##
**Families of OWA operators.**
*(English)*
Zbl 0790.94004

Summary: We introduce the ordered weighted averaging (OWA) operators. We look at some semantics and applications associated with these operators. We discuss the problem of obtaining the associated weighting parameters. We discuss the connection between OWA operators and linguistic quantifiers. We introduce a number of parametrized families of OWA operators; maximum entropy, \(S\)-OWA, step and window are among the most important of these families. We study the evaluation of quantified propositions using these operators. We introduce the idea of aggregate dependent weights.

### MSC:

94A15 | Information theory (general) |

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

94A17 | Measures of information, entropy |

92B20 | Neural networks for/in biological studies, artificial life and related topics |

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

### Keywords:

aggregation; fuzzy sets; logical operators; ordered weighted averaging operators; linguistic quantifiers; maximum entropy
Full Text:
DOI

### References:

[1] | Aczel, J.; Daroczy, Z., On Measures of Information and their Characterizations (1975), Academic Press: Academic Press New York · Zbl 0345.94022 |

[2] | Alsina, C.; Trillas, E.; Valverde, L., On some logical connectives for fuzzy set theory, J. Math. Anal. & Appl., 93, 15-26 (1983) · Zbl 0522.03012 |

[3] | Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Management Sci., 17, 4, 141-164 (1970) · Zbl 0224.90032 |

[4] | Chernoff, H.; Moses, L. E., Elementary Decision Theory (1959), John Wiley & Sons: John Wiley & Sons New York · Zbl 0089.14406 |

[5] | Dubois, D.; Prade, H., A review of fuzzy sets aggregation connectives, Inf. Sci., 36, 85-121 (1985) · Zbl 0582.03040 |

[6] | Eklund, P.; Klawonn, F., Neural fuzzy logic programming, IEEE Trans. on Neural Networks, 3, 815-819 (1992) |

[7] | Engemann, K. J.; Miller, H. E.; Yager, R. R., Decision making with belief structures: an application in risk management, (Technical Report #MII-1234 (1992), Machine Intelligence Institute, Iona College: Machine Intelligence Institute, Iona College New Rochelle, NY) · Zbl 1232.91127 |

[8] | Kacprzyk, J., Inductive learning from considerably erroneous examples with a specificity based stopping rule, (Proc. Int. Conference on Fuzzy Logic and Neutral Networks. Proc. Int. Conference on Fuzzy Logic and Neutral Networks, Iizuka, Japan (1990)), 819 |

[9] | Klement, E. P., Characterization of fuzzy measures constructed by means of triangular norms, J. of Math. Anal. & Appl., 86, 345-358 (1982) · Zbl 0491.28004 |

[10] | Klir, G. J.; Folger, T. A., Fuzzy Sets, Uncertainty and Information (1988), Prentice-Hall: Prentice-Hall Englewood Cliffs, N.J · Zbl 0675.94025 |

[11] | Lee, C. C., Fuzzy logic in control systems: fuzzy logic controller, IEEE Trans. On Systems, Man and Cybernetics, 20, 404-418 (1990), Part 1 · Zbl 0707.93036 |

[12] | Lee, C. C., Fuzzy logic in control systems: fuzzy logic controller, IEEE Trans. on Systems, Man and Cybernetics, 20, 419-435 (1990), Part II · Zbl 0707.93037 |

[13] | O’Hagan, M., Fuzzy decision aids, (Twenty First Asilomar Conference on Signal, Systems and Computers, Volume II (1987), IEEE and Maple Press: IEEE and Maple Press Pacific Grove: CA), 624-628 |

[14] | O’Hagan, M., Aggregating template rule antecedents in real-time expert systems with fuzzy set logic, (Proc. 22nd Annual IEEE Asilomar Conf. on Signals, Systems and Computers. Proc. 22nd Annual IEEE Asilomar Conf. on Signals, Systems and Computers, Pacific Grove, CA (1988)) |

[15] | Rescher, N., Many-Valued Logic (1969), McGraw-Hill: McGraw-Hill New York · Zbl 0248.02023 |

[16] | Rubinson, T., Communication newtorks, (Ph.D. Thesis (1992), Polytechnic Institute of New York) |

[17] | Shannon, C. L.; Weaver, W., The Mathematical Theory of Communication (1964), University of Illinois Press: University of Illinois Press Urbana, Ill |

[18] | Smets, P., Belief functions, (Smets, P.; Mamdani, E. H.; Dubois, D.; Prade, H., Non-Standard Logics for Automated Reasoning (1988), Academic Press: Academic Press London), 253-277 · Zbl 0669.03002 |

[19] | Widrow, B.; Hoff, M. E., Adaptive switching circuits, IRE WESCON Convention Record, 96-104 (1960) |

[20] | B. Widrow and M.A. Lehr, Adaptive neural networks and their applications, Int. J. of Intelligent Systems; B. Widrow and M.A. Lehr, Adaptive neural networks and their applications, Int. J. of Intelligent Systems · Zbl 0938.68786 |

