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

Article type: Research Article

Authors: Shakeel, M.^{a; *} | Abdullah, S.^b | Shahzad, M.^a | Fahmi, A.^a

Affiliations: [a] Department of Mathematics, Hazara University, Mansehra, Pakistan | [b] Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan

Correspondence: [*] Corresponding author. E-mail: shakeelmath50@gmail.com.

Abstract: The aim of this paper is to investigate the information aggregation methods under induced interval-valued Pythagorean trapezoidal fuzzy environment. Some Einstein operational laws on Pythagorean trapezoidal fuzzy numbers are defined based on Einstein sum and Einstein product. In this paper, we introduce the idea of induced interval-valued Pythagorean trapezoidal fuzzy Einstein ordered weighted geometric (I-IVPTFEOWG) operator and induced interval-valued Pythagorean trapezoidal fuzzy Einstein hybrid geometric (I-IVPTFEHG) operator. We discuss some basic properties of the proposed operator, including idempotency, commutativity and monotonicity. We construct an algorithm for multiple attribute group decision making problem, and apply the proposed aggregation operator to deal with multiple attribute group decision making. Finally we construct a numerical example for multiple attribute group decision making and compare the result with existing methods.

Keywords: Pythagorean trapezoidal fuzzy numbers, induced interval-valued Pythagorean trapezoidal fuzzy numbers, Einstein operations, group decision making

DOI: 10.3233/JIN-180092

Journal: Journal of Integrative Neuroscience, vol. 17, no. 3-4, pp. 633-659, 2018