scholarly journals Fuzzy Triangular Aggregation Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Ulrich Florian Simo ◽  
Henri Gwét
Keyword(s):  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Triangular Norms ◽  
New Class ◽  
Weighted Arithmetic ◽  
Wide Range ◽  
Fuzzy Aggregation ◽  
Available Information ◽  
Selection Of ◽  
Do So

We present a new class of fuzzy aggregation operators that we call fuzzy triangular aggregation operators. To do so, we focus on the situation where the available information cannot be assessed with exact numbers and it is necessary to use another approach to assess uncertain or imprecise information such as fuzzy numbers. We also use the concept of triangular norms (t-norms and t-conorms) as pseudo-arithmetic operations. As a result, we get notably the fuzzy triangular weighted arithmetic (FTWA), the fuzzy triangular ordered weighted arithmetic (FTOWA), the fuzzy generalized triangular weighted arithmetic (FGTWA), the fuzzy generalized triangular ordered weighted arithmetic (FGTOWA), the fuzzy triangular weighted quasi-arithmetic (Quasi-FTWA), and the fuzzy triangular ordered weighted quasi-arithmetic (Quasi-FTOWA) operators. Main properties of these operators are discussed as well as their comparison with other existing ones. The fuzzy triangular aggregation operators not only cover a wide range of useful existing fuzzy aggregation operators but also provide new interesting cases. Finally, an illustrative example is also developed regarding the selection of strategies.

scholarly journals The Oxford Handbook of Reasons and Normativity

2018 ◽  
Keyword(s):  
Philosophy Of Mind ◽  
Philosophy Of Language ◽  
Wide Range ◽  
Recent Philosophy ◽  
Recent Developments ◽  
Selection Of ◽  
Do So

The Oxford Handbook of Reasons and Normativity contains forty-four commissioned chapters on a wide range of topics. It will appeal especially to readers with an interest in ethics or epistemology, but also to those with an interest in philosophy of mind or philosophy of language. Both students and academics will benefit from the fact that the Handbook combines helpful overviews with innovative contributions to current debates. A diverse selection of substantive positions are defended by leading proponents of the views in question. Few concepts have received as much attention in recent philosophy as the concept of a reason. This is the first edited collection to provide broad coverage of the study of reasons and normativity across multiple philosophical subfields. In addition to focusing on reasons as part of the study of ethics and as part of the study of epistemology (as well as focusing on reasons as part of the study of the philosophy of language and as part of the study of the philosophy of mind), the Handbook covers recent developments concerning the nature of normativity in general. A number of the contributions to the Handbook explicitly address such “metanormative” issues, bridging subfields as they do so.

scholarly journals Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk

Symmetry ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 6 ◽  
Author(s):  
Rui Wang ◽  
Jie Wang ◽  
Hui Gao ◽  
Guiwu Wei
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Investment Risk ◽  
Financial Investment ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Fuzzy Madm ◽  
Decision Making Model

In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the PFWMM and PFWDMM operators to build a decision-making model to handle picture fuzzy MADM problems. In the end, we take a concrete instance of appraising a financial investment risk to demonstrate our defined model and to verify its accuracy and scientific merit.

scholarly journals Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 218 ◽  
Author(s):  
Jinming Zhou ◽  
Tomas Baležentis ◽  
Dalia Streimikiene
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Harmonic Mean ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Selection Of

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

scholarly journals Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 468 ◽  
Author(s):  
Jiahuan He ◽  
Xindi Wang ◽  
Runtong Zhang ◽  
Li Li
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Project Assessment ◽  
Fuzzy Environment ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs). Second, we propose some new aggregation operators of q-RPFNs based on the newly-developed operations, i.e., the q-rung picture fuzzy Dombi Hamy mean (q-RPFDHM) operator, the q-rung picture fuzzy Dombi weighted Hamy mean (q-RPFDWHM) operator, the q-rung picture fuzzy Dombi dual Hamy mean (q-RPFDDHM) operator, and the q-rung picture fuzzy Dombi weighted dual Hamy mean (q-RPFDWDHM) operator. Properties of these operators are also discussed. Third, a new q-rung picture fuzzy MAGDM method is proposed with the help of the proposed operators. Finally, a best project selection example is provided to demonstrate the practicality and effectiveness of the new method. The superiorities of the proposed method are illustrated through comparative analysis.

scholarly journals A Hybrid Method for Complex Pythagorean Fuzzy Decision Making

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Muhammad Akram ◽  
Samirah Alsulami ◽  
Kiran Zahid
Keyword(s):  
Decision Making ◽  
Uncertain Data ◽  
Fuzzy Model ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Average Operator ◽  
Fuzzy Aggregation ◽  
Selection Of

This article takes advantage of advancements in two different fields in order to produce a novel decision-making framework. First, we contribute to the theory of aggregation operators, which are mappings that combine large amounts of data into more advantageous forms. They are extensively used in different settings from classical to fuzzy set theory alike. Secondly, we expand the literature on complex Pythagorean fuzzy model, which has an edge over other models due to its ability to handle uncertain data of periodic nature. We propose some aggregation operators for complex Pythagorean fuzzy numbers that depend on the Hamacher t-norm and t-conorm, namely, the complex Pythagorean fuzzy Hamacher weighted average operator, the complex Pythagorean fuzzy Hamacher ordered weighted average operator, and the complex Pythagorean fuzzy Hamacher hybrid average operator. We explore some properties of these operators inclusive of idempotency, monotonicity, and boundedness. Then, the operators are applied to multicriteria decision-making problems under the complex Pythagorean fuzzy environment. Furthermore, we present an algorithm along with a flow chart, and we demonstrate their applicability with the assistance of two numerical examples (selection of most favorable country for immigrants and selection of the best programming language). We investigate the adequacy of this algorithm by conducting a comparative study with the case of complex intuitionistic fuzzy aggregation operators.

