Entropy

Research

12 pages, 254 KiB

Open AccessArticle

From Goal Programming for Continuous Multi-Criteria Optimization to the Target Decision Rule for Mixed Uncertain Problems

by Helena Gaspars-Wieloch

Entropy 2022, 24(1), 51; https://doi.org/10.3390/e24010051 - 28 Dec 2021

Cited by 5 | Viewed by 2179

Abstract

Goal programming (GP) is applied to the discrete and continuous version of multi-criteria optimization. Recently, some essential analogies between multi-criteria decision making under certainty (M-DMC) and scenario-based one-criterion decision making under uncertainty (1-DMU) have been revealed in the literature. The aforementioned similarities allow [...] Read more.

Goal programming (GP) is applied to the discrete and continuous version of multi-criteria optimization. Recently, some essential analogies between multi-criteria decision making under certainty (M-DMC) and scenario-based one-criterion decision making under uncertainty (1-DMU) have been revealed in the literature. The aforementioned similarities allow the adjustment of GP to an entirely new domain. The aim of the paper is to create a new decision rule for mixed uncertain problems on the basis of the GP methodology. The procedure can be used by pessimists, optimists and moderate decision makers. It is designed for one-shot decisions. One of the significant advantages of the novel approach is related to the possibility to analyze neutral criteria, which are not directly taken into account in existing classical procedures developed for 1-DMU. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

23 pages, 1044 KiB

Open AccessArticle

Shapley-Based Estimation of Company Value—Concept, Algorithms and Parameters

by Jacek Mercik, Barbara Gładysz, Izabella Stach and Jochen Staudacher

Entropy 2021, 23(12), 1598; https://doi.org/10.3390/e23121598 - 28 Nov 2021

Cited by 3 | Viewed by 2086

Abstract

The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing [...] Read more.

The aim of the article is to propose a new method of valuation of a company, considering its ownership relations with other companies. For this purpose, the concept of the Shapley value from cooperative game theory is used as the basis for assessing such dependent companies. The paper presents proposals for Shapley value calculation algorithms for our model. We expand our model by discussing personal relations in addition to ownership relations and point out how intuitionistic fuzzy sets may be helpful in this context. As a result, we propose two new expanded models. In the first probabilistic model, we apply Pearson’s correlation coefficient, in the second, we use a correlation coefficient between intuitionistic fuzzy sets to determine the personal relationships. Finally, we present and interpret results for a real-world economic network with 17 companies. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

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20 pages, 573 KiB

Open AccessArticle

Interactive Multiobjective Procedure for Mixed Problems and Its Application to Capacity Planning

by Maciej Nowak, Tadeusz Trzaskalik and Sebastian Sitarz

Entropy 2021, 23(10), 1243; https://doi.org/10.3390/e23101243 - 24 Sep 2021

Cited by 1 | Viewed by 1419

Abstract

A problem that appears in many decision models is that of the simultaneous occurrence of deterministic, stochastic, and fuzzy values in the set of multidimensional evaluations. Such problems will be called mixed problems. They lead to the formulation of optimization problems in ordered [...] Read more.

A problem that appears in many decision models is that of the simultaneous occurrence of deterministic, stochastic, and fuzzy values in the set of multidimensional evaluations. Such problems will be called mixed problems. They lead to the formulation of optimization problems in ordered structures and their scalarization. The aim of the paper is to present an interactive procedure with trade-offs for mixed problems, which helps the decision-maker to make a final decision. Its basic advantage consists of simplicity: after having obtained the solution proposed, the decision-maker should determine whether it is satisfactory and if not, how it should be improved by indicating the criteria whose values should be improved, the criteria whose values cannot be made worse, and the criteria whose values can be made worse. The procedure is applied in solving capacity planning treated as a mixed dynamic programming problem. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

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29 pages, 422 KiB

Open AccessArticle

On the Statistical Discrepancy and Affinity of Priority Vector Heuristics in Pairwise-Comparison-Based Methods

by Pawel Tadeusz Kazibudzki

Entropy 2021, 23(9), 1150; https://doi.org/10.3390/e23091150 - 1 Sep 2021

Cited by 4 | Viewed by 2156

Abstract

There are numerous priority deriving methods (PDMs) for pairwise-comparison-based (PCB) problems. They are often examined within the Analytic Hierarchy Process (AHP), which applies the Principal Right Eigenvalue Method (PREV) in the process of prioritizing alternatives. It is known that when decision makers (DMs) [...] Read more.

