A Multi-Criteria Decision-Making Method Based on Heronian Mean Operators Under a Linguistic Hesitant Fuzzy Environment

2015 ◽  
Vol 32 (05) ◽  
pp. 1550035 ◽  
Author(s):  
Su-Min Yu ◽  
Huan Zhou ◽  
Xiao-Hong Chen ◽  
Jian-Qiang Wang
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Fuzzy Arithmetic ◽  
New Order ◽  
Comparison Analysis ◽  
Weighted Arithmetic ◽  
Fuzzy Environment ◽  
Special Cases ◽  
Parameter Values ◽  
Heronian Mean

Linguistic hesitant fuzzy sets (LHFSs) are a very useful and appropriate means of expressing preferences of decision-makers; moreover their basic operations and comparison methods have been defined and applied to the solving of MCDM problems. However, there are a number of limitations in the related studies. In this paper, using information from existing studies, several new operations and a new order relationship are defined; moreover four linguistic hesitant fuzzy Heronian mean operators are proposed: the linguistic hesitant fuzzy arithmetic Heronian mean (LHFAHM) operator; the linguistic hesitant fuzzy weighted arithmetic Heronian mean (LHFWAHM) operator; the linguistic hesitant fuzzy geometric Heronian mean (LHFGHM) operator; and the linguistic hesitant fuzzy weighted geometric Heronian mean (LHFWGHM) operator. Furthermore, some useful and desirable properties of these operators are analyzed in some special cases, with respect to the different parameter values in these operators, are discussed. Additionally, an approach based on the LHFWAHM and LHFWGHM operators for solving MCDM problems is proposed. Finally, an illustrative example is provided to verify the validity and feasibility of the proposed approaches, and a comparison analysis is also presented to demonstrate the influences of different parameters on the results of decision-making.

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.

scholarly journals Multicriteria Decision Making Based on Archimedean Bonferroni Mean Operators of Hesitant Fermatean 2-Tuple Linguistic Terms

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Huijuan Wang ◽  
Xin Wang ◽  
Lidong Wang
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Decision Makers ◽  
Linguistic Terms ◽  
Fundamental Properties ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Geometric Bonferroni Mean ◽  
Parameter Values ◽  
Uncertainty Information

The study is concerned with the representation and aggregation of complex uncertainty information. First, the concept of hesitant Fermatean 2-tuple linguistic sets (HF2TLSs) is introduced for characterizing an individual’s imprecision preferences and assessing information by combining 2-tuple linguistic terms and Fermatean fuzzy sets. The advantage of hesitant Fermatean 2-tuple linguistic information is that it can handle higher levels of uncertainty and express the decision-makers’ hesitancy. Second, we extend Bonferroni mean (BM) operators under the background of HF2TLSs for the sake of their application in information fusion and decision making. The Archimedean t-norm and s-norm- (ATS-) based hesitant Fermatean 2-tuple linguistic weighted Bonferroni mean (A-HF2TLWBM) operator and the ATS-based hesitant Fermatean 2-tuple linguistic weighted geometric Bonferroni mean (A-HF2TLWGBM) operator are developed by considering the interrelationship between any two variables. The main benefit of the proposed operators is that these operators deliver more complete and flexible results compared to existing methods. Moreover, some fundamental properties and special cases are examined by adjusting parameter values. Finally, an approach is designed as a support for handling decision making problems, and an example regarding investment selection is provided to demonstrate the practicality of the designed method with a detailed discussion of parameter influence and comparisons with the existing methods.

scholarly journals Intuitionistic Unbalanced Linguistic Generalized Multiple Attribute Group Decision Making and Its Application to Green Products Selection

2018 ◽  
Vol 2018 ◽  
pp. 1-24
Author(s):  
Bing Han ◽  
Zhifu Tao ◽  
Huayou Chen ◽  
Ligang Zhou
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Critical Role ◽  
Multiple Attribute Decision Making ◽  
Decision Makers ◽  
Green Products ◽  
Multiple Attribute ◽  
Parameter Values ◽  
Heronian Mean

In many countries, green products play a critical role in energy recycling and environment protection. The selection of green products can be regarded as a multiple attribute decision making (MADM) problem. Due to the complexity and uncertainty of the problem, decision makers may give their personal preference values to different attributes of alternatives by intuitionistic unbalanced linguistic term sets. The main purpose of this paper is to put forward a new generalized multiple attribute group decision making (GMAGDM) approach based on the intuitionistic unbalanced linguistic dependent weighted generalized Heronian mean (IULDWGHM) operator and the intuitionistic unbalanced linguistic dependent weighted generalized geometric Heronian mean (IULDWGGHM) operator. The proposed method can not only relieve the influence of unfair assessments, but also consider the interaction effects of attributes. Furthermore, the appropriate parameter values and operators can be selected to meet the different risk preference of decision makers and actual requirements. Finally, a green products selection case is given to illustrate the effectiveness and universality of the developed approach.

