L_p-Type of Weighted Fuzzy Number Metrics Induced by Fuzzy Structured Element

Abstract:

For the objective fact that elements with different membership degrees should have different contribution to the metric measure between fuzzy numbers, this paper presents Lp-type of fuzzy number metrics weighted by structured element. Firstly, we define a metric weighted by structured element on the family (B[-1,1]) of all the same monotone and standard bounded functions on closed interval [-1,1] , and discuss the completeness and separability of those metric spaces; Next, using the fuzzy functional induced by normal fuzzy structured element, we give out a method that the metric of the closed bounded fuzzy number space is induced by the metric on function space B[-1,1]. Furthermore, a fuzzy number metric weighted by structured element which is induced by is presented ,and analyze completeness and separability of the induced fuzzy number metric spaces; Lastly, the difference and relationship between and the metric defined by traditional method are shown.

• Periodical: Advanced Materials Research (Volume 981)
• Pages: 279-286
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.981.279
• Online since: July 2014
• Authors: Fei Zhao*, Si Zong Guo
• Keywords: E-L_p Metric, Fuzzy Number, Fuzzy Structured Element, Weighted Function

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