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Entropy
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Entropy, Utility, and Logical Reasoning
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Entropy, Utility, and Logical Reasoning

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (30 November 2015) | Viewed by 40321

Special Issue Editor

Prof. Dr. Ali E. Abbas

E-Mail Website
Guest Editor
Epstein Department of Industrial and Systems Engineering, Price School of Public Policy, University of Southern California, Los Angeles, CA 90089, USA
Interests: entropy; probability theory; utility theory; Bayesian analysis; decision making; maximum entropy methods

Special Issue Information

Dear Colleagues,

Two major achievements in science were published immediately after the Second World War and have significantly changed our understanding of uncertainty and the rules of logical reasoning: Shannon’s entropy measure (Shannon 1948) and von Neumann-Morgenstern’s utility theory (von Neumann and Morgenstern 1947). At the time, both concepts appeared to be significantly different, and were taught independently in different fields. However, the merger of both entropy and utility has introduced powerful new methodologies for characterizing preferences with partial information, inferring adversary preferences, identifying rules of logical reasoning for individuals and groups, and providing new interpretations for numerous areas in physics, engineering, artificial intelligence, and the arts and sciences.

In this special issue on “Entropy, Utility, and Logical Reasoning” we seek contributions that will shed further light on the merger of utility and entropy and their connections with the rules of thought and logical reasoning. The scope of the contributions will be very broad to include philosophical discussions, theoretical derivations and solutions to practical problems. Papers highlighting new interpretations, connections, and dualities between entropy and utility using functional equations are especially welcome.

Prof. Dr. Ali E. Abbas
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

  • entropy
  • utility
  • logical reasoning
  • probability
  • inference
  • duality
  • decision analysis
  • game theory
  • bayes rule
  • machine learning
  • data mining
  • functional equations

Published Papers (7 papers)

