Triangular picture fuzzy linguistic induced ordered weighted aggregation operators and its application on decision making problems

Muhammad Qiyas; Saleem Abdullah; Shahzaib Ashraf; Saifullah Khan; Aziz Khan

doi:10.3934/mfc.2019013

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2019, Volume 2, Issue 3: 183-201. Doi: 10.3934/mfc.2019013

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Triangular picture fuzzy linguistic induced ordered weighted aggregation operators and its application on decision making problems

Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, 2320, Pakistan

^* Corresponding author: Saleem Abdullah
^* Corresponding author: Saleem Abdullah

Received: January 31, 2019

Revised: April 30, 2019

Published: September 2019

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Abstract

The primary goal of this paper is to solve the investment problem based on linguistic picture decision making method under the linguistic triangular picture linguistic fuzzy environment. First to define the triangular picture linguistic fuzzy numbers. Further, we define operations on triangular picture linguistic fuzzy numbers and their aggregation operator namely, triangular picture fuzzy linguistic induce OWA (TPFLIOWA) and triangular picture fuzzy linguistic induce OWG (TPFLIOWG) operators. Multi-criteria group decision making method is developed based on TPFLIOWA and TPFLIOWG operators and solve the uncertainty in the investment problem. We study the applicability of the proposed decision making method under triangular picture linguistic fuzzy environment and construct a descriptive example of investment problem. We conclude from the comparison and sensitive analysis that the proposed decision making method is more effective and reliable than other existing models.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Table 4.

Method	Ranking
TPFLIOWA	$\overset{\sim }{e}_{1}\succ _{PF}\overset{\sim }{e}_{2}\succ _{PF}\overset{\sim }{e}_{4}\succ _{PF}\overset{\sim }{e}_{5}\succ _{PF} \overset{\sim }{e}_{3}$
TPFLIOWG	$\overset{\sim }{e}_{1}\succ _{PF}\overset{\sim }{e}_{2}\succ _{PF}\overset{\sim }{e}_{5}\succ _{PF}\overset{\sim }{e}_{4}\succ _{PF} \overset{\sim }{e}_{3}$
IFLIOWA [53]	ş$_{\overset{\sim }{e}_{1}}\succ _{IF}$ş$_{ \overset{\sim }{e}_{4}}\succ _{IF}$ş$_{\overset{\sim }{e}_{2}}\succ _{IF} $ş$_{\overset{\sim }{e}_{5}}\succ _{IF}$ş$_{\overset{\sim }{e} _{3}}$
IFLIOWG [53]	ş$_{\overset{\sim }{e}_{1}}\succ _{IF}$ş$_{ \overset{\sim }{e}_{5}}\succ _{IF}$ş$_{\overset{\sim }{e}_{4}}\succ _{IF} $ş$_{\overset{\sim }{e}_{2}}\succ _{IF}$ş$_{\overset{\sim }{e} _{3}}$

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