scholarly journals A Novel Algorithm Based on 2-Additive Measure and Shapley Value and Its Application in Land Pollution Remediation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jian Lin ◽  
Qiongling Wu ◽  
Riqing Chen ◽  
Zhiyong Tian
Keyword(s):  
Shapley Value ◽  
Group Decision ◽  
Young Inequality ◽  
Aggregation Operator ◽  
Additive Measure ◽  
Pollution Remediation ◽  
Heterogeneous Information ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
Special Cases

In this article, a new aggregation operator called the Young–Shapley optimal weight (Y-SOW) operator is proposed to aggregate heterogeneous information in group decision-making. The Y-SOW operator combines the Shapley value with the Young inequality. Meanwhile, a series of special cases and main properties of the Y-SOW operator are studied. Furthermore, the dispersion maximization model of the Y-SOW operator is established to obtain the optimal 2-additive measure. In the Shapley value method of the cooperative game, the 2-additive measure not only simplifies the complexity of fuzzy measures but also solves the interaction between attributes. The Shapley value of the 2-additive measure is explored to the weight of the Y-SOW operator. Finally, the Y-SOW operator-based multiattribute group decision (YSMGAD) algorithm is proposed. The application of the YSMGAD algorithm for land pollution remediation is analyzed.

scholarly journals Application of Choquet Integral-Fuzzy Measures for Aggregating Customers’ Satisfaction

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Lazim Abdullah ◽  
Noor Azzah Awang ◽  
Mahmod Othman
Keyword(s):  
Shapley Value ◽  
Choquet Integral ◽  
Evaluation Process ◽  
Aggregation Operator ◽  
Interaction Index ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
New Development ◽  
The Future

Choquet integral is a type of aggregation operator that is commonly used to aggregate the interrelated information. Nowadays, this operator has been successfully embedded with fuzzy measures in solving various evaluation problems. Inspired from this new development, this paper aims to introduce a combined Choquet integral-fuzzy measures (CI-FM) operator that uses the Shapley value standard and interaction index to deal with the interactions between elements of information. The proposed operator takes into account not only the importance of elements or their ordered positions but also the interaction among criteria during the evaluation process. A case of customers’ satisfaction over two fast restaurants in Malaysia is presented to illustrate the application of the proposed aggregation operator. Based on three customers’ satisfaction criteria, restaurant 1 and restaurant 2 received CI-FM scores of 0.711011 and 0.704945, respectively. Interestingly, the criterion “services” constantly received the highest rating across both restaurants. In addition, the proposed aggregation operator successfully identified which restaurant is superior in the eyes of customers. Finally, this study offers some research ideas for the future.

A Novel Algorithm for Group Decision Making Based on Continuous Optimal Aggregation Operator and Shapley Value

2019 ◽  
Vol 27 (06) ◽  
pp. 969-1002
Author(s):  
Jian Lin ◽  
Qiang Zhang ◽  
Fanyong Meng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Aggregation Operator ◽  
Fuzzy Measure ◽  
Chi Square ◽  
Preference Relations ◽  
Special Cases ◽  
Linguistic Preference Relation

Interval linguistic preference relation is an effective tool for expressing experts’ preference in group decision making under uncertain linguistic environment. A new aggregation operator called continuous chi-square deviation based 2-tuple linguistic ordered weighted quasi-averaging (C-CDLOWQ) operator is proposed to transform the interval linguistic preference relations into precise linguistic preference relations. Some desirable properties and special cases of the C-CDLOWQ operator are analyzed in detail. To take the interactive phenomenon among experts into account, the Shapley weighting vector is presented to integrate the expected linguistic preference relations. The λ-fuzzy measure is employed to simplify the fuzzy measure on expert set. A CS-GDM algorithm is developed to group decision making with interval linguistic preference relations. The application in commercial investment problem is provided to illustrate the effectiveness of CS-GDM algorithm.

scholarly journals CAPACITIES AND GAMES ON LATTICES: A SURVEY OF RESULTS

2006 ◽  
Vol 14 (04) ◽  
pp. 371-392 ◽  
Author(s):  
MICHEL GRABISCH
Keyword(s):  
Shapley Value ◽  
Cooperative Games ◽  
Choquet Integral ◽  
Characteristic Form ◽  
Möbius Transform ◽  
Fuzzy Measures ◽  
The Shapley Value ◽  
Power Set ◽  
Recent Developments

We provide a survey of recent developments about capacities (or fuzzy measures) and cooperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

scholarly journals Linguistic Interval-Valued Intuitionistic Fuzzy Archimedean Power Muirhead Mean Operators for Multiattribute Group Decision-Making

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-28 ◽  
Author(s):  
Yuchu Qin ◽  
Xiaolan Cui ◽  
Meifa Huang ◽  
Yanru Zhong ◽  
Zhemin Tang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Intuitionistic Fuzzy Number ◽  
Specific Context ◽  
Intuitionistic Fuzzy ◽  
Special Cases ◽  
Magdm Problems ◽  
Interval Valued

Two important tasks in multiattribute group decision-making (MAGDM) are to describe the attribute values and to generate a ranking of all alternatives. A superior tool for the first task is linguistic interval-valued intuitionistic fuzzy number (LIVIFN), and an effective tool for the second task is aggregation operator (AO). To date, nearly ten AOs of LIVIFNs have been presented. Each AO has its own features and can work well in its specific context. But there is not yet an AO of LIVIFNs that can offer desirable generality and flexibility in aggregating attribute values and capturing attribute interrelationships and concurrently reduce the influence of unreasonable attribute values. To this end, a linguistic interval-valued intuitionistic fuzzy Archimedean power Muirhead mean operator and its weighted form, which have such capabilities, are presented in this paper. Firstly, the generalised expressions of the AOs are established by a combination of the Muirhead mean operator and the power average operator under the Archimedean T-norm and T-conorm operations of LIVIFNs. Then the properties of the AOs are explored and proved, their specific expressions are constructed, and the special cases of the specific expressions are discussed. After that, a new method for solving the MAGDM problems based on LIVIFNs is designed on the basis of the weighted AO. Finally, the designed method is illustrated via a practical example, and the presented AOs are evaluated via experiments and comparisons.

