Contrasting Correlation Coefficient with Distance Measure in Interval Valued Intuitionistic Trapezoidal Fuzzy MAGDM Problems

Fuzzy Systems ◽  
2017 ◽  
pp. 1478-1517 ◽  
Author(s):  
John P. Robinson
Keyword(s):  
Correlation Coefficient ◽  
Distance Measure ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Operational Laws ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Magdm Problems ◽  
Interval Valued

In this paper, Multiple Attribute Group Decision Making (MAGDM) problems in which the data is of the form of Interval Valued Intuitionistic Trapezoidal Fuzzy Numbers (IVITzFNs) is presented. Some operational laws of IVITzFNs are introduced. Then some new aggregation operators including interval valued Intuitionistic Trapezoidal Fuzzy Weighted Averaging (IVITzFWA) operator, interval valued Intuitionistic Trapezoidal Fuzzy Ordered Weighted Averaging (IVITzFOWA) operator and Interval Intuitionistic Trapezoidal Fuzzy Hybrid Averaging (IVITzFHA) operator, are proposed and some desirable properties of these operators are studied, such as Commutativity, Idempotency and Monotonicity. A new distance function and correlation coefficient are proposed for IVITzFNs which will be utilized for ranking the alternatives in MAGDM problems. Finally, numerical illustrations are given to verify the developed approach and to demonstrate its practicality and effectiveness.

Contrasting Correlation Coefficient with Distance Measure in Interval Valued Intuitionistic Trapezoidal Fuzzy MAGDM Problems

2016 ◽  
Vol 5 (4) ◽  
pp. 16-51 ◽  
Author(s):  
John P. Robinson
Keyword(s):  
Correlation Coefficient ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Group Decision ◽  
Weighted Averaging ◽  
Operational Laws ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Magdm Problems ◽  
Interval Valued

In this paper, Multiple Attribute Group Decision Making (MAGDM) problems in which the data is of the form of Interval Valued Intuitionistic Trapezoidal Fuzzy Numbers (IVITzFNs) is presented. Some operational laws of IVITzFNs are introduced. Then some new aggregation operators including interval valued Intuitionistic Trapezoidal Fuzzy Weighted Averaging (IVITzFWA) operator, interval valued Intuitionistic Trapezoidal Fuzzy Ordered Weighted Averaging (IVITzFOWA) operator and Interval Intuitionistic Trapezoidal Fuzzy Hybrid Averaging (IVITzFHA) operator, are proposed and some desirable properties of these operators are studied, such as Commutativity, Idempotency and Monotonicity. A new distance function and correlation coefficient are proposed for IVITzFNs which will be utilized for ranking the alternatives in MAGDM problems. Finally, numerical illustrations are given to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals Some Aggregation Operators Based on Einstein Operations under Interval-Valued Dual Hesitant Fuzzy Setting and Their Application

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Wenkai Zhang ◽  
Xia Li ◽  
Yanbing Ju
Keyword(s):  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Einstein Operations ◽  
The Relationship ◽  
Interval Valued

We investigate the multiple attribute decision making (MADM) problems in which attribute values take the form of interval-valued dual hesitant fuzzy information. Firstly, some operational laws for interval-valued dual hesitation fuzzy elements (IVDHFEs) based on Einstein operations are developed. Then we develop some aggregation operators based on Einstein operations: the interval-valued dual hesitant fuzzy Einstein weighted averaging (IVDHFEWA) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted averaging (IVDHFEOWA) operator, interval-valued dual hesitant fuzzy Einstein hybrid averaging (IVDHFEHA) operator, interval-valued dual hesitant fuzzy Einstein weighted geometric (IVDHFEWG) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted geometric (IVDHFEOWG) operator, and interval-valued dual hesitant fuzzy Einstein hybrid geometric (IVDHFEHG) operator. Furthermore, we discuss some desirable properties of these operators, and investigate the relationship between the developed operators and the existing ones. Based on the IVDHFEWA operator, an approach to MADM problems is proposed under the interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to show the application of the developed method, and a comparison analysis is conducted to demonstrate the effectiveness of the proposed approach.

MAGDM Problems with Correlation Coefficient of Triangular Fuzzy IFS

2017 ◽  
pp. 154-192
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E. C.
Keyword(s):  
Decision Making ◽  
Correlation Coefficient ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Decision Making Models ◽  
Magdm Problems ◽  
Interval Valued

Correlation coefficient of Intuitionistic Fuzzy Set (IFS), Interval valued IFS, Triangular IFS and Trapezoidal IFS are already present in the literature. This paper proposes the correlation coefficient for Triangular Fuzzy Intuitionistic Fuzzy set (TrFIFS). The method on uncertain Multiple Attribute Group Decision Making (MAGDM) problems based on aggregating intuitionistic fuzzy information is investigated for TrFIFSs. The Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted Averaging (TrFIFOWA) operator is proposed for TrFIFSs and the Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted Geometric (TrFIFOWG) operator is utilized for decision making models where expert weights are completely unknown. Based on these operators and the correlation coefficient defined for the TrFIFSs, new decision making models are proposed with numerical illustrations. Some comparisons are also made with existing ranking methods for validity.

