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**A method of inference in approximate reasoning based on interval-valued fuzzy sets.**
*(English)*
Zbl 0635.68103

This paper introduces and discusses a method of approximate inference which operates on the extension of the concept of a fuzzy set by the concept of an interval-valued fuzzy set. This method allows a formal, fuzzy representation to be built for verbal decision algorithms. Furthermore, it can have an effective computer representation. An example showing how this method operates is provided.

### MSC:

68T99 | Artificial intelligence |

### Keywords:

approximate reasoning; approximate inference; interval-valued fuzzy set; verbal decision algorithms
Full Text:
DOI

### References:

[1] | Baldwin, J. F.; Pilsworth, B. W., A model of fuzzy reasoning through multi-valued logic and set theory, Internat. J. Man-Machine Stud., 11, 351-380 (1979) · Zbl 0413.03015 |

[2] | Czogala, E., On distribution function description of probabilistic sets and its application in decision making, Fuzzy Sets and Systems, 10, 21-29 (1983) · Zbl 0535.62011 |

[3] | Czogała, E.; Pedrycz, W., On the concept of fuzzy probabilistic controllers, Fuzzy Sets and Systems, 10, 109-121 (1983) · Zbl 0544.93003 |

[4] | Dubois, D.; Prade, H., Operations in a fuzzy-valued logic, Inform. and Control, 43, 224-240 (1979) · Zbl 0434.03020 |

[5] | A. Dziech and M.B. Gorzałczany, Effectiveness evaluation of the interval-valued fuzzy decisional rule in some decisionmaking problems of signal transmission, Zeszyty Kieleckiego Towarzystwa Naukowego “Studia Kieleckie” (to appear) (in Polish).; A. Dziech and M.B. Gorzałczany, Effectiveness evaluation of the interval-valued fuzzy decisional rule in some decisionmaking problems of signal transmission, Zeszyty Kieleckiego Towarzystwa Naukowego “Studia Kieleckie” (to appear) (in Polish). |

[6] | Dziech, A.; Gorzałczany, M. B., Application of interval-valued fuzzy sets in signal transmission problems, (Polish Symp. on Interval and Fuzzy Mathematics. Polish Symp. on Interval and Fuzzy Mathematics, Poznań, Poland (1983)), 77-82 |

[7] | Gorzalczany, M. B.; Stachowicz, M. S., On certain ideas of designing fuzzy controllers, (Zeszyty Naukowe AGH. Zeszyty Naukowe AGH, Elektryfikacja i Mechanizacja Górnictwa i Hutnictwa z., 131 (1980)), 167-188, (in Polish) |

[8] | Gorzalczany, M. B.; Kiszka, J. B.; Stachowicz, M. S., Some problems of studying adequacy of fuzzy models, (Yager, R., Fuzzy Set and Possibility Theory, Recent Developments (1982), Pergamon Press: Pergamon Press Oxford), 14-34 |

[9] | M.B. Gorzałczany, Interval-valued fuzzy formalisation method of verbal decisional rules taking into consideration the hierarchy of their importance, Zeszyty Kieleckiego Towarzystwa Naukowego “Studia Kieleckie” (to appear) (in Polish).; M.B. Gorzałczany, Interval-valued fuzzy formalisation method of verbal decisional rules taking into consideration the hierarchy of their importance, Zeszyty Kieleckiego Towarzystwa Naukowego “Studia Kieleckie” (to appear) (in Polish). |

[10] | Gorzałczany, M. B., Approximate inference with interval-valued fuzzy sets - an outline, (Proc. Polish Symp. on Interval and Fuzzy Mathematics. Proc. Polish Symp. on Interval and Fuzzy Mathematics, Poznań, Poland (1983)), 89-95 · Zbl 0597.60007 |

[11] | Gorzałczany, M. B., Interval-valued fuzzy method of approximate inference and its application to the problems of signal transmission and construction of control algorithms, (Ph.D. Thesis (1983), Technical University of Poznań: Technical University of Poznań Poland), (in Polish) |

[12] | Hirota, K., Concept of probabilistic sets, Fuzzy Sets and Systems, 5, 31-46 (1981) · Zbl 0442.60008 |

[13] | Kania, A. A.; Kiszka, J. B.; Gorzałczany, M. B.; Maj, J. R.; Stachowicz, M. S., On stability of formal fuzziness systems, Inform. Sci., 22, 51-68 (1980) · Zbl 0464.93005 |

[14] | Zadeh, L. A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Systems Man Cybernet., 1, 28-44 (1973) · Zbl 0273.93002 |

[15] | Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning - I, Inform. Sci., 8, 199-249 (1975) · Zbl 0397.68071 |

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