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The order structure of fuzzy numbers based on the level characteristics and its application to optimization problems

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Abstract

Ranking and comparing fuzzy numbers is an important part in many fuzzy optimization problems such as intelligent control and manufacturing system production line scheduling with uncertainty environments. In this paper, based on the level characteristic function andα-average of level cut sets of fuzzy number, we establish the IMα-metric method for measuring fuzzy number as a whole, and introduce the concept of IDα-difference that describes the reliability of IMα-metric value. Further, the basic properties and the separability of IMα-metric and IDα-difference are discussed. Finally, we give a mathematical model to solve fuzzy optimization problems by means of IMα-metric.

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Authors and Affiliations

  1. Department of Automation, Tsinghua University, 100084, Beijing, China

    Liu Min, Li Fachao & Wu Cheng

Authors
  1. Liu Min
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  2. Li Fachao
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  3. Wu Cheng
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Correspondence to Liu Min.

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Liu, M., Li, F. & Wu, C. The order structure of fuzzy numbers based on the level characteristics and its application to optimization problems. Sci China Ser F 45, 433–441 (2002). https://doi.org/10.1360/02yf9037

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  • DOI: https://doi.org/10.1360/02yf9037

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