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Entropy
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Decision Optimization in Information Theory and Game Theory
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Decision Optimization in Information Theory and Game Theory

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 9711

Special Issue Editor

Prof. Dr. Marek Szopa

E-Mail Website
Guest Editor
Department of Operations Research College of Informatics and Communication, University of Economics in Katowice, Ul. Bogucicka 3, 40-287 Katowice, Poland
Interests: game theory; quantum games; matching markets; fair share; quantum communication; application of game theory to negotiation and decision making
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The development of information theory and game theory opens up new possibilities of using it to optimize decision making. Methods based on artificial intelligence and machine learning will in the future set the standards for optimization of decisions in key areas of the economy and human life.

Advances in quantum information processing also open up new opportunities. Quantum methods allow achieving new ways of strategy randomization and offer a classically unavailable level of information security.

The aim of the project is to explore various theoretical methods of decision optimization based both on the classical and quantum approach.

The scope of the project includes the development of tools and techniques to optimize decisions via:

  • Machine- and deep-learning-based decisions in different areas of social life;
  • Negotiation analysis and scoring systems;
  • Game theory applications to decision making (e.g., the fair-share and matching algorithms);
  • Quantum game theory applications to decision making;
  • Bayesian methods for decision optimization;
  • Entropy-based measures in machine learning;
  • Fuzzy multicriteria decision analysis.

Prof. Dr. Marek Szopa
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • decision optimization
  • game theory
  • quantum game theory
  • negotiation
  • machine learning
  • deep learning
  • Pareto optimization

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Published Papers (5 papers)