scholarly journals A New Ranking Methodology for Pythagorean Trapezoidal Uncertain Linguistic Fuzzy Sets Based on Einstein Operations

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 440 ◽  
Author(s):  
Arshad Khan ◽  
Saleem Abdullah ◽  
Muhammad Shakeel ◽  
Faisal Khan ◽  
Noor Amin ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Decision Making Process ◽  
Ordered Weighted Averaging ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Einstein Operations

In this article, we proposed new Pythagorean trapezoidal uncertain linguistic fuzzy aggregation information—namely, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein weighted averaging (PTULFEWA) operator, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein ordered weighted averaging (PTULFEOWA) operator, and the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein hybrid weighted averaging (PTULFEHWA) operator—using the Einstein operational laws. We studied some important properties of the suggested aggregation operators and showed that the PTULFEHWA is more general than the other proposed operators, which simplifies these aggregation operators. Furthermore, we presented a multiple attribute group decision making (MADM) process for the proposed aggregation operators under the Pythagorean trapezoidal uncertain linguistic fuzzy (PTULF) environment. A numerical example was constructed to determine the effectiveness and practicality of the proposed approach. Lastly, a comparative analysis was performed of the presented approach with existing approaches to show that the proposed method is consistent and provides more information that may be useful for complex problems in the decision-making process.

scholarly journals Some Generalized Dependent Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and Their Application to Exploitation Investment Evaluation

2013 ◽  
Vol 2013 ◽  
pp. 1-24 ◽  
Author(s):  
Xiao-wen Qi ◽  
Chang-yong Liang ◽  
Junling Zhang
Keyword(s):  
Aggregation Operators ◽  
Weighted Averaging ◽  
Weighting Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Investment Evaluation ◽  
Ordered Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Wide Range ◽  
Interval Valued

We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees of arguments indirectly and directly, based on which the Gaussian generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator (Gaussian-GIIFOWA) and geometric operator (Gaussian-GIIFOWG), the power generalized interval-valued intuitionistic fuzzy ordered weighted averaging (P-GIIFOWA) operator and geometric (P-GIIFOWA) operator are proposed to generalize a wide range of aggregation operators for decision makers to flexibly choose in decision modelling. And some desirable properties of the proposed operators are also analyzed. Further, application of an approach integrating proposed operators to exploitation investment evaluation of tourist spots has shown the effectiveness and practicality of developed methods; experimental results also verify the properties of proposed operators.

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.

scholarly journals Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator and Its Application to Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 658 ◽  
Author(s):  
Aliya Fahmi ◽  
Fazli Amin ◽  
Florentin Smarandache ◽  
Madad Khan ◽  
Nasruddin Hassan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Linguistic Information ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Multiple Attribute ◽  
The Relationship

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach.

scholarly journals Fuzzy Linguistic Induced Ordered Weighted Averaging Operator and Its Application

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Sidong Xian
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Averaging ◽  
Attribute Weights ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Ordered Weighted Averaging Operator ◽  
Fuzzy Linguistic ◽  
Magdm Problems

With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of fuzzy linguistic scale variables, a decision analysis approach is proposed. In this paper, we develop a new fuzzy linguistic induce OWA (FLIOWA) operator and analyze the properties of it by utilizing some operational laws of fuzzy linguistic scale variables. A method based on the FLIOWA operators for multiple attribute group decision making is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.

scholarly journals Multiple Attribute Group Decision-Making Based on Power Heronian Aggregation Operators under Interval-Valued Dual Hesitant Fuzzy Environment

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Shenqing Jiang ◽  
Wei He ◽  
Fangfang Qin ◽  
Qingqing Cheng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Fuzzy Environment ◽  
Multiple Attribute ◽  
Special Cases ◽  
Magdm Problems ◽  
Interval Valued ◽  
Heronian Mean

In this paper, we focus on new methods to deal with multiple attribute group decision-making (MAGDM) problems and a new comparison law of interval-valued dual hesitant fuzzy elements (IVDHFEs). More explicitly, the interval-valued dual hesitant fuzzy 2nd-order central polymerization degree (IVDHFCP2) function is introduced, for the case that score values of different IVDHFEs are identical. This function can further compare different IVDHFEs. Then, we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation operators, i.e., the interval-valued dual hesitant fuzzy power Heronian mean (IVDHFPHM) operator, the interval-valued dual hesitant fuzzy power geometric Heronian mean (IVDHFPGHM) operator, and their weighted forms. Some desirable properties and their special cases are discussed. These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values. Finally, two approaches for interval-valued dual hesitant fuzzy MAGDM with known or unknown weight information are presented. An illustrative example and comparative studies are given to verify the advantages of our methods. A sensitivity analysis of the decision results is analyzed with different parameters.

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

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