IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i18p2337-d639714.html
   My bibliography  Save this article

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

Author

Listed:
  • Gia Sirbiladze

    (Department of Computer Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, 0186 Tbilisi, Georgia)

Abstract

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms ( T p , S p q ) and ( T min , S max ) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

Suggested Citation

  • Gia Sirbiladze, 2021. "Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment," Mathematics, MDPI, vol. 9(18), pages 1-36, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2337-:d:639714
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/18/2337/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/18/2337/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    2. Chou, Shuo-Yan & Chang, Yao-Hui & Shen, Chun-Ying, 2008. "A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes," European Journal of Operational Research, Elsevier, vol. 189(1), pages 132-145, August.
    3. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    4. Peide Liu & Xinli You, 2018. "Some linguistic neutrosophic Hamy mean operators and their application to multi-attribute group decision making," PLOS ONE, Public Library of Science, vol. 13(3), pages 1-26, March.
    5. Merigó, José M. & Casanovas, Montserrat & Yang, Jian-Bo, 2014. "Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators," European Journal of Operational Research, Elsevier, vol. 235(1), pages 215-224.
    6. Wen Jiang & Boya Wei, 2018. "Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(3), pages 582-594, February.
    7. Guiwu Wei, 2018. "Uncertain Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making," International Journal of Decision Support System Technology (IJDSST), IGI Global, vol. 10(2), pages 40-64, April.
    8. Aikens, C. H., 1985. "Facility location models for distribution planning," European Journal of Operational Research, Elsevier, vol. 22(3), pages 263-279, December.
    9. Erkut, Erhan & Karagiannidis, Avraam & Perkoulidis, George & Tjandra, Stevanus A., 2008. "A multicriteria facility location model for municipal solid waste management in North Greece," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1402-1421, June.
    10. Terry Ross, G. & Soland, Richard M., 1980. "A multicriteria approach to the location of public facilities," European Journal of Operational Research, Elsevier, vol. 4(5), pages 307-321, May.
    11. Muhammad Riaz & Wojciech Sałabun & Hafiz Muhammad Athar Farid & Nawazish Ali & Jarosław Wątróbski, 2020. "A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management," Energies, MDPI, vol. 13(9), pages 1-39, May.
    12. Guiwu Wei, 2016. "Picture fuzzy cross-entropy for multiple attribute decision making problems," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 17(4), pages 491-502, July.
    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. Jiahuan He & Xindi Wang & Runtong Zhang & Li Li, 2019. "Some q -Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment," Mathematics, MDPI, vol. 7(5), pages 1-28, May.
    2. Gia Sirbiladze & Otar Badagadze, 2017. "Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 245-279, January.
    3. Olivares-Benitez, Elias & Ríos-Mercado, Roger Z. & González-Velarde, José Luis, 2013. "A metaheuristic algorithm to solve the selection of transportation channels in supply chain design," International Journal of Production Economics, Elsevier, vol. 145(1), pages 161-172.
    4. Siqi Zhang & Hui Gao & Guiwu Wei & Yu Wei & Cun Wei, 2019. "Evaluation Based on Distance from Average Solution Method for Multiple Criteria Group Decision Making under Picture 2-Tuple Linguistic Environment," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    5. Bhuvnesh Sharma & M. Ramkumar & Nachiappan Subramanian & Bharat Malhotra, 2019. "Dynamic temporary blood facility location-allocation during and post-disaster periods," Annals of Operations Research, Springer, vol. 283(1), pages 705-736, December.
    6. Meiling Liu & Shouzhen Zeng & Tomas Baležentis & Dalia Streimikiene, 2019. "Picture Fuzzy Weighted Distance Measures and their Application to Investment Selection," The AMFITEATRU ECONOMIC journal, Academy of Economic Studies - Bucharest, Romania, vol. 21(52), pages 682-682, August.
    7. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    8. Liangping Wu & Guiwu Wei & Hui Gao & Yu Wei, 2018. "Some Interval-Valued Intuitionistic Fuzzy Dombi Hamy Mean Operators and Their Application for Evaluating the Elderly Tourism Service Quality in Tourism Destination," Mathematics, MDPI, vol. 6(12), pages 1-20, December.
    9. Toso, Eli Angela V. & Alem, Douglas, 2014. "Effective location models for sorting recyclables in public management," European Journal of Operational Research, Elsevier, vol. 234(3), pages 839-860.
    10. Gia Sirbiladze, 2016. "New Fuzzy Aggregation Operators Based on the Finite Choquet Integral — Application in the MADM Problem," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 517-551, May.
    11. Elias Olivares-Benitez & José González-Velarde & Roger Ríos-Mercado, 2012. "A supply chain design problem with facility location and bi-objective transportation choices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 729-753, October.
    12. Feng, Cheng-Min & Wu, Pei-Ju & Chia, Kai-Chieh, 2010. "A hybrid fuzzy integral decision-making model for locating manufacturing centers in China: A case study," European Journal of Operational Research, Elsevier, vol. 200(1), pages 63-73, January.
    13. Vladimir Simić & Radovan Soušek & Stefan Jovčić, 2020. "Picture Fuzzy MCDM Approach for Risk Assessment of Railway Infrastructure," Mathematics, MDPI, vol. 8(12), pages 1-29, December.
    14. Liu, Yanchao, 2023. "An elliptical cover problem in drone delivery network design and its solution algorithms," European Journal of Operational Research, Elsevier, vol. 304(3), pages 912-925.
    15. Gia Sirbiladze & Anna Sikharulidze, 2018. "Extensions of Probability Intuitionistic Fuzzy Aggregation Operators in Fuzzy MCDM/MADM," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 621-655, March.
    16. Tehreem Ayaz & Mohammad M. Al-Shomrani & Saleem Abdullah & Amjad Hussain, 2020. "Evaluation of Enterprise Production Based on Spherical Cubic Hamacher Aggregation Operators," Mathematics, MDPI, vol. 8(10), pages 1-40, October.
    17. Coutinho-Rodrigues, João & Tralhão, Lino & Alçada-Almeida, Luís, 2012. "A bi-objective modeling approach applied to an urban semi-desirable facility location problem," European Journal of Operational Research, Elsevier, vol. 223(1), pages 203-213.
    18. Farahani, Reza Zanjirani & Fallah, Samira & Ruiz, Rubén & Hosseini, Sara & Asgari, Nasrin, 2019. "OR models in urban service facility location: A critical review of applications and future developments," European Journal of Operational Research, Elsevier, vol. 276(1), pages 1-27.
    19. Suizhi Luo & Lining Xing, 2019. "Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection," Mathematics, MDPI, vol. 8(1), pages 1-23, December.
    20. Jesus Gonzalez-Feliu, 2013. "Multi-stage LTL transport systems in supply chain management," Post-Print halshs-00796714, HAL.

    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:9:y:2021:i:18:p:2337-:d:639714. 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.