[21] | Yager, R. R., Cardinality of fuzzy sets via bags, Math. Modeling, 9, 441-446 (1987) · Zbl 0625.04007 |

[22] | Yager, R. R., On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Trans. on Systems, Man and Cybernetics, 18, 183-190 (1988) · Zbl 0637.90057 |

[23] | Yager, R. R., Fuzzy quotient operators for fuzzy relational data bases, (Proc. Int. Fuzzy Engineering Symposium. Proc. Int. Fuzzy Engineering Symposium, Yokohama (1991)), 289-296 |

[24] | Yager, R. R., Connectives and quantifiers in fuzzy sets, Fuzzy Sets and Systems, 40, 39-76 (1991) · Zbl 0725.03033 |

[25] | R.R. Yager, Interpreting linguistically quantified propositions, Int. J. of Intelligent Systems; R.R. Yager, Interpreting linguistically quantified propositions, Int. J. of Intelligent Systems · Zbl 0807.68069 |

[26] | Yager, R. R., OWA Neurons: A new class fuzzy neurons, (Proc. Int. Joint on Neural Networks, Vol. I (1992)), 226-231, Baltimore, I |

[27] | Yager, R. R., Fuzzy quotient operator, (Proc. Fourth Int. Conf. on Information Processing a Management of Uncertainty. Proc. Fourth Int. Conf. on Information Processing a Management of Uncertainty, Palma de Majorca, Spain (1992)), 317-322 |

[28] | Yager, R. R., Default knowledge and measures of specificity, (Inf. Sci., 61 (1992)), 1-44 · Zbl 0738.68075 |

[29] | Yager, R. R., Decision making under Dempster-Shafer uncertainties, Int. J. of General Systems, 20, 233-245 (1992) · Zbl 0756.90005 |

[30] | Yager, R. R., On the specificity of a possibility distribution, Fuzzy Sets and Systems, 50, 279-292 (1992) · Zbl 0783.94035 |

[31] | Yager, R. R., On the maximum entropy negation of a probability distribution, (Technical Report #MII-1303 (1993), Machine Intelligence Institute, Iona College: Machine Intelligence Institute, Iona College New Rochelle, NY) · Zbl 0424.90080 |

[32] | R.R. Yager, On the completion of priority orderings in nonmonotonic reasoning systems, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems; R.R. Yager, On the completion of priority orderings in nonmonotonic reasoning systems, Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems · Zbl 1232.68116 |

[33] | R.R. Yager, On the completion of qualitative possibility measures, IEEE Trans. on Fuzzy Systems; R.R. Yager, On the completion of qualitative possibility measures, IEEE Trans. on Fuzzy Systems |

[34] | Yager, R. R.; Filev, D. P., Fuzzy logic controllers with flexible structures, (Proc. Second Int. Conf. on Fuzzy Sets and Neural Networks. Proc. Second Int. Conf. on Fuzzy Sets and Neural Networks, Iizuka Japan (1992)), 317-320 |

[35] | R.R. Yager and D.P. Filev, Analysis of flexible structured fuzzy logic controllers IEEE Trans. of Systems, Man and Cybernetics; R.R. Yager and D.P. Filev, Analysis of flexible structured fuzzy logic controllers IEEE Trans. of Systems, Man and Cybernetics |

[36] | R.R. Yager and D.P. Filev, Parametrized ‘andlike’ and ‘orlike’ OWA operators, Int. J. of General Systems; R.R. Yager and D.P. Filev, Parametrized ‘andlike’ and ‘orlike’ OWA operators, Int. J. of General Systems |

[37] | Yager, R. R.; Filev, D. P., On the issue of defuzzification and selection based on a fuzzy set, Fuzzy Sets and Systems, 55, 255-271 (1993) · Zbl 0785.93060 |

[38] | Zadeh, L. A., A theory of approximate reasoning, (Hayes, J.; Michie, D.; Mikulich, L. I., Maching Intelligence, Vol. 9 (1979), Halstead Press: Halstead Press New York), 149-194 |

[39] | Zadeh, L. A., A computational approach to fuzzy quantifiers in natural languages, Computing and Mathematics with Applications, 9, 149-184 (1983) · Zbl 0517.94028 |

[40] | Zadeh, L. A., A theory of commonsense knowledge, (Skala, H. J.; Termini, S.; Trillas, E., Aspects of Vagueness (1983), Reidel: Reidel Dodrecht), 257-296 |

[41] | Zadeh, L. A., A computational theory of dispositions, (Proc. Int. Conf. of Association of Computational Linguistics (1984), Stanford University), 312-318 |

[42] | Zadeh, L. A., Syllogistic reasoning in fuzzy logic and its application to usuality and reasoning with dispositions, IEEE Trans. on Systems, Man, and Cybernetics, 15, 754-763 (1985) · Zbl 0593.03033 |

[43] | Zadeh, L. A., A computational theory of dispositions, Int. J. of Intelligent Systems, 2, 39-63 (1987) · Zbl 0641.68153 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.