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Research

14 pages, 293 KiB  
Article
Applications of Depth Minimization of Decision Trees Containing Hypotheses for Multiple-Value Decision Tables
by Mohammad Azad and Mikhail Moshkov
Entropy 2023, 25(4), 547; https://doi.org/10.3390/e25040547 - 23 Mar 2023
Cited by 2 | Viewed by 1403
Abstract
In this research, we consider decision trees that incorporate standard queries with one feature per query as well as hypotheses consisting of all features’ values. These decision trees are used to represent knowledge and are comparable to those investigated in exact learning, in [...] Read more.
In this research, we consider decision trees that incorporate standard queries with one feature per query as well as hypotheses consisting of all features’ values. These decision trees are used to represent knowledge and are comparable to those investigated in exact learning, in which membership queries and equivalence queries are used. As an application, we look into the issue of creating decision trees for two cases: the sorting of a sequence that contains equal elements and multiple-value decision tables which are modified from UCI Machine Learning Repository. We contrast the efficiency of several forms of optimal (considering the parameter depth) decision trees with hypotheses for the aforementioned applications. We also investigate the efficiency of decision trees built by dynamic programming and by an entropy-based greedy method. We discovered that the greedy algorithm produces very similar results compared to the results of dynamic programming algorithms. Therefore, since the dynamic programming algorithms take a long time, we may readily apply the greedy algorithms. Full article
(This article belongs to the Special Issue Decision Optimization in Information Theory and Game Theory)
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27 pages, 708 KiB  
Article
Aggregated Power Indices for Measuring Indirect Control in Complex Corporate Networks with Float Shareholders
by Izabella Stach, Jacek Mercik, Cesarino Bertini, Barbara Gładysz and Jochen Staudacher
Entropy 2023, 25(3), 429; https://doi.org/10.3390/e25030429 - 27 Feb 2023
Viewed by 1651
Abstract
The purpose of this paper is to introduce new methods to measure the indirect control power of firms in complex corporate shareholding structures using the concept of power indices from cooperative game theory. The proposed measures vary in desirable properties satisfied, as well [...] Read more.
The purpose of this paper is to introduce new methods to measure the indirect control power of firms in complex corporate shareholding structures using the concept of power indices from cooperative game theory. The proposed measures vary in desirable properties satisfied, as well as in the bargaining models of power indices used to construct them. Hence, they can be used to produce different pictures of the coalitional strength of firms in control of other firms in mutual shareholding networks with the presence of cycles. Precisely, in the framework of Karos and Peters from 2015, ten power indices substitute the original Shapley and Shubik power index in a modular fashion. In this way, we obtain a set of new measures called aggregated indices. The float shareholders typically hold less than 5 percent of the outstanding shares, which is an uncertain element of indirect control in complex shareholding structures. The fuzzy number seems appropriate to model these shareholders’ behavior. The novelty is that we model the behavior of float using Z-fuzzy numbers. The new methods are tested in an example. Full article
(This article belongs to the Special Issue Decision Optimization in Information Theory and Game Theory)
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22 pages, 443 KiB  
Article
A Clustering Multi-Criteria Decision-Making Method for Large-Scale Discrete and Continuous Uncertain Evaluation
by Siyuan Wang, Wenjun Ma and Jieyu Zhan
Entropy 2022, 24(11), 1621; https://doi.org/10.3390/e24111621 - 8 Nov 2022
Viewed by 1959
Abstract
In recent years, Dempster–Shafer (D–S) theory has been widely used in multi-criteria decision-making (MCDM) problems due to its excellent performance in dealing with discrete ambiguous decision alternative (DA) evaluations. In the general framework of D–S-theory-based MCDM problems, the preference of the DAs for [...] Read more.
In recent years, Dempster–Shafer (D–S) theory has been widely used in multi-criteria decision-making (MCDM) problems due to its excellent performance in dealing with discrete ambiguous decision alternative (DA) evaluations. In the general framework of D–S-theory-based MCDM problems, the preference of the DAs for each criterion is regarded as a mass function over the set of DAs based on subjective evaluations. Moreover, the multi-criteria preference aggregation is based on Dempster’s combination rule. Unfortunately, this an idea faces two difficulties in real-world applications: (i) D–S theory can only deal with discrete uncertain evaluations, but is powerless in the face of continuous uncertain evaluations. (ii) The generation of the mass function for each criterion relies on the empirical judgments of experts, making it time-consuming and laborious in terms of the MCDM problem for large-scale DAs. To the best of our knowledge, these two difficulties cannot be addressed with existing D–S-theory-based MCDM methods. To this end, this paper proposes a clustering MCDM method combining D–S theory with the analytic hierarchy process (AHP) and the Silhouette coefficient. By employing the probability distribution and the D–S theory to represent discrete and continuous ambiguous evaluations, respectively, determining the focal element set for the mass function of each criterion through the clustering method, assigning the mass values of each criterion through the AHP method, and aggregating preferences according to Dempster’s combination rule, we show that our method can indeed address these two difficulties in MCDM problems. Finally, an example is given and comparative analyses with related methods are conducted to illustrate our method’s rationality, effectiveness, and efficiency. Full article
(This article belongs to the Special Issue Decision Optimization in Information Theory and Game Theory)
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28 pages, 2843 KiB  
Article
The Extended Linguistic Hellwig’s Methods Based on Oriented Fuzzy Numbers and Their Application to the Evaluation of Negotiation Offers
by Ewa Roszkowska, Tomasz Wachowicz, Marzena Filipowicz-Chomko and Anna Łyczkowska-Hanćkowiak
Entropy 2022, 24(11), 1617; https://doi.org/10.3390/e24111617 - 6 Nov 2022
Cited by 8 | Viewed by 1697
Abstract
This study proposes a novel fuzzy framework for eliciting and organizing the preference information of the negotiator to allow for the evaluation of negotiation offers. The approach is based on verbal evaluation of negotiation options that operates with linguistic variables to handle vague [...] Read more.
This study proposes a novel fuzzy framework for eliciting and organizing the preference information of the negotiator to allow for the evaluation of negotiation offers. The approach is based on verbal evaluation of negotiation options that operates with linguistic variables to handle vague preferences and operationalizes them through oriented trapezoidal fuzzy numbers. Two variants of the linguistic method based on Hellwig’s approach and oriented fuzzy numbers are proposed, which can be applied to building a scoring system for the negotiation template. Then, an example of determining such a scoring system and using it to evaluate the negotiation offers in typical multi-issue negotiation is shown. The results are discussed and compared with other methods known from the literature, in which the preference information is organized similarly but processed differently. The comparison shows that the presented methods can be an alternative to Simple Additive Weighting or TOPSIS methods that may also operate with oriented fuzzy numbers, but some of their characteristics may be problematic from the viewpoint of data interpretation. The former requires defuzzification of the global scores determined, while the latter requires the compulsory use of two reference points derived mechanically out of the negotiation space. By applying modified Hellwig’s approaches, the former and the latter may be easily avoided. Full article
(This article belongs to the Special Issue Decision Optimization in Information Theory and Game Theory)
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13 pages, 474 KiB  
Article
On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights
by Ewa Roszkowska, Bartłomiej Jefmański and Marta Kusterka-Jefmańska
Entropy 2022, 24(8), 1081; https://doi.org/10.3390/e24081081 - 5 Aug 2022
Cited by 8 | Viewed by 1631
Abstract
In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic [...] Read more.
In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig’s method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented. Full article
(This article belongs to the Special Issue Decision Optimization in Information Theory and Game Theory)
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