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Simplified interval-valued intuitionistic fuzzy integrals and their use in park siting

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Abstract

The interval-valued intuitionistic fuzzy sets have received great attention of researchers because they can comprehensively depict the characters of things. In the past few years, some scholars have investigated the calculus of intuitionistic fuzzy information, but yet there is no research on the integrals in interval-valued intuitionistic fuzzy circumstance. To fill this vacancy, in this paper, we shall focus on investigating the integrals of simplified interval-valued intuitionistic fuzzy functions (SIVIFFs) and give their application in group decision making. We first develop the indefinite and definite integrals of SIVIFFs, and study their characteristics in detail. Then we establish the relationship between these two classes of integrals by giving two Newton–Leibniz formulas for SIVIFFs. Finally, a practical example concerning the park siting problem is given to illustrate the application of simplified interval-valued intuitionistic fuzzy integrals.

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Authors and Affiliations

  1. Business School, Sichuan University, Chengdu, 610064, Sichuan, China

    Peijia Ren, Zeshui Xu & Jiuping Xu

  2. College of Science, PLA University of Science and Technology, Nanjing, 210007, Jiangsu, China

    Hua Zhao

Authors
  1. Peijia Ren
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  2. Zeshui Xu
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  3. Hua Zhao
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  4. Jiuping Xu
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Correspondence to Peijia Ren.

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The authors declare that they have no conflict of interest.

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Communicated by A. Di Nola.

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Ren, P., Xu, Z., Zhao, H. et al. Simplified interval-valued intuitionistic fuzzy integrals and their use in park siting. Soft Comput 20, 4377–4393 (2016). https://doi.org/10.1007/s00500-015-1996-7

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