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Geometric aggregation operators with interval-valued Pythagorean trapezoidal fuzzy numbers based on Einstein operations and their application in group decision making

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Abstract

The aim of this paper is to investigate information aggregation methods under interval-valued Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on interval-valued Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. Based on Einstein operations, we define interval-valued Pythagorean trapezoidal fuzzy aggregation operators, such as interval-valued Pythagorean trapezoidal fuzzy Einstein weighted geometric operator, interval-valued Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric operator and interval-valued Pythagorean trapezoidal fuzzy Einstein hybrid geometric operator. Furthermore, we apply the proposed aggregation operators to deal with multiple attribute group decision making problem. Finally we construct a numerical example for multiple attribute group decision making problem and compare the result with existing methods.

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Authors and Affiliations

  1. Department of Mathematics, Hazara University Mansehra Kpk, Dhodial, Pakistan

    M. Shakeel & M. Shahzad

  2. Department of Mathematics, Abdul Wali Khan University Mardan Kpk, Mardan, Pakistan

    S. Abdullah

  3. Department of Mathematics, University of Engineering and Technology Taxila, Taxila, Pakistan

    Nasir Siddiqui

Authors
  1. M. Shakeel
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  2. S. Abdullah
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  3. M. Shahzad
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  4. Nasir Siddiqui
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Correspondence to M. Shakeel.

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Shakeel, M., Abdullah, S., Shahzad, M. et al. Geometric aggregation operators with interval-valued Pythagorean trapezoidal fuzzy numbers based on Einstein operations and their application in group decision making. Int. J. Mach. Learn. & Cyber. 10, 2867–2886 (2019). https://doi.org/10.1007/s13042-018-00909-y

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  • DOI: https://doi.org/10.1007/s13042-018-00909-y

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