On generalized fuzzy numbers
Authors
Abstract:
This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrated into a partial ordering set, a semi-ring and a complete non-separable metric space. Again, through two isomorphism theorem, the relationship between generalized fuzzy number space and fuzzy number space is established. Finally, as an application of generalized fuzzy numbers, the concept of continuous generalized fuzzy number-valued functions is introduced. And it is pointed out that many results of trapezoidal generalized fuzzy numbers can also be extended to generalized fuzzy numbers.
similar resources
New Generalized Interval Valued Intuitionistic Fuzzy Numbers
The aim of this paper is investigate the notion of a generalized interval valued intuitionistic fuzzy number (GIVIFN), which extends the interval valuedintuitionistic fuzzy number. Firstly, the concept of GIVIFNBs is introduced.Arithmetic operations and cut sets over GIVIFNBBs are investigated. Then the values and ambiguities of the membership degree and the non-membership degree and the value ...
full textFuzzy Similarity Measure for Generalized Fuzzy Numbers
This paper proposes a new fuzzy similarity measure to calculate the degree of similarity of generalized fuzzy numbers (GFN’s).The fuzzy similarity measure is developed by integrating the concept of centre of gravity (COG) points and fuzzy difference of distance of points of fuzzy numbers. A fuzzy description for difference of distances between fuzzy numbers in its turn exploits appropriate simi...
full textFUZZY RISK ANALYSIS BASED ON A NEW METHOD FOR RANKING GENERALIZED FUZZY NUMBERS
Fuzzy risk analysis, as a powerful tool to address uncertain information, can provide an appropriate method for risk analysis. However, the previous fuzzy risk analysis methods still have some weaknesses. To overcome the weaknesses of existing fuzzy risk analysis methods, a novel method for ranking generalized fuzzy numbers is proposed for addressing fuzzy risk analysis problems. In the propose...
full textGeneralized Fuzzy Numbers Comparison by Geometric Moments
-In the field of engineering and economic studies, mathematical manipulation of fuzzy numbers is cumbersome and does not provide a neatly ordered set of results in the same way that crisp numbers do. Moreover, the generalized fuzzy number (i.e. non-normalized and normalized fuzzy number) have been approved more flexible and more intelligent than the normalized fuzzy number since it takes the de...
full textMy Resources
Journal title
volume 16 issue 1
pages 61- 73
publication date 2019-02-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023