Using the Shapley Value to Determine the Expert’s Discourse Right in Group Decision-Making

2015 ◽  
Vol 713-715 ◽  
pp. 2029-2036
Author(s):  
Jin Tang ◽  
Chun Dong Guo ◽  
Yan Gao
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Knowledge Spillover ◽  
Expert Group ◽  
The Shapley Value ◽  
Decision Making Problem ◽  
Different Types ◽  
Index Weight

In terms of different decision-making problem and expert groups, experts’ discourse right is dynamic and relative. Therefore, scientific and rationality of experts empowerment are directly affect final evaluation results. For solving the problem of the objectivity of the evaluation index weight assignment, a method which based on the Shapley value to determine the expert’s weight has been proposed and illustrated in this paper. Firstly, on the basis of analyzing the characteristics of the expert group decision making process, the correlation of experts’ knowledge stock has been defined to represent knowledge spillover among the experts group. Secondly, based on the contribution degree of each expert’s knowledge spillover which has been discussed through correlation analysis, and weight has been allocated to experts. The results show that the method can not only avoid experts empowerment evenly phenomenon, and fully respect the differences of evaluation experts. Finally, the author suggests different types of expert group decisions should be invited to participate in decision-making which helps to give play to brainstorming effect, producing more knowledge spillover and promoting scientific and rationality of decision-making.

A Theil coefficient-based combination prediction method with interval heterogeneous information for wind energy prediction

2021 ◽  
pp. 1-18
Author(s):  
Qiongling Wu ◽  
Jian Lin ◽  
Shaohan Zhang ◽  
Zhiyong Tian
Keyword(s):  
Wind Energy ◽  
Prediction Method ◽  
Interval Data ◽  
Young Inequality ◽  
Heterogeneous Information ◽  
Energy Prediction ◽  
Weighted Arithmetic ◽  
Special Cases ◽  
Accuracy Of Prediction ◽  
The Empirical Analysis

This paper constructs the continuous-Young optimal weighted arithmetic averaging (C-YOWA) operator and the continuous-Young optimal weighted geometric (C-YOWG) operator based on definite integral and Young inequality. A series of special cases and main properties of the proposed aggregation operators are also investigated. In order to integrate heterogeneous interval data and obtain more accurate prediction results, the heterogeneous interval combination prediction (HICP) model based on C-YOWA operator, C-YOWG operator and Theil coefficient is proposed. The HICP model consider not only the existence of both additive and multiplicative interval information, but also the preference information of experts. Finally, the model is applied to the empirical analysis of wind energy prediction. The comparison of results shows that the established model can effectively improve the accuracy of prediction.

A novel q-rung orthopair fuzzy TODIM approach for multi-criteria group decision making based on Shapley value and relative entropy

2021 ◽  
Vol 40 (1) ◽  
pp. 235-250
Author(s):  
Liuxin Chen ◽  
Nanfang Luo ◽  
Xiaoling Gou
Keyword(s):  
Decision Making ◽  
Relative Entropy ◽  
Group Decision Making ◽  
Shapley Value ◽  
Group Decision ◽  
Similarity Measures ◽  
Entropy Measure ◽  
Shapley Values ◽  
Interactive Relationship ◽  
The Difference

In the real multi-criteria group decision making (MCGDM) problems, there will be an interactive relationship among different decision makers (DMs). To identify the overall influence, we define the Shapley value as the DM’s weight. Entropy is a measure which makes it better than similarity measures to recognize a group decision making problem. Since we propose a relative entropy to measure the difference between two systems, which improves the accuracy of the distance measure.In this paper, a MCGDM approach named as TODIM is presented under q-rung orthopair fuzzy information.The proposed TODIM approach is developed for correlative MCGDM problems, in which the weights of the DMs are calculated in terms of Shapley values and the dominance matrices are evaluated based on relative entropy measure with q-rung orthopair fuzzy information.Furthermore, the efficacy of the proposed Gq-ROFWA operator and the novel TODIM is demonstrated through a selection problem of modern enterprises risk investment. A comparative analysis with existing methods is presented to validate the efficiency of the approach.

Query Games in Databases

2021 ◽  
Vol 50 (1) ◽  
pp. 78-85
Author(s):  
Ester Livshits ◽  
Leopoldo Bertossi ◽  
Benny Kimelfeld ◽  
Moshe Sebag
Keyword(s):  
Game Theory ◽  
Cooperative Game ◽  
Shapley Value ◽  
Cooperative Game Theory ◽  
The Shapley Value ◽  
Computational Aspects ◽  
Aggregate Query ◽  
Boolean Query

Database tuples can be seen as players in the game of jointly realizing the answer to a query. Some tuples may contribute more than others to the outcome, which can be a binary value in the case of a Boolean query, a number for a numerical aggregate query, and so on. To quantify the contributions of tuples, we use the Shapley value that was introduced in cooperative game theory and has found applications in a plethora of domains. Specifically, the Shapley value of an individual tuple quantifies its contribution to the query. We investigate the applicability of the Shapley value in this setting, as well as the computational aspects of its calculation in terms of complexity, algorithms, and approximation.

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