scholarly journals Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 3 ◽  
Author(s):  
Suizhi Luo ◽  
Lining Xing
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Sensitivity Analyses ◽  
Special Cases ◽  
Different Parts

Picture fuzzy numbers (PFNs), as the generalization of fuzzy sets, are good at fully expressing decision makers’ opinions with four membership degrees. Since aggregation operators are simple but powerful tools, this study aims to explore some aggregation operators with PFNs to solve practical decision-making problems. First, new operational rules, the interaction operations of PFNs, are defined to overcome the drawbacks of existing operations. Considering that interrelationships may exist only in part of criteria, rather than all of the criteria in reality, the partitioned Heronian aggregation operator is modified with PFNs to deal with this condition. Then, desirable properties are proved and several special cases are discussed. New decision-making methods with these presented aggregation operators are suggested to process hotel selection issues. Last, their practicability and merits are certified by sensitivity analyses and comparison analyses with other existing approaches. The results indicate that our methods are feasible to address such situations where criteria interact in the same part, but are independent from each other at different parts.

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.

scholarly journals Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1081 ◽  
Author(s):  
Peng ◽  
Tian ◽  
Zhang ◽  
Song ◽  
Wang
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Preference Information ◽  
Fuzzy Measures ◽  
Correlative Relationship

Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.

On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making

2016 ◽  
Vol 15 (05) ◽  
pp. 1055-1114 ◽  
Author(s):  
Sheng-Hua Xiong ◽  
Zhen-Song Chen ◽  
Yan-Lai Li ◽  
Kwai-Sang Chin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Individual Decision ◽  
Hesitant Fuzzy Sets ◽  
Variable Power ◽  
Interval Valued

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some “false” or “biased” arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques.

scholarly journals Inclusion of uncertainty with different types of fuzzy numbers into DEMATEL

2021 ◽  
Vol 16 (1) ◽  
pp. 49-59
Author(s):  
Tjaša Šmidovnik ◽  
Petra Grošelj
Keyword(s):  
Complex System ◽  
Decision Making ◽  
Fuzzy Sets ◽  
Construction Projects ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Different Types

Nowadays the multi-criteria decision making is very complicated due to uncertainty, vagueness, limited sources, knowledge and time. The Decision-making Trial and Evaluation Laboratory (DEMATEL) method is a widely used multi-criteria decision-making method to analyze the structure of a complex system. It is useful in analysing the cause and effect relationships between the components of the system. Fuzzy sets can be used to include uncertainty in multi-criteria decision making. Linguistic assessments of decision makers can be translated into fuzzy numbers. In this study, fuzzy numbers, intuitionistic fuzzy numbers and neutrosophic fuzzy numbers were used for the decision makers evaluations in the DEMATEL method. The aim of this study was to evaluate how different types of fuzzy numbers affect the final results. An application of risk in construction projects was selected from the literature, where seven experts used a linguistic scale to evaluate different criteria. The results showed that there are only slight differences between the weights of the criteria with regard to the type of fuzzy numbers.

scholarly journals A Multi-Criteria Decision-Making Method Based on the Improved Single-Valued Neutrosophic Weighted Geometric Operator

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1051 ◽  
Author(s):  
Chao Tian ◽  
Juan Juan Peng
Keyword(s):  
Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Special Cases ◽  
Mcdm Method ◽  
Geometric Operator

The aggregation operator is one of the most common techniques to solve multi-criteria decision-making (MCDM) problems. The aim of this paper is to propose an MCDM method based on the improved single-valued neutrosophic weighted geometric (ISVNWG) operator. First, the defects of several existing single-valued neutrosophic weighted geometric aggregation operators in terms of producing uncertain results in some special cases are analyzed. Second, an ISVNWG operator is proposed to avoid the defects of existing operators. Further, the properties of the proposed ISVNWG operator, including idempotency, boundedness, monotonicity, and commutativity, are discussed. Finally, a single-valued neutrosophic MCDM method based on the developed ISVNWG operator is proposed to overcome the defects of existing MCDM methods based on existing operators. Application examples demonstrate that our proposed operator and corresponding MCDM method are effective and rational for avoiding uncertain results in some special cases.

scholarly journals Multiple attribute group decision-making based on cubic linguistic Pythagorean fuzzy sets and power Hamy mean

2021 ◽  
Author(s):  
Wuhuan Xu ◽  
Xiaopu Shang ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Distance Measure ◽  
Group Decision ◽  
Comparison Method ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Pythagorean Fuzzy Sets ◽  
Multiple Attribute

AbstractThe linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.

