scholarly journals Algorithm for T-Spherical Fuzzy Multi-Attribute Decision Making Based on Improved Interactive Aggregation Operators

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 670 ◽  
Author(s):  
Harish Garg ◽  
Muhammad Munir ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Naeem Jan
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Counter Example ◽  
Operational Laws ◽  
Special Cases ◽  
Multi Attribute Decision Making ◽  
Picture Fuzzy Sets

The objective of this manuscript is to present some new, improved aggregation operators for the T-spherical fuzzy sets, which is an extension of the several existing sets, such as intuitionistic fuzzy sets, picture fuzzy sets, neutrosophic sets, and Pythagorean fuzzy sets. In it, some new, improved operational laws and their corresponding properties are studied. Further, based on these laws, we propose some geometric aggregation operators and study their various relationships. Desirable properties, as well as some special cases of the proposed operators, are studied. Then, based on these proposed operators, we present a decision-making approach to solve the multi-attribute decision-making problems. The reliability of the presented decision-making method is explored with the help of a numerical example and the proposed results are compared with several prevailing studies’ results. Finally, the superiority of the proposed approach is explained with a counter example to show the advantages of the proposed work.

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

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 365 ◽  
Author(s):  
Muhammad Munir ◽  
Humaira Kalsoom ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Yu-Ming Chu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Multi Attribute Decision Making ◽  
Algebraic Operations ◽  
Einstein Operations ◽  
Picture Fuzzy Sets ◽  
Einstein Product

T-spherical fuzzy set is a recently developed model that copes with imprecise and uncertain events of real-life with the help of four functions having no restrictions. This article’s aim is to define some improved algebraic operations for T-SFSs known as Einstein sum, Einstein product and Einstein scalar multiplication based on Einstein t-norms and t-conorms. Then some geometric and averaging aggregation operators have been established based on defined Einstein operations. The validity of the defined aggregation operators has been investigated thoroughly. The multi-attribute decision-making method is described in the environment of T-SFSs and is supported by a comprehensive numerical example using the proposed Einstein aggregation tools. As consequences of the defined aggregation operators, the same concept of Einstein aggregation operators has been proposed for q-rung orthopair fuzzy sets, spherical fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and intuitionistic fuzzy sets. To signify the importance of proposed operators, a comparative analysis of proposed and existing studies is developed, and the results are analyzed numerically. The advantages of the proposed study are demonstrated numerically over the existing literature with the help of examples.

scholarly journals TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1739
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Unit Interval ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Special Cases ◽  
Order Preference ◽  
Multi Attribute Decision Making

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

scholarly journals Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Hong-yu Zhang ◽  
Jian-qiang Wang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
The Real ◽  
Comparison Approach ◽  
Interval Neutrosophic Sets

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number. However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decision making method. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, a method for multicriteria decision making problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.

scholarly journals Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 459 ◽  
Author(s):  
Qaisar Khan ◽  
Peide Liu ◽  
Tahir Mahmood ◽  
Florentin Smarandache ◽  
Kifayat Ullah
Keyword(s):  
Decision Making ◽  
Hybrid Structure ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Geometric Bonferroni Mean ◽  
Dombi Operations ◽  
The Impact

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

scholarly journals Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 547 ◽  
Author(s):  
Shouzhen Zeng ◽  
Azmat Hussain ◽  
Tahir Mahmood ◽  
Muhammad Irfan Ali ◽  
Shahzaib Ashraf ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Rough Set ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Rough Set ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Topsis Technique ◽  
Picture Fuzzy Sets

In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy β -neighborhoods (SF β -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF β -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems.

scholarly journals Multi-Attribute Multi-Perception Decision-Making Based on Generalized T-Spherical Fuzzy Weighted Aggregation Operators on Neutrosophic Sets

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 780 ◽  
Author(s):  
Quek ◽  
Selvachandran ◽  
Munir ◽  
Mahmood ◽  
Ullah ◽  
...  
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Do So

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

On Generalized Correlation Coefficients of Picture Fuzzy Sets With Their Applications

2021 ◽  
Vol 10 (2) ◽  
pp. 59-81
Author(s):  
Surender Singh ◽  
Abdul Haseeb Ganie ◽  
Sumita Lalotra
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Crucial Role ◽  
Correlation Coefficients ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Multi Attribute Decision Making ◽  
Picture Fuzzy Sets ◽  
Generalized Correlation

Picture fuzzy sets (PFSs) play a crucial role in uncertain/vague environments than intuitionistic fuzzy sets (IFSs) which do not take into consideration the degree of neutrality of an element. In this paper, the authors have proposed generalized correlation coefficients of PFSs along with some properties. The effectiveness and application of the proposed generalized correlation coefficients of PFSs in pattern recognition and multi-attribute decision making (MADM) is also discussed with the help of numerical examples.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

A Novel spherical fuzzy CRITIC method and its application to prioritization of supplier selection criteria

2021 ◽  
pp. 1-8
Author(s):  
Cengiz Kahraman ◽  
Sezi Cevik Onar ◽  
Başar Öztayşi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Supplier Selection ◽  
Selection Criteria ◽  
Business Processes ◽  
Multiple Criteria Decision Making ◽  
Decision Matrix ◽  
Neutrosophic Sets ◽  
Numerical Illustration ◽  
Picture Fuzzy Sets

Linguistic terms are quite suitable to make evaluations in multiple criteria decision making problems since humans prefer them rather than sharp evaluations. When linguistic evaluations are used in the decision matrix instead of exact numerical values, fuzzy set theory can capture the vagueness in the linguistic evaluations. Ordinary fuzzy sets have been extended to many new types of fuzzy sets such as intuitionistic fuzzy sets, neutrosophic sets, spherical fuzzy sets and picture fuzzy sets. Spherical fuzzy sets are an extension of picture fuzzy sets whose squared sum of their parameters is at most equal to one. This paper develops a novel spherical fuzzy CRiteria Importance Through Intercriteria Correlation (CRITIC) method and applies it for prioritizing supplier selection criteria. Supplier selection is one of the most critical aspects of any organization since any mistake in this process may cause poor supplier performance and inefficiencies in the business processes. Supplier selection is a multi-criteria decision making problem involving several conflicting criteria and alternatives. A numerical illustration of the proposed method is also given for this problem.

scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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