scholarly journals Generalized Fuzzy Soft Power Bonferroni Mean Operators and Their Application in Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 810
Author(s):  
Zitai Xu ◽  
Chunfang Chen ◽  
Yutao Yang
Keyword(s):  
Decision Making ◽  
Soft Power ◽  
Original Data ◽  
Decision Makers ◽  
Decision Making Process ◽  
Software Selection ◽  
Decision Method ◽  
Bonferroni Mean ◽  
Special Cases ◽  
Multi Attribute Decision Making

In decision-making process, decision-makers may make different decisions because of their different experiences and knowledge. The abnormal preference value given by the biased decision-maker (the value that is too large or too small in the original data) may affect the decision result. To make the decision fair and objective, this paper combines the advantages of the power average (PA) operator and the Bonferroni mean (BM) operator to define the generalized fuzzy soft power Bonferroni mean (GFSPBM) operator and the generalized fuzzy soft weighted power Bonferroni mean (GFSWPBM) operator. The new operator not only considers the overall balance between data and information but also considers the possible interrelationships between attributes. The excellent properties and special cases of these ensemble operators are studied. On this basis, the idea of the bidirectional projection method based on the GFSWPBM operator is introduced, and a multi-attribute decision-making method, with a correlation between attributes, is proposed. The decision method proposed in this paper is applied to a software selection problem and compared to the existing methods to verify the effectiveness and feasibility of the proposed method.

scholarly journals Some q-Rung Dual Hesitant Fuzzy Heronian Mean Operators with Their Application to Multiple Attribute Group Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 472 ◽  
Author(s):  
Yuan Xu ◽  
Xiaopu Shang ◽  
Jun Wang ◽  
Wen Wu ◽  
Huiqun Huang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Hesitant Fuzzy Sets ◽  
Multiple Attribute ◽  
A New Technique ◽  
Supplier Selection Problem ◽  
Heronian Mean

The q-rung orthopair fuzzy sets (q-ROFSs), originated by Yager, are good tools to describe fuzziness in human cognitive processes. The basic elements of q-ROFSs are q-rung orthopair fuzzy numbers (q-ROFNs), which are constructed by membership and nonmembership degrees. As realistic decision-making is very complicated, decision makers (DMs) may be hesitant among several values when determining membership and nonmembership degrees. By incorporating dual hesitant fuzzy sets (DHFSs) into q-ROFSs, we propose a new technique to deal with uncertainty, called q-rung dual hesitant fuzzy sets (q-RDHFSs). Subsequently, we propose a family of q-rung dual hesitant fuzzy Heronian mean operators for q-RDHFSs. Further, the newly developed aggregation operators are utilized in multiple attribute group decision-making (MAGDM). We used the proposed method to solve a most suitable supplier selection problem to demonstrate its effectiveness and usefulness. The merits and advantages of the proposed method are highlighted via comparison with existing MAGDM methods. The main contribution of this paper is that a new method for MAGDM is proposed.

scholarly journals Simplified neutrosophic linguistic normalized weighted bonferroni mean operator and its application to multi-criteria decision-making problems

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3339-3360 ◽  
Author(s):  
Zhang-Peng Tian ◽  
Jing Wang ◽  
Hong-Yu Zhang ◽  
Xiao-Hong Chen ◽  
Jian-Qiang Wang
Keyword(s):  
Decision Making ◽  
Comparison Method ◽  
Multi Criteria Decision Making ◽  
Comparison Analysis ◽  
Scale Functions ◽  
Bonferroni Mean ◽  
Special Cases

The main purpose of this paper is to provide a method of multi-criteria decision-making that combines simplified neutrosophic linguistic sets and normalized Bonferroni mean operator to address the situations where the criterion values take the form of simplified neutrosophic linguistic numbers and the criterion weights are known. Firstly, the new operations and comparison method for simplified neutrosophic linguistic numbers are defined and some linguistic scale functions are employed. Subsequently, a Bonferroni mean operator and a normalized weighted Bonferroni mean operator of simplified neutrosophic linguistic numbers are developed, in which some desirable characteristics and special cases with respect to the parameters p and q in Bonferroni mean operator are studied. Then, based on the simplified neutrosophic linguistic normalized weighted Bonferroni mean operator, a multi-criteria decision-making approach is proposed. Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing method to demonstrate the effectiveness and feasibility of the developed approach.

Explaining monotonic ranking functions

2020 ◽  
Vol 14 (4) ◽  
pp. 640-652
Author(s):  
Abraham Gale ◽  
Amélie Marian
Keyword(s):  
Decision Making ◽  
Selection Process ◽  
A Priori ◽  
Data Distribution ◽  
Synthetic Data ◽  
Decision Processes ◽  
Decision Makers ◽  
Ranking Functions ◽  
High School Admissions ◽  
Parameter Values

Ranking functions are commonly used to assist in decision-making in a wide variety of applications. As the general public realizes the significant societal impacts of the widespread use of algorithms in decision-making, there has been a push towards explainability and transparency in decision processes and results, as well as demands to justify the fairness of the processes. In this paper, we focus on providing metrics towards explainability and transparency of ranking functions, with a focus towards making the ranking process understandable, a priori , so that decision-makers can make informed choices when designing their ranking selection process. We propose transparent participation metrics to clarify the ranking process, by assessing the contribution of each parameter used in the ranking function in the creation of the final ranked outcome, using information about the ranking functions themselves, as well as observations of the underlying distributions of the parameter values involved in the ranking. To evaluate the outcome of the ranking process, we propose diversity and disparity metrics to measure how similar the selected objects are to each other, and to the underlying data distribution. We evaluate the behavior of our metrics on synthetic data, as well as on data and ranking functions on two real-world scenarios: high school admissions and decathlon scoring.

