IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i7p1143-d383832.html
   My bibliography  Save this article

Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values

Author

Listed:
  • Feng Feng

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
    Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

  • Yujuan Zheng

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

  • José Carlos R. Alcantud

    (BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain)

  • Qian Wang

    (Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China)

Abstract

In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article.

Suggested Citation

  • Feng Feng & Yujuan Zheng & José Carlos R. Alcantud & Qian Wang, 2020. "Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values," Mathematics, MDPI, vol. 8(7), pages 1-30, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1143-:d:383832
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/7/1143/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/7/1143/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xiaoyan Liu & Hee Sik Kim & Feng Feng & José Carlos R. Alcantud, 2018. "Centroid Transformations of Intuitionistic Fuzzy Values Based on Aggregation Operators," Mathematics, MDPI, vol. 6(11), pages 1-17, October.
    2. José Carlos R. Alcantud & María D. García-Sanz, 2013. "Evaluations of Infinite Utility Streams: Pareto Efficient and Egalitarian Axiomatics," Metroeconomica, Wiley Blackwell, vol. 64(3), pages 432-447, July.
    3. Feng Feng & Meiqi Liang & Hamido Fujita & Ronald R. Yager & Xiaoyan Liu, 2019. "Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships," Mathematics, MDPI, vol. 7(2), pages 1-26, February.
    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. Sakamoto, Norihito & 坂本, 徳仁, 2011. "Impossibilities of Paretian Social Welfare Functions for Infinite Utility Streams with Distributive Equity," Discussion Papers 2011-09, Graduate School of Economics, Hitotsubashi University.
    2. Alcantud, José Carlos R., 2012. "Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto," Journal of Economic Theory, Elsevier, vol. 147(1), pages 353-363.
    3. Sakamoto, Norihito, 2012. "Impossibilities Of Paretian Social Welfare Functions For Infinite Utility Streams With Distributive Equity," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 53(2), pages 121-130, December.
    4. Dubey, Ram Sewak, 2016. "On construction of social welfare orders satisfying Hammond equity and Weak Pareto axioms," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 119-124.
    5. José Carlos R. Alcantud, 2013. "The impossibility of social evaluations of infinite streams with strict inequality aversion," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(2), pages 123-130, November.
    6. Toyotaka Sakai, 2010. "Intergenerational equity and an explicit construction of welfare criteria," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(3), pages 393-414, September.
    7. Gulfam Shahzadi & Muhammad Akram & Ahmad N. Al-Kenani, 2020. "Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    8. José Alcantud, 2013. "Liberal approaches to ranking infinite utility streams: when can we avoid interference?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 381-396, July.
    9. Peter Vassilev & Todor Stoyanov & Lyudmila Todorova & Alexander Marazov & Velin Andonov & Nikolay Ikonomov, 2023. "Orderings over Intuitionistic Fuzzy Pairs Generated by the Power Mean and the Weighted Power Mean," Mathematics, MDPI, vol. 11(13), pages 1-15, June.
    10. Dubey, Ram Sewak & Laguzzi, Giorgio, 2021. "Equitable preference relations on infinite utility streams," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    11. Ram Dubey & Tapan Mitra, 2014. "Combining monotonicity and strong equity: construction and representation of orders on infinite utility streams," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(3), pages 591-602, October.
    12. Anam Luqman & Muhammad Akram & Ahmad N. Al-Kenani, 2019. "q -Rung Orthopair Fuzzy Hypergraphs with Applications," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    13. Dubey, Ram Sewak & Mitra, Tapan, 2014. "On construction of equitable social welfare orders on infinite utility streams," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 53-60.
    14. Ram Sewak Dubey & Tapan Mitra, 2015. "On social welfare functions on infinite utility streams satisfying Hammond Equity and Weak Pareto axioms: a complete characterization," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 169-180, October.

    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:gam:jmathe:v:8:y:2020:i:7:p:1143-:d:383832. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.