Linguistic Pythagorean Einstein Operators and Their Application to Decision Making

Abstract

Linguistic Pythagorean fuzzy (LPF) set is an efficacious technique to comprehensively represent uncertain assessment information by combining the Pythagorean fuzzy numbers and linguistic variables. In this paper, we define several novel essential operations of LPF numbers based upon Einstein operations and discuss several relations between these operations. For solving the LPF numbers fusion problem, several LPF aggregation operators, including LPF Einstein weighted averaging (LPFEWA) operator, LPF Einstein weighted geometric (LPFEWG) operator and LPF Einstein hybrid operator, are propounded; the prominent characteristics of these operators are investigated as well. Furthermore, a multi-attribute group decision making (MAGDM) approach is presented on the basis of the developed operators under an LPF environment. Ultimately, two application cases are utilized to demonstrate the practicality and feasibility of the developed decision approach and the comparison analysis is provided to manifest the merits of it.

Multiple Attribute Group Decision-Making process based on Generalized Archimedean Linguistic Pythagorean Fuzzy Averaging Aggregation Operators

“…Especially, if F * = F * 1 , then aggregation operators mentioned in Eqs. ( 46)-( 48) become the aggregation operators proposed by Rong et al [37].…”

“…Besides, he also defined some linguistic Pythagorean fuzzy AOs for solving MAGDM problems. Rong et al [37] given some Einstein AOs for linguistic Pythagorean fuzzy information. Recently, Liu et al [38] defined some new AOs under LPF environment using Archimedean t-norm & t-conorm.…”

“…Remark 2 Note that if F * = F * 1 , then above defined operational laws are reduced to the Einstein operations for LPFNs proposed by Rong et al [37].…”

Novel Multiple Attribute Group Decision-Making Methods Based on Linguistic Intuitionistic Fuzzy Information

“…The concept of LIFN firstly proposed by Chen et al [44] in 2015, which is defined as below. 8] , with κ = 2, then we have…”

“…Multiple attribute group decision-making (MAGDM) is a significant constituent of modern decision science domains, the essence of which is to select the optimal alternatives on the basis of the assessment information obtained from a group of experts in terms of several given attributes. MAGDM problems are ubiquitous in various aspects of human life and have been paid a growing amount of attention by many scholars and fruitful research achievements have been made in this area [1][2][3][4][5][6][7][8]. As a result of the vagueness and uncertainty of DM settings and the difference of diverse experts' knowledge levels, how to accurately represent the attribute assessment information in vague and nondeterminate environments is one of the most arduous challenges in the course of DM.…”