Cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators

Riaz, Muhammad; Tehrim, Syeda Tayyba

doi:10.1007/s00500-020-04927-3

Cited by 43 publications

(22 citation statements)

References 46 publications

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“…Riaz et al [46] introduced a robust q-rung orthopair fuzzy Einstein prioritized aggregation operators with application towards MCGDM. Riaz and Tehrim [47,48] introduced the concept of cubic bipolar fuzzy set with application to multicriteria group decision making using geometric aggregation operators. ey proposed a robust extension of the VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory-based metric spaces.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Pythagorean $m$ -Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making

Riaz

Naeem

Chinram

et al. 2021

Journal of Mathematics

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The role of multipolar uncertain statistics cannot be unheeded while confronting daily life problems on well-founded basis. Fusion (aggregation) of a number of input values in multipolar form into a sole multipolar output value is an essential tool not merely of physics or mathematics but also of widely held problems of economics, commerce and trade, engineering, social sciences, decision-making problems, life sciences, and many more. The problem of aggregation is very wide-ranging and fascinating, in general. We use, in this article, Pythagorean fuzzy numbers (PFNs) in multipolar form to contrive imprecise information. We introduce Pythagorean m -polar fuzzy weighted averaging (P m FWA), Pythagorean m -polar fuzzy weighted geometric (P m FWG), symmetric Pythagorean m -polar fuzzy weighted averaging (SP m FWA), and symmetric Pythagorean m -polar fuzzy weighted geometric (SP m FWG) operators for aggregating uncertain data. Finally, we present a practical example to illustrate the application of the proposed operators and to demonstrate its practicality and effectiveness towards investment strategic decision making.

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Section: Introduction and Literature Reviewmentioning

confidence: 99%

Pythagorean $m$ -Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making

Riaz

Naeem

Chinram

et al. 2021

Journal of Mathematics

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“…LDFS with indicative attributes improves the existing approaches and the decision experts (DEs) can select the grading values without any restriction. Riaz and Tehrim [24] introduced cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators. Riaz and Tehrim [25] used a robust extension of VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory based metric spaces.…”

Section: Literature Reviewmentioning

confidence: 99%

q-Rung Orthopair Fuzzy Geometric Aggregation Operators Based on Generalized and Group-Generalized Parameters with Application to Water Loss Management

et al. 2020

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The notions of fuzzy set (FS) and intuitionistic fuzzy set (IFS) make a major contribution to dealing with practical situations in an indeterminate and imprecise framework, but there are some limitations. Pythagorean fuzzy set (PFS) is an extended form of the IFS, in which degree of truthness and degree of falsity meet the condition 0≤Θ˘2(x)+K2(x)≤1. Another extension of PFS is a q´-rung orthopair fuzzy set (q´-ROFS), in which truthness degree and falsity degree meet the condition 0≤Θ˘q´(x)+Kq´(x)≤1,(q´≥1), so they can characterize the scope of imprecise information in more comprehensive way. q´-ROFS theory is superior to FS, IFS, and PFS theory with distinguished characteristics. This study develops a few aggregation operators (AOs) for the fusion of q´-ROF information and introduces a new approach to decision-making based on the proposed operators. In the framework of this investigation, the idea of a generalized parameter is integrated into the q´-ROFS theory and different generalized q´-ROF geometric aggregation operators are presented. Subsequently, the AOs are extended to a “group-based generalized parameter”, with the perception of different specialists/decision makers. We developed q´-ROF geometric aggregation operator under generalized parameter and q´-ROF geometric aggregation operator under group-based generalized parameter. Increased water requirements, in parallel with water scarcity, force water utilities in developing countries to follow complex operating techniques for the distribution of the available amounts of water. Reducing water losses from water supply systems can help to bridge the gap between supply and demand. Finally, a decision-making approach based on the proposed operator is being built to solve the problems under the q´-ROF environment. An illustrative example related to water loss management has been given to show the validity of the developed method. Comparison analysis between the proposed and the existing operators have been performed in term of counter-intuitive cases for showing the liability and dominance of proposed techniques to the existing one is also considered.

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“…Riaz and Tehrim [ 54 , 55 ] introduced geometric aggregation operators under cubic bipolar fuzzy sets. They presented a robust extension of VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory based metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets

Riaz

Hamid

Afzal³

et al. 2021

PLoS ONE

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q-Rung orthopair fuzzy set (qROFS) and m-polar fuzzy set (mPFS) are rudimentary concepts in the computational intelligence, which have diverse applications in fuzzy modeling and decision making under uncertainty. The aim of this paper is to introduce the hybrid concept of q-rung orthopair m-polar fuzzy set (qROmPFS) as a hybrid model of q-rung orthopair fuzzy set and m-polar fuzzy set. A qROmPFS has the ability to deal with real life situations when decision experts are interested to deal with multi-polarity as well as membership and non-membership grades to the alternatives in an extended domain with q-ROF environment. Certain operations on qROmPFSs and several new notions like support, core, height, concentration, dilation, α-cut and (α, β)-cut of qROmPFS are defined. Additionally, grey relational analysis (GRA) and choice value method (CVM) are presented under qROmPFSs for multi-criteria decision making (MCDM) in robotic agri-farming. The proposed methods are suitable to find out an appropriate mode of farming among several kinds of agri-farming. The applications of proposed MCDM approaches are illustrated by respective numerical examples. To justify the feasibility, superiority and reliability of proposed techniques, the comparison analysis of the final ranking in the robotic agri-farming computed by the proposed techniques with some existing MCDM methods is also given.

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Cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators

Cited by 43 publications

References 46 publications

Pythagorean $m$ -Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making

Pythagorean $m$ -Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making

q-Rung Orthopair Fuzzy Geometric Aggregation Operators Based on Generalized and Group-Generalized Parameters with Application to Water Loss Management

Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets

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Cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators

Cited by 43 publications

References 46 publications

Pythagoreanm-Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making

Pythagoreanm-Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making

q-Rung Orthopair Fuzzy Geometric Aggregation Operators Based on Generalized and Group-Generalized Parameters with Application to Water Loss Management

Multi-criteria decision making in robotic agri-farming with q-rung orthopair m-polar fuzzy sets

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Pythagorean $m$ -Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making

Pythagorean $m$ -Polar Fuzzy Weighted Aggregation Operators and Algorithm for the Investment Strategic Decision Making