scholarly journals Multiattribute Decision-Making Problems in terms of the Weighted Mean Operation of Two Aggregation Operators of Orthopair Z-Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mailing Zhao ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Geometric Mean ◽  
Real Life ◽  
Arithmetic Mean ◽  
Aggregation Operators ◽  
Weighted Mean ◽  
Reliability Measure ◽  
Reliability Level ◽  
Weighted Arithmetic

The Z number defined by Zadeh can depict the fuzzy restriction/value and reliability measure by an ordered pair of fuzzy values to strengthen the reliability of the fuzzy restriction/value. However, there exist truth and falsehood Z-numbers in real life. Thus, the Z number cannot reflect both. To indicate both, this study presents an orthopair Z-number (OZN) set to depict truth and falsehood values (intuitionistic fuzzy values) and their reliability levels in uncertain and incomplete cases. Next, we define the operations, score and accuracy functions, and sorting rules of OZNs. Further, the OZN weighted arithmetic mean (OZNWAM) and OZN weighted geometric mean (OZNWGM) operators are proposed based on the operations of OZNs. According to the weighted mean operation of the OZNWAM and OZNWGM operators, a multiattribute decision-making (MADM) model is established in the case of OZNs. Lastly, a numerical example is presented to reflect the flexibility and rationality of the presented MADM model. Comparative analysis indicates that the presented MADM model can indicate its superiority in the reliability and flexibility of decision results. Meanwhile, the resulting advantage of this study is that the presented MADM model can strengthen the reliability level of orthopair fuzzy values and make the decision results more reliable and flexible.

Intuitionistic Fuzzy Hybrid Weighted Arithmetic Mean and Its Application in Decision Making

2019 ◽  
Vol 27 (03) ◽  
pp. 353-373
Author(s):  
Weize Wang ◽  
Jerry M. Mendel
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Arithmetic Mean ◽  
Aggregation Operators ◽  
Total Order ◽  
Intuitionistic Fuzzy ◽  
Weighted Arithmetic ◽  
Multi Attribute Decision Making ◽  
A Company ◽  
Interval Valued

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set. There are various intuitionistic fuzzy hybrid weighted aggregation operators to deal with multi-attribute decision making problems which consider the importance degrees of the arguments and their ordered positions simultaneously. However, these existing hybrid weighed aggregation operators are not monotone with respect to the total order on intuitionistic fuzzy values (AIFVs), which is undesirable. Based on the Łukasiewicz triangular norm, we propose an intuitionistic fuzzy hybrid weighted arithmetic mean, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a company intends to select a project manager to illustrate the validity and applicability of the proposed aggregation operator. Moreover, we extend this kind of hybrid weighted arithmetic mean to the interval-valued intuitionistic fuzzy environments.

scholarly journals Economic Security in Post-Soviet Countries: Level of Ensuring and Development Trends

2021 ◽  
Vol 22 (2) ◽  
pp. 86-101
Author(s):  
Ganna Kozachenko ◽  
◽  
Igor Andrushchenko ◽  
Yuriy Pogorelov ◽  
Larysa Gerasymenko ◽  
...  
Keyword(s):  
Comparative Analysis ◽  
Geometric Mean ◽  
National Level ◽  
Economic Security ◽  
Arithmetic Mean ◽  
Security Studies ◽  
Economic Systems ◽  
Economic Potential ◽  
Weighted Arithmetic ◽  
Low Levels

At the national level of economic security studies, a special place has alway s b e lon ged t o t he estimating side of the issue. Estimations of state economic security serve as input data for the determinat ion of directions and ways of further security provision. At the same time, such estimations should be considered not only as a result of a certain methodology application in a certain co un try b ut a lso i n t h e c o nte xt o f comparing the economic security estimations across a set of countries. The aim of the article is to determin e the level of ensuring economic security in post-Soviet countries and recognize patterns, ri sk s, a n d t h rea ts that affect the future development of state economic security. For comparative analysis of economic security, Ukraine, Azerbaijan, Kazakhstan, Moldova, Georgia, and period 2016-2020 have been selected. The methodological basis of the study included the followingmethods: comparative economic studies, methods of summation, arithmetic mean, weighted arithmetic, geometric mean, rating; international index systems we re used as a basis for comparative analysis. Using the suggested methodology of estimation allowed obta ini ng results that characterize level real economic security, is lower than average. None of the analyzed countri es has managed to maintain an acceptable level of economic security. The determined levels allow u s t o st a te that the economic systems of the analyzed post-Soviet countries demonstrat e h i gh p erc ep ti ve ne ss t o t h e actualization of various threats. And this perceptiveness, in its turn, leads to various negative changes in t h e economic systems of these countries. The high perceptiveness of the economic systems in the analyze d p o st-Soviet countries to the actualization of various threats can be explained by the c h an gin g q u ali ty o f t he ir economic potential, low levels of their innovativeness, and also the lack of proper condi ti ons t o a p ply t h e innovations

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

scholarly journals Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

2021 ◽  
Author(s):  
Faruk Karaaslan ◽  
Mohammed Allaw Dawood Dawood
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Two Dimensional ◽  
Weighted Arithmetic ◽  
Mcdm Method ◽  
Dombi Operations

