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Decision and Game Theory in Management With Intuitionistic Fuzzy Sets pp 1–46Cite as

Intuitionistic Fuzzy Set Theories

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 308))

Abstract

In real-life management situations, there exist a great deal of fuzziness. In 1965, Zadeh [1] firstly introduced the concept of the fuzzy set, which is an effective tool to deal with fuzziness. However, the fuzzy set employs single index (i.e., membership degree or function) to describe the two states of the support and opposition simultaneously. Namely, if the membership degree of supporting some proposition or phenomena \( x \) is \( \mu (x) \), then the membership degree of opposing the proposition or phenomena \( x \) is just equal to the complement to 1, i.e., \( 1 - \mu (x) \). Hereby, the fuzzy set is no means to describe the neutral state, i.e., neither support nor opposition.

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Notes

  1. 1.

    Reference [2] is not the article on the intuitionistic fuzzy set firstly published by Atanassov. In fact, the first article on the intuitionistic fuzzy set is the one in Bulgarian, which is "Intuitionistic fuzzy sets" published in Seventh Scientific Session of ITKR, Sofia, June 1983 (Deposited in the Central Science-Technical Library of Bulgarian Academy of Science, 1697/84) [7, 8].

  2. 2.

    According to the notations in Sect. 1.5.2, the symbols of the addition, subtraction, multiplication and division based on the extension principle of the intuitionistic fuzzy set should be denoted by \( \tilde{ + } \), \( \tilde{ - } \), \( \tilde{ \times } \) and \( \tilde{ \div } \) (or \( {\tilde{/}} \)), respectively. However, for the sake of convenience, they are respectively denoted by \( + \), \( - \), \( \times \) and \( \div \) (or /) for short unless otherwise stated.

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  1. School of Management, Fuzhou University, Fuzhou, People’s Republic of China

    Deng-Feng Li

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Li, DF. (2014). Intuitionistic Fuzzy Set Theories. In: Decision and Game Theory in Management With Intuitionistic Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40712-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-40712-3_1

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