Linguistic interval-valued intuitionistic fuzzy copula power aggregation operators for multiattribute group decision making

2021 ◽  
Vol 40 (1) ◽  
pp. 605-624 ◽  
Author(s):  
Lei Xu ◽  
Yi Liu ◽  
Haobin Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Uncertain Information ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

For the sake of better handle the imprecise and uncertain information in decision making problems(DMPs), linguistic interval-valued intuitionistic fuzzy numbers(LIVIFNs) based aggregation operators (AOS) are proposed by combining extended Copulas (ECs), extended Co-copulas (ECCs), power average operator and linguistic interval-valued intuitionistic fuzzy information (LIVIFI). First of all, ECs and ECCs, some specifics of ECs and ECCs, score and accuracy functions of LIVIFNs are gained. Then, based on ECs and ECCs, several aggregation operators are proposed to aggregate LIVIFI, which can offer decision makers (DMs) desirable generality and flexibility. In addition, the desired properties of proposed AOS are discussed. Last but not least, a MAGDM approach is constructed based on proposed AOs; Consequently, the effectiveness of the proposed approach is verified by a numerical example, and then the advantages are showed by comparing with other approaches.

Density aggregation operators for interval-valued q-rung orthopair fuzzy numbers and their application in multiple attribute decision making

2021 ◽  
pp. 1-14
Author(s):  
Huijuan Guo ◽  
Ruipu Yao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Novel Approach ◽  
Multiple Attribute ◽  
Interval Valued

The symmetry between fuzzy evaluations and crisp numbers provides an effective solution to multiple attribute decision making (MADM) problems under fuzzy environments. Considering the effect of information distribution on decision making, a novel approach to MADM problems under the interval-valued q-rung orthopair fuzzy (Iq-ROF) environments is put forward. Firstly, the clustering method of interval-valued q-rung orthopair fuzzy numbers (Iq-ROFNs) is defined. Secondly, Iq-ROF density weighted arithmetic (Iq-ROFDWA) intermediate operator and Iq-ROF density weighted geometric average (Iq-ROFDWGA) intermediate operator are developed based on the density weighted intermediate operators for crisp numbers. Thirdly, combining the density weighted intermediate operators with the Iq-ROF weighted aggregation operators, Iq-ROF density aggregation operators including Iq-ROF density weighted arithmetic (Iq-ROFDWAA) aggregation operator and Iq-ROF density weighted geometric (Iq-ROFDWGG) aggregation operator are proposed. Finally, effectiveness of the proposed method is verified through a numerical example.

scholarly journals Multicriteria Decision-Making Approach with Hesitant Interval-Valued Intuitionistic Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Juan-juan Peng ◽  
Jian-qiang Wang ◽  
Jing Wang ◽  
Xiao-hong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Definition Of ◽  
Interval Valued

The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based ont-conorms andt-norms are proposed, which can be used to aggregate decision-makers' information in multicriteria decision-making (MCDM) problems. Some valuable proposals of these operators are studied. In particular, based on algebraic and Einsteint-conorms andt-norms, some hesitant interval-valued intuitionistic fuzzy algebraic aggregation operators and Einstein aggregation operators can be obtained, respectively. Furthermore, an approach of MCDM problems based on the proposed aggregation operators is given using hesitant interval-valued intuitionistic fuzzy information. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the developed approach, and the study is supported by a sensitivity analysis and a comparison analysis.

Complex hesitant fuzzy sets and its applications in multiple attributes decision-making problems

2021 ◽  
pp. 1-29
Author(s):  
Mohammad Talafha ◽  
Abd Ulazeez Alkouri ◽  
Sahar Alqaraleh ◽  
Hamzeh Zureigat ◽  
Anas Aljarrah
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
Multiple Attributes ◽  
The Right ◽  
Multiple Attributes Decision Making ◽  
The Mathematical Model

Decision-makers (DMs) usually face many obstacles to give the right decision, multiplicity of them highlights a problem to represent a set of potential values to assign a collective membership degree of an object to a set for several DM’s opinions. However, a hesitant fuzzy set (HFS) deals with such problems. The complexity appears in DM’s opinion which can be changed for the same object but with different times/phases. Each of them has a set of potential values in different times/phases of an object. In this paper, the periodicity of hesitant fuzzy information is studied and applied by extending the range of HFS from [0, 1] to the unit disk in the complex plane to provide more ability for illustrating the full meaning of information to overcome the obstacles in decision making in the mathematical model. Moreover, the advantage of CHFS is that the amplitude and phase terms of CHFSs can represent hesitant fuzzy information, some basic operations on CHFS are also presented and we study its properties, in addition, several aggregation operators under CHFS are introduced, also, the relation between CHFS and complex intuitionistic fuzzy sets (CIFS) are presented. Finally, an efficient algorithm with a consistent process and an application in multiple attributes decision-making (MADM) problems are presented to show the effectiveness of the presented approach by using CHFS aggregation operators.

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