There are numerous priority deriving methods (PDMs) for pairwise-comparison-based (PCB) problems. They are often examined within the Analytic Hierarchy Process (AHP), which applies the Principal Right Eigenvalue Method (PREV) in the process of prioritizing alternatives. It is known that when decision makers (DMs) are consistent with their preferences when making evaluations concerning various decision options, all available PDMs result in the same priority vector (PV). However, when the evaluations of DMs are inconsistent and their preferences concerning alternative solutions to a particular problem are not transitive (cardinally), the outcomes are often different. This research study examines selected PDMs in relation to their ranking credibility, which is assessed by relevant statistical measures. These measures determine the approximation quality of the selected PDMs. The examined estimates refer to the inconsistency of various Pairwise Comparison Matrices (PCMs)—i.e., W = (w_ij), w_ij > 0, where i, j = 1,…, n—which are obtained during the pairwise comparison simulation process examined with the application of Wolfram’s Mathematica Software. Thus, theoretical considerations are accompanied by Monte Carlo simulations that apply various scenarios for the PCM perturbation process and are designed for hypothetical three-level AHP frameworks. The examination results show the similarities and discrepancies among the examined PDMs from the perspective of their quality, which enriches the state of knowledge about the examined PCB prioritization methodology and provides further prospective opportunities. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

13 pages, 1426 KiB

Open AccessArticle

Market Choices Driven by Reference Groups: A Comparison of Analytical and Simulation Results on Random Networks

by Michał Ramsza

Entropy 2021, 23(8), 1007; https://doi.org/10.3390/e23081007 - 1 Aug 2021

Viewed by 1885

Abstract

The present paper reports simulation results for a simple model of reference group influence on market choices, e.g., brand selection. The model was simulated on three types of random graphs, Erdos–Renyi, Barabasi–Albert, and Watts–Strogatz. The estimates of equilibria based on the simulation results [...] Read more.

The present paper reports simulation results for a simple model of reference group influence on market choices, e.g., brand selection. The model was simulated on three types of random graphs, Erdos–Renyi, Barabasi–Albert, and Watts–Strogatz. The estimates of equilibria based on the simulation results were compared to the equilibria of the theoretical model. It was verified that the simulations exhibited the same qualitative behavior as the theoretical model, and for graphs with high connectivity and low clustering, the quantitative predictions offered a viable approximation. These results allowed extending the results from the simple theoretical model to networks. Thus, by increasing the positive response towards the reference group, the third party may create a bistable situation with two equilibria at which respective brands dominate the market. This task is easier for large reference groups. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

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19 pages, 868 KiB

Open AccessArticle

Fuzzy Representation of Principal’s Preferences in Inspire Negotiation Support System

by Krzysztof Piasecki, Ewa Roszkowska, Tomasz Wachowicz, Marzena Filipowicz-Chomko and Anna Łyczkowska-Hanćkowiak

Entropy 2021, 23(8), 981; https://doi.org/10.3390/e23080981 - 29 Jul 2021

Cited by 3 | Viewed by 2197

Abstract

We consider the negotiation problem, in which an agent negotiates on behalf of a principal. Our considerations are focused on the Inspire negotiation support system in which the principal’s preferences are visualised by circles. In this way, the principal describes the importance of [...] Read more.

