scholarly journals Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 119
Author(s):  
Minxia Luo ◽  
Huifeng Long
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Intuitionistic Fuzzy Set ◽  
Information Aggregation ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Trapezoidal Fuzzy Number ◽  
Picture Fuzzy Set ◽  
Multi Attribute Decision Making

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.

scholarly journals Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 357 ◽  
Author(s):  
Kifayat Ullah ◽  
Nasruddin Hassan ◽  
Tahir Mahmood ◽  
Naeem Jan ◽  
Mazlan Hassan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Investment Policies ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Interval Valued

Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators.

scholarly journals Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 593 ◽  
Author(s):  
Hongran Zhang ◽  
Runtong Zhang ◽  
Huiqun Huang ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Good Ability ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Heronian Mean

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed.

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

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1236
Author(s):  
Muhammad Riaz ◽  
Ayesha Razzaq ◽  
Humaira Kalsoom ◽  
Dragan Pamučar ◽  
Hafiz Muhammad Athar Farid ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Water Loss ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Water Supply Systems ◽  
Pythagorean Fuzzy Set ◽  
Water Losses ◽  
Water Loss Management

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.

scholarly journals Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 608 ◽  
Author(s):  
Saifullah Khan ◽  
Saleem Abdullah ◽  
Lazim Abdullah ◽  
Shahzaib Ashraf
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Vital Role ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted averaging/geometric and logarithmic picture fuzzy ordered weighted averaging/geometric aggregation operators and characterized their desirable properties. Finally, a novel algorithm technique was developed to solve multi-attribute decision making (MADM) problems with picture fuzzy information. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.

Protraction of Einstein operators for decision-making under q-rung orthopair fuzzy model

2020 ◽  
pp. 1-20
Author(s):  
Muhammad Akram ◽  
Gulfam Shahzadi ◽  
Sundas Shahzadi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Fuzzy Model ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Pythagorean Fuzzy Set ◽  
Career Selection ◽  
Ordered Weighted Averaging ◽  
Multi Attribute Decision Making

An q-rung orthopair fuzzy set is a generalized structure that covers the modern extensions of fuzzy set, including intuitionistic fuzzy set and Pythagorean fuzzy set, with an adjustable parameter q that makes it flexible and adaptable to describe the inexact information in decision making. The condition of q-rung orthopair fuzzy set, i.e., sum of q th power of membership degree and nonmembership degree is bounded by one, makes it highly competent and adequate to get over the limitations of existing models. The basic purpose of this study is to establish some aggregation operators under the q-rung orthopair fuzzy environment with Einstein norm operations. Motivated by innovative features of Einstein operators and dominant behavior of q-rung orthopair fuzzy set, some new aggregation operators, namely, q-rung orthopair fuzzy Einstein weighted averaging, q-rung orthopair fuzzy Einstein ordered weighted averaging, generalized q-rung orthopair fuzzy Einstein weighted averaging and generalized q-rung orthopair fuzzy Einstein ordered weighted averaging operators are defined. Furthermore, some properties related to proposed operators are presented. Moreover, multi-attribute decision making problems related to career selection, agriculture land selection and residential place selection are presented under these operators to show the capability and proficiency of this new idea. The comparison analysis with existing theories shows the superiorities of proposed model.

scholarly journals Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 413 ◽  
Author(s):  
Huanhuan Jin ◽  
Shahzaib Ashraf ◽  
Saleem Abdullah ◽  
Muhammad Qiyas ◽  
Mahwish Bano ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Operational Laws ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable.

scholarly journals Some Improved q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications to Multiattribute Group Decision-Making

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Lei Xu ◽  
Yi Liu ◽  
Haobin Liu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Pythagorean Fuzzy Set ◽  
Fuzzy Aggregation

As a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), q-rung orthopair fuzzy set (q-ROFS) is a new concept in describing complex fuzzy uncertainty information. The present work focuses on the multiattribute group decision-making (MAGDM) approach under the q-rung orthopair fuzzy information. To begin with, some drawbacks of the existing MAGDM methods based on aggregation operators (AOs) are firstly analyzed. In addition, some improved operational laws put forward to overcome the drawbacks along with some properties of the operational law are proved. Thirdly, we put forward the improved q-rung orthopair fuzzy-weighted averaging (q-IROFWA) aggregation operator and improved q-rung orthopair fuzzy-weighted power averaging (q-IROFWPA) aggregation operator and present some of their properties. Then, based on the q-IROFWA operator and q-IROFWPA operator, we proposed a new method to deal with MAGDM problems under the fuzzy environment. Finally, some numerical examples are provided to illustrate the feasibility and validity of the proposed method.

scholarly journals Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 280 ◽  
Author(s):  
Harish Garg ◽  
Nancy
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
New Method ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Special Cases

The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.

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