IDEAS home Printed from https://ideas.repec.org/a/spr/fuzodm/v17y2018i3d10.1007_s10700-017-9275-y.html
   My bibliography  Save this article

The chain and substitution rules of interval-valued intuitionistic fuzzy calculus

Author

Listed:
  • Yanmin Liu

    (PLA University of Science and Technology)

  • Hua Zhao

    (PLA University of Science and Technology)

  • Zeshui Xu

    (Sichuan University)

Abstract

The interval-valued intuitionistic fuzzy set proposed by Atanassov is the extension of intuitionistic fuzzy set. It extends the membership degree and non-membership to interval values instead of a single value. So it contains more possible values and maybe more considerate. Among all the researches, the exploration on the calculus of interval-valued intuitionistic fuzzy set is entirely new. Recently, Zhao et al. (Int J Comput Intell Syst 9:36–56, 2016) proposed the concept of interval-valued intuitionistic fuzzy function (IVIFF) and gave a calculation method of derivative and differential of IVIFF. Based on this work, in this paper, firstly, we utilize a new and easier method to express the derivative and differential of IVIFF. Secondly, we propose the chain rules of derivative and the form invariance of differential in the interval-valued intuitionistic fuzzy environment. In addition, some properties of the substation rules for interval-valued intuitionistic fuzzy indefinite integrals and definite integrals are also developed.

Suggested Citation

  • Yanmin Liu & Hua Zhao & Zeshui Xu, 2018. "The chain and substitution rules of interval-valued intuitionistic fuzzy calculus," Fuzzy Optimization and Decision Making, Springer, vol. 17(3), pages 265-285, September.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:3:d:10.1007_s10700-017-9275-y
    DOI: 10.1007/s10700-017-9275-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10700-017-9275-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10700-017-9275-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Joshi, Deepa & Kumar, Sanjay, 2016. "Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making," European Journal of Operational Research, Elsevier, vol. 248(1), pages 183-191.
    2. Xunjie Gou & Zeshui Xu, 2017. "Exponential operations for intuitionistic fuzzy numbers and interval numbers in multi-attribute decision making," Fuzzy Optimization and Decision Making, Springer, vol. 16(2), pages 183-204, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shuli Liu & Xinwang Liu, 2016. "A Sample Survey Based Linguistic MADM Method with Prospect Theory for Online Shopping Problems," Group Decision and Negotiation, Springer, vol. 25(4), pages 749-774, July.
    2. Dheeraj Kumar Joshi & Ismat Beg & Sanjay Kumar, 2018. "Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems," Mathematics, MDPI, vol. 6(4), pages 1-20, March.
    3. Kuo, Ting, 2017. "A modified TOPSIS with a different ranking index," European Journal of Operational Research, Elsevier, vol. 260(1), pages 152-160.
    4. Shouzhen Zeng & Jianping Chen & Xingsen Li, 2016. "A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 403-422, March.
    5. Babak Daneshvar Rouyendegh & Kazim Topuz & Ali Dag & Asil Oztekin, 2019. "An AHP-IFT Integrated Model for Performance Evaluation of E-Commerce Web Sites," Information Systems Frontiers, Springer, vol. 21(6), pages 1345-1355, December.
    6. Kumar, S. Charles Ruskin & Anuradha, R. & Dharmaraj, R., 2021. "Numerical investigation on ultra-high performance concrete beam under pure bending," Resources Policy, Elsevier, vol. 74(C).
    7. Yuan Rong & Yi Liu & Zheng Pei, 2020. "Novel Multiple Attribute Group Decision-Making Methods Based on Linguistic Intuitionistic Fuzzy Information," Mathematics, MDPI, vol. 8(3), pages 1-30, March.
    8. Runtong Zhang & Yuping Xing & Jun Wang & Xiaopu Shang & Xiaomin Zhu, 2018. "A Novel Multiattribute Decision-Making Method Based on Point–Choquet Aggregation Operators and Its Application in Supporting the Hierarchical Medical Treatment System in China," IJERPH, MDPI, vol. 15(8), pages 1-29, August.
    9. Tian Chen & Shiyao Li & Chun-Ming Yang & Wenting Deng, 2022. "Developing an Enterprise Diagnostic Index System Based on Interval-Valued Hesitant Fuzzy Clustering," Mathematics, MDPI, vol. 10(14), pages 1-22, July.
    10. Chen, J.J. & Wu, Q.H. & Zhang, L.L. & Wu, P.Z., 2017. "Multi-objective mean–variance–skewness model for nonconvex and stochastic optimal power flow considering wind power and load uncertainties," European Journal of Operational Research, Elsevier, vol. 263(2), pages 719-732.
    11. Wan, Shuping & Wang, Feng & Dong, Jiuying, 2017. "Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making," European Journal of Operational Research, Elsevier, vol. 263(2), pages 571-582.
    12. Junling Zhang & Xiaowen Qi & Changyong Liang, 2018. "Tackling Complexity in Green Contractor Selection for Mega Infrastructure Projects: A Hesitant Fuzzy Linguistic MADM Approach with considering Group Attitudinal Character and Attributes’ Interdependen," Complexity, Hindawi, vol. 2018, pages 1-31, December.
    13. Roman Vavrek, 2019. "Evaluation of the Impact of Selected Weighting Methods on the Results of the TOPSIS Technique," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1821-1843, November.
    14. Xiaohong Chen & Mengjing Wu & Chunqiao Tan & Tao Zhang, 2021. "A random intuitionistic fuzzy factor analysis model for complex multi-attribute large group decision-making in dynamic environments," Fuzzy Optimization and Decision Making, Springer, vol. 20(1), pages 101-127, March.
    15. Zhang, Zhi-Gang & Hu, Xiao & Liu, Zhao-Ting & Zhao, Lu-Tao, 2021. "Multi-attribute decision making: An innovative method based on the dynamic credibility of experts," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    16. Song-Man Wu & Hu-Chen Liu & Li-En Wang, 2017. "Hesitant fuzzy integrated MCDM approach for quality function deployment: a case study in electric vehicle," International Journal of Production Research, Taylor & Francis Journals, vol. 55(15), pages 4436-4449, August.
    17. Zacharoula Andreopoulou & Christiana Koliouska, 2018. "Benchmarking Internet Promotion of Renewable Energy Enterprises: Is Sustainability Present?," Sustainability, MDPI, vol. 10(11), pages 1-12, November.
    18. Mei Cai & Stephen M. Marson, 2021. "A regional Natech risk assessment based on a Natech-prone facility network for dependent events," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(3), pages 2155-2174, July.
    19. Zhang, Mei-Jing & Wang, Ying-Ming & Li, Ling-Hui & Chen, Sheng-Qun, 2017. "A general evidential reasoning algorithm for multi-attribute decision analysis under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1005-1015.
    20. Meimei Xia & Jian Chen & Xiao-Jun Zeng, 2018. "Decision Analysis on Choquet Integral-Based Multi-Criteria Decision-Making with Imprecise Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 677-704, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:fuzodm:v:17:y:2018:i:3:d:10.1007_s10700-017-9275-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.