We consider the negotiation problem, in which an agent negotiates on behalf of a principal. Our considerations are focused on the Inspire negotiation support system in which the principal’s preferences are visualised by circles. In this way, the principal describes the importance of each negotiation issue and the relative utility of each considered option. The paper proposes how this preference information may be implemented by the agent for determining a scoring function used to support decisions throughout the negotiation process. The starting point of our considerations is a discussion regarding the visualisation of the principal’s preferences. We assume here that the importance of each issue and the utility of each option increases with the size of the circle representing them. The imprecise meaning of the notion of “circle size” implies that in a considered case, the utility of an option should be evaluated by a fuzzy number. The proposed utility fuzzification is justified by a simple analysis of results obtained from the empirical prenegotiation experiment. A novel method is proposed to determine trapezoidal fuzzy numbers, which evaluates an option’s utility using a series of answers given by the participants of the experiment. The utilities obtained this way are applied to determine the fuzzy scoring function for an agent. By determining such a common generalised fuzzy scoring system, our approach helps agents handle the differences in human cognitive processes associated with understanding the principal’s preferences. This work is the first approach to fuzzification of the preferences in the Inspire negotiation support system. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

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22 pages, 1853 KiB

Open AccessArticle

Reducing Cognitive Effort in Scoring Negotiation Space Using the Fuzzy Clustering Model

by Marzena Filipowicz-Chomko, Rafał Mierzwiak, Marcin Nowak, Ewa Roszkowska and Tomasz Wachowicz

Entropy 2021, 23(6), 752; https://doi.org/10.3390/e23060752 - 15 Jun 2021

Cited by 1 | Viewed by 2490

Abstract

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator’s preferences [...] Read more.

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator’s preferences precisely and ensure that the support is reliable. However, the methods classically used in the preference elicitation require much cognitive effort from the negotiators, and hence, do not prevent them from using heuristics and making simple errors that result in inaccurate scoring systems. This paper aims to develop an alternative tool that allows scoring the negotiation offers by implementing a sorting approach and the reference set of limiting profiles defined individually by the negotiators in the form of complete packages. These limiting profiles are evaluated holistically and verbally by the negotiator. Then the fuzzy decision model is built that uses the notion of increasing the preference granularity by introducing a series of limiting sub-profiles for corresponding sub-categories of offers. This process is performed automatically by the support algorithm and does not require any additional preferential information from the negotiator. A new method of generating reference fuzzy scores to allow a detailed assignment of any negotiation offer from feasible negotiation space to clusters and sub-clusters is proposed. Finally, the efficient frontier and Nash’s fair division are used to identify the recommended packages for negotiation in the bargaining phase. This new approach allows negotiators to obtain economically efficient, fair, balanced, and reciprocated agreements while minimizing information needs and effort. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

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13 pages, 632 KiB

Open AccessArticle

Non-Classical Rules in Quantum Games

by Piotr Frąckiewicz

Entropy 2021, 23(5), 604; https://doi.org/10.3390/e23050604 - 13 May 2021

Cited by 3 | Viewed by 1698

Abstract

Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens [...] Read more.

Over the last twenty years, quantum game theory has given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing bimatrix games introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players’ strategies are unitary operations and the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper was to identify some of non-classical features of the quantum scheme. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

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14 pages, 1228 KiB

Open AccessArticle

Efficiency of Classical and Quantum Games Equilibria

by Marek Szopa

Entropy 2021, 23(5), 506; https://doi.org/10.3390/e23050506 - 22 Apr 2021

Cited by 12 | Viewed by 2803

Abstract

Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoner’s dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of [...] Read more.

Nash equilibria and correlated equilibria of classical and quantum games are investigated in the context of their Pareto efficiency. The examples of the prisoner’s dilemma, battle of the sexes and the game of chicken are studied. Correlated equilibria usually improve Nash equilibria of games but require a trusted correlation device susceptible to manipulation. The quantum extension of these games in the Eisert–Wilkens–Lewenstein formalism and the Frąckiewicz–Pykacz parameterization is analyzed. It is shown that the Nash equilibria of these games in quantum mixed Pauli strategies are closer to Pareto optimal results than their classical counter-parts. The relationship of mixed Pauli strategies equilibria and correlated equilibria is also studied. Full article

(This article belongs to the Special Issue Decision Making, Classical and Quantum Optimization Methods)

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