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Research

272 KiB  
Article
Stochastic Reorder Point-Lot Size (r,Q) Inventory Model under Maximum Entropy Principle
by Davide Castellano
Entropy 2016, 18(1), 16; https://doi.org/10.3390/e18010016 - 30 Dec 2015
Cited by 11 | Viewed by 4678
Abstract
This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that [...] Read more.
This paper takes into account the continuous-review reorder point-lot size (r,Q) inventory model under stochastic demand, with the backorders-lost sales mixture. Moreover, to reflect the practical circumstance in which full information about the demand distribution lacks, we assume that only an estimate of the mean and of the variance is available. Contrarily to the typical approach in which the lead-time demand is supposed Gaussian or is obtained according to the so-called minimax procedure, we take a different perspective. That is, we adopt the maximum entropy principle to model the lead-time demand distribution. In particular, we consider the density that maximizes the entropy over all distributions with given mean and variance. With the aim of minimizing the expected total cost per time unit, we then propose an exact algorithm and a heuristic procedure. The heuristic method exploits an approximated expression of the total cost function achieved by means of an ad hoc first-order Taylor polynomial. We finally carry out numerical experiments with a twofold objective. On the one hand we examine the efficiency of the approximated solution procedure. On the other hand we investigate the performance of the maximum entropy principle in approximating the true lead-time demand distribution. Full article
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
206 KiB  
Article
Choice Overload and Height Ranking of Menus in Partially-Ordered Sets
by Marcello Basili and Stefano Vannucci
Entropy 2015, 17(11), 7584-7595; https://doi.org/10.3390/e17117584 - 30 Oct 2015
Cited by 3 | Viewed by 4462
Abstract
When agents face incomplete information and their knowledge about the objects of choice is vague and imprecise, they tend to consider fewer choices and to process a smaller portion of the available information regarding their choices. This phenomenon is well-known as choice overload [...] Read more.
When agents face incomplete information and their knowledge about the objects of choice is vague and imprecise, they tend to consider fewer choices and to process a smaller portion of the available information regarding their choices. This phenomenon is well-known as choice overload and is strictly related to the existence of a considerable amount of option-pairs that are not easily comparable. Thus, we use a finite partially-ordered set (poset) to model the subset of easily-comparable pairs within a set of options/items. The height ranking, a new ranking rule for menus, namely subposets of a finite poset, is then introduced and characterized. The height ranking rule ranks subsets of options in terms of the size of the longest chain that they include and is therefore meant to assess menus of available options in terms of the maximum number of distinct and easily-comparable alternative options that they offer. Full article
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
369 KiB  
Article
Expected Utility and Entropy-Based Decision-Making Model for Large Consumers in the Smart Grid
by Bingtuan Gao, Cheng Wu, Yingjun Wu and Yi Tang
Entropy 2015, 17(10), 6560-6575; https://doi.org/10.3390/e17106560 - 25 Sep 2015
Cited by 12 | Viewed by 5531
Abstract
In the smart grid, large consumers can procure electricity energy from various power sources to meet their load demands. To maximize its profit, each large consumer needs to decide their energy procurement strategy under risks such as price fluctuations from the spot market [...] Read more.
In the smart grid, large consumers can procure electricity energy from various power sources to meet their load demands. To maximize its profit, each large consumer needs to decide their energy procurement strategy under risks such as price fluctuations from the spot market and power quality issues. In this paper, an electric energy procurement decision-making model is studied for large consumers who can obtain their electric energy from the spot market, generation companies under bilateral contracts, the options market and self-production facilities in the smart grid. Considering the effect of unqualified electric energy, the profit model of large consumers is formulated. In order to measure the risks from the price fluctuations and power quality, the expected utility and entropy is employed. Consequently, the expected utility and entropy decision-making model is presented, which helps large consumers to minimize their expected profit of electricity procurement while properly limiting the volatility of this cost. Finally, a case study verifies the feasibility and effectiveness of the proposed model. Full article
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
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1803 KiB  
Article
Setting Diverging Colors for a Large-Scale Hypsometric Lunar Map Based on Entropy
by Xingguo Zeng, Lingli Mu, Jianjun Liu and Yiman Yang
Entropy 2015, 17(7), 5133-5144; https://doi.org/10.3390/e17075133 - 22 Jul 2015
Cited by 2 | Viewed by 4243
Abstract
A hypsometric map is a type of map used to represent topographic characteristics by filling different map areas with diverging colors. The setting of appropriate diverging colors is essential for the map to reveal topographic details. When lunar real environmental exploration programs are [...] Read more.
A hypsometric map is a type of map used to represent topographic characteristics by filling different map areas with diverging colors. The setting of appropriate diverging colors is essential for the map to reveal topographic details. When lunar real environmental exploration programs are performed, large-scale hypsometric maps with a high resolution and greater topographic detail are helpful. Compared to the situation on Earth, fewer lunar exploration objects are available, and the topographic waviness is smaller at a large scale, indicating that presenting the topographic details using traditional hypsometric map-making methods may be difficult. To solve this problem, we employed the Chang’E2 (CE2) topographic and imagery data with a resolution of 7 m and developed a new hypsometric map-making method by setting the diverging colors based on information entropy. The resulting map showed that this method is suitable for presenting the topographic details and might be useful for developing a better understanding of the environment of the lunar surface. Full article
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
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737 KiB  
Article
An Entropy-Based Approach to Path Analysis of Structural Generalized Linear Models: A Basic Idea
by Nobuoki Eshima, Minoru Tabata, Claudio Giovanni Borroni and Yutaka Kano
Entropy 2015, 17(7), 5117-5132; https://doi.org/10.3390/e17075117 - 22 Jul 2015
Cited by 3 | Viewed by 6773
Abstract
A path analysis method for causal systems based on generalized linear models is proposed by using entropy. A practical example is introduced, and a brief explanation of the entropy coefficient of determination is given. Direct and indirect effects of explanatory variables are discussed [...] Read more.
A path analysis method for causal systems based on generalized linear models is proposed by using entropy. A practical example is introduced, and a brief explanation of the entropy coefficient of determination is given. Direct and indirect effects of explanatory variables are discussed as log odds ratios, i.e., relative information, and a method for summarizing the effects is proposed. The example dataset is re-analyzed by using the method. Full article
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
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1303 KiB  
Article
Intransitivity in Theory and in the Real World
by Alexander Y. Klimenko
Entropy 2015, 17(6), 4364-4412; https://doi.org/10.3390/e17064364 - 19 Jun 2015
Cited by 18 | Viewed by 8307
Abstract
This work considers reasons for and implications of discarding the assumption of transitivity—the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity [...] Read more.
This work considers reasons for and implications of discarding the assumption of transitivity—the fundamental postulate in the utility theory of von Neumann and Morgenstern, the adiabatic accessibility principle of Caratheodory and most other theories related to preferences or competition. The examples of intransitivity are drawn from different fields, such as law, biology and economics. This work is intended as a common platform that allows us to discuss intransitivity in the context of different disciplines. The basic concepts and terms that are needed for consistent treatment of intransitivity in various applications are presented and analysed in a unified manner. The analysis points out conditions that necessitate appearance of intransitivity, such as multiplicity of preference criteria and imperfect (i.e., approximate) discrimination of different cases. The present work observes that with increasing presence and strength of intransitivity, thermodynamics gradually fades away leaving space for more general kinetic considerations. Intransitivity in competitive systems is linked to complex phenomena that would be difficult or impossible to explain on the basis of transitive assumptions. Human preferences that seem irrational from the perspective of the conventional utility theory, become perfectly logical in the intransitive and relativistic framework suggested here. The example of competitive simulations for the risk/benefit dilemma demonstrates the significance of intransitivity in cyclic behaviour and abrupt changes in the system. The evolutionary intransitivity parameter, which is introduced in the Appendix, is a general measure of intransitivity, which is particularly useful in evolving competitive systems. Full article
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
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1048 KiB  
Article
Collaborative Performance Research on Multi-level Hospital Management Based on Synergy Entropy-HoQ
by Lei Chen, Xuedong Liang and Tao Li
Entropy 2015, 17(4), 2409-2431; https://doi.org/10.3390/e17042409 - 20 Apr 2015
Cited by 7 | Viewed by 5666
Abstract
Because of the general lack of multi-level hospital management collaboration performance effectiveness research, this paper proposes a multi-level hospital management Synergy Entropy-House of Quality (HoQ) Measurement Model by innovatively combining the House of Quality (HoQ) measure model with a Synergy Entropy computing principle. [...] Read more.
Because of the general lack of multi-level hospital management collaboration performance effectiveness research, this paper proposes a multi-level hospital management Synergy Entropy-House of Quality (HoQ) Measurement Model by innovatively combining the House of Quality (HoQ) measure model with a Synergy Entropy computing principle. Triangular fuzzy functions are used to determine the importance degree parameter of each hospital management element which combined with the results from the Synergy Entropy evaluation of the hospital management elements, arrive at a comprehensive collaborative computation result for the various elements, ensuring results objectivity. Finally, the analysis of the collaborative research on multi-level hospital management demonstrated the scientific effectiveness of the hospital management Synergy Entropy-House of Quality (HoQ) Measurement Model. Full article
(This article belongs to the Special Issue Entropy, Utility, and Logical Reasoning)
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