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Exponential, Logarithmic and Compensative Generalized Aggregation Operators Under Complex Intuitionistic Fuzzy Environment

Author

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  • Harish Garg

    (Thapar Institute of Engineering and Technology (Deemed University))

  • Dimple Rani

    (Thapar Institute of Engineering and Technology (Deemed University))

Abstract

This manuscript presents some new exponential, logarithmic and compensative exponential of logarithmic operational laws based on t-norm and co-norm for complex intuitionistic fuzzy (CIF) numbers. The prevailing extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can deal with only one-dimensional problems due to which some important information may be lost in some situations. A modification to these, CIF sets are characterized by complex-valued degrees of satisfaction and dissatisfaction and handle two dimensional data simultaneously in one set using additional terms, called phase terms, which generally give information related with periodicity. Motivated by the characteristics of CIF model, we present some new operational laws and compensative operators namely generalized CIF compensative weighted averaging and generalized CIF compensative weighted geometric. Some properties related to proposed operators are discussed. In light of the developed operators, a group decision-making method is put forward in which weights are determined objectively and is illustrated with the aid of an example. The reliability of the presented decision-making method is explored by comparing it with several prevailing studies. The influence of the parameters used in exponential and logarithmic operations on CIF numbers is also discussed.

Suggested Citation

  • Harish Garg & Dimple Rani, 2019. "Exponential, Logarithmic and Compensative Generalized Aggregation Operators Under Complex Intuitionistic Fuzzy Environment," Group Decision and Negotiation, Springer, vol. 28(5), pages 991-1050, October.
    • Handle: RePEc:spr:grdene:v:28:y:2019:i:5:d:10.1007_s10726-019-09631-8
    DOI: 10.1007/s10726-019-09631-8
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    References listed on IDEAS

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    1. Tanuj Kumar & Rakesh Kumar Bajaj, 2014. "On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies," Journal of Mathematics, Hindawi, vol. 2014, pages 1-12, December.
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    Cited by:

    1. Harish Garg & Jeonghwan Gwak & Tahir Mahmood & Zeeshan Ali, 2020. "Power Aggregation Operators and VIKOR Methods for Complex q-Rung Orthopair Fuzzy Sets and Their Applications," Mathematics, MDPI, vol. 8(4), pages 1-34, April.
    2. Jiefeng Wang & Shouzhen Zeng & Chonghui Zhang, 2020. "Single-Valued Neutrosophic Linguistic Logarithmic Weighted Distance Measures and Their Application to Supplier Selection of Fresh Aquatic Products," Mathematics, MDPI, vol. 8(3), pages 1-14, March.
    3. Shouzhen Zeng & Harish Garg & Muhammad Munir & Tahir Mahmood & Azmat Hussain, 2019. "A Multi-Attribute Decision Making Process with Immediate Probabilistic Interactive Averaging Aggregation Operators of T-Spherical Fuzzy Sets and Its Application in the Selection of Solar Cells," Energies, MDPI, vol. 12(23), pages 1-26, November.

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