sides. The results found plead in favour of measures based on the max operation, rather than measures of the additive type.

##### MSC:

94D05 | Fuzzy sets and logic (in connection with information, communication, or circuits theory) |

94A17 | Measures of information, entropy |

##### Keywords:

fuzzy sets; fuzzy Cartesian products; information measure; Shannon entropy; U-uncertainty; fuzziness measures
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##### References:

[1] | Guiaşu, S., Information theory and applications, (1977), McGraw-Hill New York |

[2] | Csiszár, I.; Körner, J., Information theory. coding theorems for discrete memoryless systems, (1981), Academic Press New York · Zbl 0568.94012 |

[3] | Klir, G.J.; Mariano, M., On the uniqueness of possibilistic measure of uncertainty and information, Fuzzy sets and systems, 24, 197-219, (1987) · Zbl 0632.94039 |

[4] | Ramer, A.; Lander, L., Classification of possibilistic uncertainty and information functions, Fuzzy sets and systems, 24, 221-230, (1987) · Zbl 0637.94027 |

[5] | Ramer, A., Uniqueness of information measure in the theory of evidence, Fuzzy sets and systems, 24, 183-196, (1987) · Zbl 0638.94027 |

[6] | Klir, G.J., Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?, Fuzzy sets and systems, 24, 141-160, (1987) · Zbl 0633.94026 |

[7] | Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049 |

[8] | Yager, R.R., On the measure of fuzziness and negation. part I: membership in the unit interval, Internat. J. general systems, 5, 221-229, (1979) · Zbl 0429.04007 |

[9] | Yager, R.R., On the measure of fuzziness and negation. part II: lattices, Inform. and control, 44, 235-242, (1980) · Zbl 0443.04008 |

[10] | Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning, Inform. sci., Inform. sci., Inform. sci., 9, 43-80, (1975) · Zbl 0404.68075 |

[11] | De Luca, A.; Termini, S., A definition of nonprobabilistic entropy in the setting of fuzzy sets theory, Inform. and control, 20, 301-312, (1972) · Zbl 0239.94028 |

[12] | Trillas, E.; Riera, T., Entropies in finite fuzzy sets, Inform. sci., 15, 159-168, (1978) · Zbl 0436.94012 |

[13] | Batle, N.; Trillas, E., Entropy and fuzzy integral, J. math. anal. appl., 69, 469-474, (1979) · Zbl 0421.28015 |

[14] | Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002 |

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