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A novel method to rank fuzzy numbers using the developed golden rule representative value

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Abstract

Ranking fuzzy numbers is an important subject of fuzzy set theory, which has been widely studied and applied to many practical problems. However, the previous fuzzy number ranking methods have some weaknesses, such as incomplete ranking objects, complicated calculations, and ignoring interpretability. To overcome these weaknesses and develop a ranking method that performs better in all aspects, the concept of the golden rule representative value is used. The golden rule representative value was first introduced by Yager to solve the order of interval values. This paper expands it and proposes a novel fuzzy number ranking method based on the developed golden rule representative value. The centroid point and area of fuzzy numbers are considered, and some new rules are formulated to capture the preference of the decision-maker. The TSK fuzzy model is used to model the rules. The constructed Rep function associates each fuzzy number with a scalar value. By comparing these scalar values, we get the ranking order of fuzzy numbers. The proposed ranking method is simple to use and can overcome the shortcomings of existing methods. Some specific numerical examples are used to illustrate the property of the proposed method, and the corresponding explanations show the interpretability of the ranking process. The comparative experiment with the existing ranking method shows the advantages of the proposed method. An application example of fuzzy risk analysis proves the effectiveness of the proposed method.

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Acknowledgment

The work is partially supported by the Fund of the National Natural Science Foundation of China (Grant No.61903307), China Postdoctoral Science Foundation (Grant No. 2020M683575), Chinese Universities Scientific Fund (Grant No. 2452018066), Key R&D Program of Shaanxi Province, China (Grant No.2019NY-164) and the National College Students Innovation and Entrepreneurship Training Program (Grant No. 202110712143, No.202110712146).

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Authors and Affiliations

  1. College of Information Engineering, Northwest A, F University, Yangling, Shaanxi, 712100, China

    Ruolan Cheng, Bingyi Kang & Jianfeng Zhang

  2. Key Laboratory of Agricultural Internet of Things, Ministry of Agriculture and Rural Affairs, Yangling, Shaanxi, 712100, China

    Bingyi Kang

  3. Shaanxi Key Laboratory of Agricultural Information Perception and Intelligent Service, Yangling, Shaanxi, 712100, China

    Bingyi Kang

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  1. Ruolan Cheng
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  2. Bingyi Kang
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  3. Jianfeng Zhang
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Correspondence to Bingyi Kang.

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Cheng, R., Kang, B. & Zhang, J. A novel method to rank fuzzy numbers using the developed golden rule representative value. Appl Intell 52, 9751–9767 (2022). https://doi.org/10.1007/s10489-021-02965-4

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