A method to solve strategy based decision making problems with logarithmic T-spherical fuzzy aggregation framework

2021 ◽  
pp. 1-19
Author(s):  
Shouzhen Zeng ◽  
Amina Azam ◽  
Kifayat Ullah ◽  
Zeeshan Ali ◽  
Awais Asif
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Human Judgment ◽  
Induction Method ◽  
Fuzzy Aggregation ◽  
The Impact

T-Spherical fuzzy set (TSFS) is an improved extension in fuzzy set (FS) theory that takes into account four angles of the human judgment under uncertainty about a phenomenon that is membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). The purpose of this manuscript is to introduce and investigate logarithmic aggregation operators (LAOs) in the layout of TSFSs after observing the shortcomings of the previously existing AOs. First, we introduce the notions of logarithmic operations for T-spherical fuzzy numbers (TSFNs) and investigate some of their characteristics. The study is extended to develop T-spherical fuzzy (TSF) logarithmic AOs using the TSF logarithmic operations. The main theory includes the logarithmic TSF weighted averaging (LTSFWA) operator, and logarithmic TSF weighted geometric (LTSFWG) operator along with the conception of ordered weighted and hybrid AOs. An investigation about the validity of the logarithmic TSF AOs is established by using the induction method and examples are solved to examine the practicality of newly developed operators. Additionally, an algorithm for solving the problem of best production choice is developed using TSF information and logarithmic TSF AOs. An illustrative example is solved based on the proposed algorithm where the impact of the associated parameters is examined. We also did a comparative analysis to examine the advantages of the logarithmic TSF AOs.

Weighted aggregation operators of fuzzy credibility cubic numbers and their decision making strategy for slope design schemes

2020 ◽  
Vol 01 ◽  
Author(s):  
Jun Ye ◽  
Shigui Du ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Real World ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Open Pit Mine ◽  
Open Pit ◽  
Weighted Arithmetic ◽  
Ranking Of Alternatives ◽  
Slope Design

Background: A fuzzy cubic set (FCS) is composed of a fuzzy set (FS) (certain fuzzy numbers) and an intervalvalued fuzzy set (IVFS) (uncertain fuzzy numbers) to describe the hybrid information of both. To enhance the credibility of both, they should be closely related to the measures/degrees of credibility owing to the vagueness and uncertainty of humans’ cognitions regarding the real world. Objective: This paper presents the notions of a fuzzy cubic credibility set (FCCS) and a fuzzy cubic credibility number (FCCN) as the new generalization of the FCS notion so as to enhance the credibility level of FCS by means of the credibility degrees of both FS and IVFS. Next, we define operations of FCCNs, an expected value of FCCN, and the FCCN weighted arithmetic averaging (FCCNWAA) and FCCN weighted geometric averaging (FCCNWGA) operators for decision making (DM) strategy. Method: A decision making (DM) strategy using the FCCNWAA or FCCNWGA operator is proposed to solve multicriteria DM problems in the environment of FCCNs. Then, the proposed DM strategy is applied to a DM example of slope design schemes for an open pit mine in the environment of FCCNs to reflect the feasibility of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Conclusion: However, the highlighting advantage of this study is that the proposed DM strategy not only indicates the degrees of credibility regarding the assessed values of FCNs in the DM process but also enhances the DM reliability in the environment of FCCNs. Hence, the proposed DM strategy is superior to the fuzzy cubic DM strategy in the environment of FCCNs.

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.

On Ranking of Intuitionistic Fuzzy Values Based on Dominance Relations

2014 ◽  
Vol 22 (02) ◽  
pp. 315-335 ◽  
Author(s):  
Xiaohan Yu ◽  
Zeshui Xu ◽  
Shousheng Liu ◽  
Qi Chen
Keyword(s):  
Decision Making ◽  
Order Relation ◽  
Aggregation Operators ◽  
Fuzzy Subset ◽  
Dominance Relations ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Do So

For intuitionistic fuzzy values (IFVs), there are more or less some drawbacks in the existing comparison methods, so it is necessary for us to develop a more proper technique for comparing or ranking IFVs in this paper. To do so, we first formalize an IFV as a fuzzy subset in order to analyze the fuzzy meaning of an IFV, and then according to the basic properties of the fuzzy subset, we determine the dominance relation (order relation) between two IFVs by defining a dominance degree. In order to explain the feasibility of the dominance relations, we validate the monotonicity of intuitionistic fuzzy operational laws, and additionally, we improve and prove the monotonicity of several intuitionistic fuzzy aggregation operators on the basis of the dominance relations. Because it is of importance for some practical problems (e.g., intuitionistic fuzzy multi-attribute decision making) to rank IFVs, we finally develop a method for ranking IFVs by constructing a dominance matrix based on the dominance degrees. A simple example is taken to illustrate the validity of our ranking method.

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.

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