scholarly journals Multiattribute Group Decision-Making Based on Linguistic Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Aggregation Operators

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Mingwei Lin ◽  
Jiuhan Wei ◽  
Zeshui Xu ◽  
Riqing Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Bonferroni Mean ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Special Cases ◽  
Geometric Bonferroni Mean ◽  
Decision Making Model ◽  
Pythagorean Fuzzy Numbers

The partitioned Bonferroni mean (PBM) operator can efficiently aggregate inputs, which are divided into parts based on their interrelationships. To date, it has not been used to aggregate linguistic Pythagorean fuzzy numbers (LPFNs). In this paper, we extend the PBM operator and partitioned geometric Bonferroni mean (PGBM) operator to the linguistic Pythagorean fuzzy sets (LPFSs) and use them to develop a novel multiattribute group decision-making model under the linguistic Pythagorean fuzzy environment. We first define some novel operational laws for LPFNs, which take into consideration the interactions between the membership degree (MD) and nonmembership degree (NMD) from two different LPFNs. Based on these novel operational laws, we put forward the interaction PBM (LPFIPBM) operator, the weighted interaction PBM (LPFWIPBM) operator, the interaction PGBM (LPFIPGBM) operator, and the weighted interaction PGBM (LPFWIPGBM) operator. Then, we study some properties of these proposed operators and discuss their special cases. Based on the proposed LPFWIPBM and LPFWIPGBM operators, a novel multiattribute group decision-making model is developed to process the linguistic Pythagorean fuzzy information. Finally, some illustrative examples are introduced to compare our proposed methods with the existing ones.

scholarly journals Linguistic Interval-Valued Intuitionistic Fuzzy Copula Heronian Mean Operators for Multiattribute Group Decision-Making

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Lei Xu ◽  
Yi Liu ◽  
Haobin Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Group Decision ◽  
Decision Makers ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy ◽  
Uncertainty Information ◽  
The Relationship ◽  
Interval Valued ◽  
Heronian Mean

As a generalization of the intuitionistic fuzzy number (IFN), the linguistic interval-valued intuitionistic fuzzy number (LIVIFN) is a flexible and superior tool to describe complex fuzzy uncertainty information. Heronian mean (HM) operator has the characteristic of considering the relationship between attributes. Extended copulas (ECs) and extended cocopulas (ECCs) are the promotion form of Archimedean t-norm and t-conorm (ATT). ECs and ECCs can generate versatile operational rules and can provide more choice for decision makers (DMs). Therefore, it is very necessary to take advantages of them. In this paper, ECs and ECCs, some specifics of ECs and ECCs, and score and accuracy functions of IVILFNs are gained first. Then, we propose the linguistic interval-valued intuitionistic fuzzy weighted copula Heronian mean (LIVIFWCHM) operator; also, some properties and five specific expressions of the LIVIFWCHM operator are discussed. Moreover, we also propose a new MAGDM approach based on the proposed LIVIFWCHM operator. Finally, a set of examples are used to demonstrate the effectiveness, generality, and flexibility of the proposed method.

scholarly journals Significance of multi-objective optimization in logistics problem for multi-product supply chain network under the intuitionistic fuzzy environment

2021 ◽  
Author(s):  
Srikant Gupta ◽  
Ahteshamul Haq ◽  
Irfan Ali ◽  
Biswajit Sarkar
Keyword(s):  
Decision Making ◽  
Supply Chain ◽  
Real Life ◽  
Decision Makers ◽  
Supply Chain Network ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Hierarchical Decision

AbstractDetermining the methods for fulfilling the continuously increasing customer expectations and maintaining competitiveness in the market while limiting controllable expenses is challenging. Our study thus identifies inefficiencies in the supply chain network (SCN). The initial goal is to obtain the best allocation order for products from various sources with different destinations in an optimal manner. This study considers two types of decision-makers (DMs) operating at two separate groups of SCN, that is, a bi-level decision-making process. The first-level DM moves first and determines the amounts of the quantity transported to distributors, and the second-level DM then rationally chooses their amounts. First-level decision-makers (FLDMs) aimed at minimizing the total costs of transportation, while second-level decision-makers (SLDM) attempt to simultaneously minimize the total delivery time of the SCN and balance the allocation order between various sources and destinations. This investigation implements fuzzy goal programming (FGP) to solve the multi-objective of SCN in an intuitionistic fuzzy environment. The FGP concept was used to define the fuzzy goals, build linear and nonlinear membership functions, and achieve the compromise solution. A real-life case study was used to illustrate the proposed work. The obtained result shows the optimal quantities transported from the various sources to the various destinations that could enable managers to detect the optimum quantity of the product when hierarchical decision-making involving two levels. A case study then illustrates the application of the proposed work.

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