AbstractComplex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

scholarly journals DUAL HESITANT FUZZY AGGREGATION OPERATORS

2015 ◽  
Vol 22 (2) ◽  
pp. 194-209 ◽  
Author(s):  
Dejian YU ◽  
Wenyu ZHANG ◽  
George HUANG
Keyword(s):  
Human Resources ◽  
Fuzzy Sets ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Aggregation Operators ◽  
Fuzzy Arithmetic ◽  
Hesitant Fuzzy Sets ◽  
Numerical Example ◽  
Fuzzy Environment ◽  
Fuzzy Aggregation

Dual hesitant fuzzy sets (DHFSs) is a generalization of fuzzy sets (FSs) and it is typical of membership and non-membership degrees described by some discrete numerical. In this article we chiefly concerned with introducing the aggregation operators for aggregating dual hesitant fuzzy elements (DHFEs), including the dual hesitant fuzzy arithmetic mean and geometric mean. We laid emphasis on discussion of properties of newly introduced operators, and give a numerical example to describe the function of them. Finally, we used the proposed operators to select human resources outsourcing suppliers in a dual hesitant fuzzy environment.

scholarly journals The Weighted Arithmetic Mean–Geometric Mean Inequality is Equivalent to the Hölder Inequality

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 380 ◽  
Author(s):  
Yongtao Li ◽  
Xian-Ming Gu ◽  
Jianxing Zhao
Keyword(s):  
Geometric Mean ◽  
Arithmetic Mean ◽  
Hölder Inequality ◽  
Power Mean ◽  
Weighted Arithmetic ◽  
Mathematical Equivalence ◽  
Power Mean Inequality ◽  
Mathematical Relations

In the current note, we investigate the mathematical relations among the weighted arithmetic mean–geometric mean (AM–GM) inequality, the Hölder inequality and the weighted power-mean inequality. Meanwhile, the proofs of mathematical equivalence among the weighted AM–GM inequality, the weighted power-mean inequality and the Hölder inequality are fully achieved. The new results are more generalized than those of previous studies.

Geospatial Suitability Indices Toolbox (GSI Toolbox)

2021 ◽  
Author(s):  
Christina Saltus ◽  
Todd Swannack ◽  
S. McKay
Keyword(s):  
Habitat Suitability ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Limiting Factor ◽  
Ecological Processes ◽  
Weighted Arithmetic ◽  
Suitability Index ◽  
Multiple Parameter ◽  
Spatially Distributed

Habitat suitability models are widely adopted in ecosystem management and restoration, where these index models are used to assess environmental impacts and benefits based on the quantity and quality of a given habitat. Many spatially distributed ecological processes require application of suitability models within a geographic information system (GIS). Here, we present a geospatial toolbox for assessing habitat suitability. The Geospatial Suitability Indices (GSI) toolbox was developed in ArcGIS Pro 2.7 using the Python® 3.7 programming language and is available for use on the local desktop in the Windows 10 environment. Two main tools comprise the GSI toolbox. First, the Suitability Index Calculator tool uses thematic or continuous geospatial raster layers to calculate parameter suitability indices based on user-specified habitat relationships. Second, the Overall Suitability Index Calculator combines multiple parameter suitability indices into one overarching index using one or more options, including: arithmetic mean, weighted arithmetic mean, geometric mean, and minimum limiting factor. The resultant output is a raster layer representing habitat suitability values from 0.0 to 1.0, where zero is unsuitable habitat and one is ideal suitability. This report documents the model purpose and development as well as provides a user’s guide for the GSI toolbox.

scholarly journals Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 278 ◽  
Author(s):  
Lilian Shi ◽  
Yue Yuan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Multi Attribute Decision Making

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

scholarly journals Generalized Linguistic Hesitant Intuitionistic Fuzzy Hybrid Aggregation Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Yang ◽  
Jiarong Shi ◽  
Yongfeng Pang
Keyword(s):  
Decision Making ◽  
Geometric Mean ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
New Method ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Special Cases

Some hybrid aggregation operators have been developed based on linguistic hesitant intuitionistic fuzzy information. The generalized linguistic hesitant intuitionistic fuzzy hybrid weighted averaging (GLHIFHWA) operator and the generalized linguistic hesitant intuitionistic fuzzy hybrid geometric mean (GLHIFHGM) operator are defined. Some special cases of the new aggregation operators are studied and many existing aggregation operators are special cases of the new operators. A new multiple attribute decision making method based on the new aggregation operators is proposed and a practical numerical example is presented to illustrate the feasibility and practical advantages of the new method.

scholarly journals Multi-Attribute Decision Making Based on Interval Neutrosophic Trapezoid Linguistic Aggregation Operators

2016 ◽  
pp. 344-365
Author(s):  
Broumi Said ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Neutrosophic Sets ◽  
Numerical Example ◽  
Inconsistent Information ◽  
Weighted Arithmetic ◽  
Multi Attribute Decision Making ◽  
Interval Neutrosophic Sets

Multi-attribute decision making (MADM) play an important role in many applications, due to the efficiency to handle indeterminate and inconsistent information, interval neutrosophic sets is widely used to model indeterminate information. In this paper, a new MADM method based on interval neutrosophic trapezoid linguistic weighted arithmetic averaging aggregation (INTrLWAA) operator and interval neutrosophic trapezoid linguistic weighted geometric aggregation (INTrLWGA) operatoris presented. A numerical example is presented to demonstrate the application and efficiency of the proposed method.

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