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**Soft set theory – first results.**
*(English)*
Zbl 0936.03049

The paper briefly discusses the properties of three of the existing models of uncertainty, namely probability, fuzziness and interval mathematics, and suggests another one called soft sets. Soft sets are defined as parametrized classes of subsets of a universe. Operations with soft sets are defined and discussed. The main part of the paper is devoted to the soft set theoretical approaches to regulation, non-cooperative games and differential calculus.

Reviewer: M.Mareš (Praha)

### MSC:

03E70 | Nonclassical and second-order set theories |

03E75 | Applications of set theory |

26E50 | Fuzzy real analysis |

28E10 | Fuzzy measure theory |

03E72 | Theory of fuzzy sets, etc. |

91A44 | Games involving topology, set theory, or logic |

### Keywords:

fuzzy set; soft function; models of uncertainty; probability; fuzziness; interval mathematics; soft sets; regulation; non-cooperative games; differential calculus
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\textit{D. Molodtsov}, Comput. Math. Appl. 37, No. 4--5, 19--31 (1999; Zbl 0936.03049)

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### References:

[1] | Zadeh, L. A., Fuzzy set, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606 |

[2] | Molodtsov, D. A., Stability of Optimality Principles (1987), Nauka: Nauka Moscow, (in Russian) · Zbl 0632.49001 |

[3] | Tikhonov, A. N.; Ya, V., Arsenin, The Methods for Solving Ill-Posed Problems (1979), Nauka: Nauka Moscow, (in Russian) |

[4] | Molodtsov, D. A., Optimality principles as a model of player behaviour in game theory (1991), Preprint of Computer Center of Russian Academy of Sciences: Preprint of Computer Center of Russian Academy of Sciences Moscow · Zbl 1189.93019 |

[5] | Molodtsov, D. A., Optimality principles as a model of person’s behaviour, Mathematical Modelling, 3, 5, 29-48 (1991), (in Russian) · Zbl 1189.93019 |

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[7] | Molodtsov, D. A., To a general theory of abstract interval integral (1991), Preprint of Computer Center of Russian Academy of Sciences: Preprint of Computer Center of Russian Academy of Sciences Moscow, (in Russian) · Zbl 0760.28009 |

[8] | Molodtsov, D. A., An approximate integral in multidimensional case (1989), Preprint of Computer Center of Russian Academy of Sciences: Preprint of Computer Center of Russian Academy of Sciences Moscow, (in Russian) · Zbl 0767.26009 |

[9] | Molodtsov, D. A., The law of large numbers for interval probability (mathematical apparatus) (1992), Preprint of Computer Center of Russian Academy of Sciences: Preprint of Computer Center of Russian Academy of Sciences Moscow, (in Russian) |

[10] | Molodtsov, D. A., The law of large numbers for interval probability (product space) (1992), Preprint of Computer Center of Russian Academy of Sciences: Preprint of Computer Center of Russian Academy of Sciences Moscow, (in Russian) |

[11] | Kuznetsov, V. P., Interval Statistical Models (1991), Radio and Svyaz: Radio and Svyaz Moscow, (in Russian) |

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