scholarly journals MADM Based on Generalized Interval Neutrosophic Schweizer-Sklar Prioritized Aggregation Operators

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1187 ◽  
Author(s):  
Khan ◽  
Abdullah ◽  
Mahmood ◽  
Naeem ◽  
Rashid
Keyword(s):  
Decision Making ◽  
Variable Parameter ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Neutrosophic Set ◽  
High Tech ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Prioritized Aggregation Operators

The interval neutrosophic set (INS) can make it easier to articulate incomplete, indeterminate, and inconsistent information, and the Schweizer-Sklar (Sh-Sk) t-norm (tm) and t-conorm (tcm) can make the information aggregation process more flexible due to a variable parameter. To take full advantage of INS and Sh-Sk operations, in this article, we expanded the Sh-Sk and to IN numbers (INNs) in which the variable parameter takes values from , develop the Sh-Sk operational laws for INNs and discussed its desirable properties. After that, based on these newly developed operational laws, two types of generalized prioritized aggregation operators are established, the generalized IN Sh-Sk prioritized weighted averaging (INSh-SkPWA) operator and the generalized IN Sh-Sk prioritized weighted geometric (INSh-SkPWG) operator. Additionally, we swot a number of valuable characteristics of these intended aggregation operators (AGOs) and created two novel decision-making models to match with multiple-attribute decision-making (MADM) problems under IN information established on INSh-SkPWA and INSh-SkPRWG operators. Finally, an expressive example regarding evaluating the technological innovation capability for the high-tech enterprises is specified to confirm the efficacy of the intended models.

scholarly journals Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chunyong Wang ◽  
Qingguo Li ◽  
Xiaoqiang Zhou ◽  
Tian Yang
Keyword(s):  
Decision Making ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Special Cases ◽  
Fuzzy Aggregation

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

Dependent Interval 2-Tuple Linguistic Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

2014 ◽  
Vol 22 (05) ◽  
pp. 717-735 ◽  
Author(s):  
Hu-Chen Liu ◽  
Qing-Lian Lin ◽  
Jing Wu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Linguistic Variables ◽  
Preference Information ◽  
Operational Laws ◽  
Multiple Attribute

Consider the various types of uncertain preference information provided by the decision makers and the importance of determining the associated weights for the aggregation operator, the multiple attribute group decision making (MAGDM) methods based on some dependent interval 2-tuple linguistic aggregation operators are proposed in this paper. Firstly some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop a dependent interval 2-tuple weighted averaging (DITWA) operator and a dependent interval 2-tuple weighted geometric (DITWG) operator, in which the associated weights only depend on the aggregated interval 2-tuple arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to them. Based on the DITWA and the DITWG operators, some approaches for multiple attribute group decision making with interval 2-tuple linguistic information are proposed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approaches.

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 Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Schweizer–Sklar Muirhead Mean Aggregation Operators

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 152 ◽  
Author(s):  
Huanying Zhang ◽  
Fei Wang ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Variable Parameter ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Uncertain Information ◽  
Neutrosophic Sets ◽  
Decision Systems ◽  
Parameter Values

Schweizer–Sklar (SS) operation can make information aggregation more flexible, and the Muirhead mean (MM) operator can take into account the correlation between inputs by a variable parameter. Because traditional MM is only available for real numbers and single-valued neutrosophic set (SVNS) can better express incomplete and uncertain information in decision systems, in this paper, we applied MM operators to single-valued neutrosophic sets (SVNSs) and presented two new MM aggregation operators with the SS operation, i.e., a single-valued neutrosophic SS Muirhead mean (SVNSSMM) operator and a weighted single-valued neutrosophic SS MM (WSVNSSMM) operator. We listed some properties of them and some particular cases about various parameter values. We also proposed the multi-criteria decision-making method based on the WSVNSSMM operator in SVNS. At last, we illustrated the feasibility of this method using a numerical example of company investment.

scholarly journals Probabilistic Linguistic Aggregation Operators Based on Einstein t-Norm and t-Conorm and Their Application in Multi-Criteria Group Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 39 ◽  
Author(s):  
Kobina Agbodah ◽  
Adjei Peter Darko
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Knowledge Based ◽  
Multiple Attribute ◽  
Linguistic Term ◽  
Probabilistic Linguistic Term Sets

One of the major problems of varied knowledge-based systems has to do with aggregation and fusion. Pang’s probabilistic linguistic term sets denotes aggregation of fuzzy information and it has attracted tremendous interest from researchers recently. The purpose of this article is to deal investigating methods of information aggregation under the probabilistic linguistic environment. In this situation we defined certain Einstein operational laws on probabilistic linguistic term elements (PLTESs) based on Einstein product and Einstein sum. Consequently, we develop some probabilistic linguistic aggregation operators, notably the probabilistic linguistic Einstein average (PLEA) operators, probabilistic linguistic Einstein geometric (PLEG) operators, weighted probabilistic linguistic Einstein average (WPLEA) operators, weighted probabilistic linguistic Einstein geometric (WPLEG) operators. These operators extend the weighted averaging operator and the weighted geometric operator for the purpose of aggregating probabilistic linguistic terms values respectively. Einstein t-norm and Einstein t-conorm constitute effective aggregation tools and they allow input arguments to reinforce each other downwardly and upwardly respectively. We then generate various properties of these operators. With the aid of the WPLEA and WPLEG, we originate the approaches for the application of multiple attribute group decision making (MAGDM) with the probabilistic linguistic term sets (PLTSs). Lastly, we apply an illustrative example to elucidate our proposed methods and also validate their potentials.

scholarly journals Hesitant Probabilistic Fuzzy Information Aggregation Using Einstein Operations

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 226 ◽  
Author(s):  
Jin Park ◽  
Yu Park ◽  
Mi Son
Keyword(s):  
Decision Making ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multiple Attribute ◽  
Special Cases ◽  
Fuzzy Aggregation ◽  
Einstein Operations ◽  
Geometric Operator

In this paper, a hesitant probabilistic fuzzy multiple attribute group decision making is studied. First, some Einstein operations on hesitant probability fuzzy elements such as the Einstein sum, Einstein product, and Einstein scalar multiplication are presented and their properties are discussed. Then, several hesitant probabilistic fuzzy Einstein aggregation operators, including the hesitant probabilistic fuzzy Einstein weighted averaging operator and the hesitant probabilistic fuzzy Einstein weighted geometric operator and so on, are introduced. Moreover, some desirable properties and special cases are investigated. It is shown that some existing hesitant fuzzy aggregation operators and hesitant probabilistic fuzzy aggregation operators are special cases of the proposed operators. Further, based on the proposed operators, a new approach of hesitant probabilistic fuzzy multiple attribute decision making is developed. Finally, a practical example is provided to illustrate the developed approach.

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 Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

Information ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 201 ◽  
Author(s):  
Jiongmei Mo ◽  
Han-Liang Huang
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Ranking Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Geometric Bonferroni Mean ◽  
Neutrosophic Number

For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle. Moreover, the proposed operators do not take into account the correlation between any aggregation arguments. In order to overcome the deficiencies of the existing ranking method, based on the nonnegative normal neutrosophic number, this paper redefines the score function, the accuracy function, and partial operational laws. Considering the correlation between any aggregation arguments, the dual generalized nonnegative normal neutrosophic weighted Bonferroni mean operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean operator were investigated, and their properties are presented. Here, these two operators are applied to deal with a multiple attribute decision making problem. Example results show that the proposed method is effective and superior.

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.

Sign in / Sign up

Export Citation Format

Share Document