Discussing an Expected Utility and Weighted Entropy Framework

Casquilho, José Pinto

doi:10.4236/ns.2014.67054

Cited by 5 publications

(8 citation statements)

References 33 publications

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“…This work is an analogous development of another paper recently published, where it was discussed an expected utility and weighted entropy framework, with acronym EU-WE [7]. We shall prove that the claimed analogy has here a proper sense, as either weighted Shannon entropy or weighted Gini-Simpson index may be considered two cases of generalized useful information measures.…”

Section: Introductionsupporting

confidence: 56%

“…First, we shall focus the discussion comparing optimal proportions of function u Z with index u K presented and discussed in [7]. The analogy stated in the introduction follows from the standard result that Taylor's first order (linear) approximation of the real function…”

Section: Discussionmentioning

confidence: 99%

“…In what follows, the simple lottery In this setting used to characterize the discrete random variable U we shall denote the EU-WGS mathematical device as u Z in analogy with the formula of the EU-WE framework discussed in [7], to be defined as:…”

Section: Definition and Rangementioning

confidence: 99%

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Combining Expected Utility and Weighted Gini-Simpson Index into a Non-Expected Utility Device

Casquilho¹

2015

TEL

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We present and discuss a conceptual decision-making procedure supported by a mathematical device combining expected utility and a generalized information measure: the weighted GiniSimpson index, linked to the scientific fields of information theory and ecological diversity analysis. After a synthetic review of the theoretical background relative to those themes, such a devicean EU-WGS framework denoting a real function defined with positive utility values and domain in the simplex of probabilities-is analytically studied, identifying its range with focus on the maximum point, using a Lagrange multiplier method associated with algorithms, exemplified numerically. Yet, this EU-WGS device is showed to be a proper analog of an expected utility and weighted entropy (EU-WE) framework recently published, both being cases of mathematical tools that can be referred to as non-expected utility methods using decision weights, framed within the field of decision theory linked to information theory. This kind of decision modeling procedure can also be interpreted to be anchored in Kurt Lewin utility's concept and may be used to generate scenarios of optimal compositional mixtures applied to generic lotteries associated with prospect theory, financial risk assessment, security quantification and natural resources management. The epistemological method followed in the reasoned choice procedure that is presented in this paper is neither normative nor descriptive in an empirical sense, but instead it is heuristic and hermeneutical in its conception.

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Section: Introductionsupporting

confidence: 56%

Section: Discussionmentioning

confidence: 99%

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Combining Expected Utility and Weighted Gini-Simpson Index into a Non-Expected Utility Device

Casquilho¹

2015

TEL

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“…According to basic principles of information theory, information is a measure of ordering degree in the system, but the entropy is a measure of disorder degree in the system [18][19]. Information augment means the entropy reduction.…”

Section: Entropy Weightmentioning

confidence: 99%

Research on the assessment indicators for crime prevention lighting in residential areas based on AHP and Entropy Weight

Chen

Zhou

et al. 2016

MATEC Web of Conferences

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Abstract. Lighting can affect the probability of crime. In order to establish safe and secure residential areas' lighting environment, the elements for crime prevention are researched. Originally propose 14 assessment indicators of lighting environment which can be recognized subjectively and may influence crime rate. They are horizontal illuminance illuminance uniformity surround ratio vertical illuminance threedimensional color rendering glare lamp pole height light pole distance lamp aesthetic lamp conciseness color temperature lamp distribution light source. The data came from residents in China. Through screening and giving weights by Analytic Hierarchy Process, there are 7 key assessment indicators left. Then give weights to the ultimate 7 key assessment indicators by Entropy Weight to verify their rank. The results show that 7 key assessment indicators have the same rank in contrast of the two methods. According to the crime prevention influence of the lighting environment, the sort is: vertical illuminance, horizontal illuminance, three-dimensional, color temperature, glare, uniformity of illuminance, color rendering.

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“…The real function W 1 was previously presented and discussed (see [43]); in summary, W 1 is a differentiable concave function in the interior of the simplex, attaining minimum and maximum values in the domain. The minimum value is minW 1 = min i=1,··· ,n u i and it is possible to locate the maximum point with a Lagrange multiplier method, the coordinates of the maximum point thus being evaluated by computing p * 1,i = exp(−α * /u i ) for i = 1, · · · , n, the optimal value of the Lagrange multiplier (α * ) defined implicitly by the equation α * : ∑ n i=1 exp(−α/u i ) = 1 which can be solved with numerical methods providing a unique solution.…”

Section: The Case For β =mentioning

confidence: 99%

Discussing Landscape Compositional Scenarios Generated with Maximization of Non-Expected Utility Decision Models Based on Weighted Entropies

Casquilho

Rego

2017

Entropy

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Abstract:The search for hypothetical optimal solutions of landscape composition is a major issue in landscape planning and it can be outlined in a two-dimensional decision space involving economic value and landscape diversity, the latter being considered as a potential safeguard to the provision of services and externalities not accounted in the economic value. In this paper, we use decision models with different utility valuations combined with weighted entropies respectively incorporating rarity factors associated to Gini-Simpson and Shannon measures. A small example of this framework is provided and discussed for landscape compositional scenarios in the region of Nisa, Portugal. The optimal solutions relative to the different cases considered are assessed in the two-dimensional decision space using a benchmark indicator. The results indicate that the likely best combination is achieved by the solution using Shannon weighted entropy and a square root utility function, corresponding to a risk-averse behavior associated to the precautionary principle linked to safeguarding landscape diversity, anchoring for ecosystem services provision and other externalities. Further developments are suggested, mainly those relative to the hypothesis that the decision models here outlined could be used to revisit the stability-complexity debate in the field of ecological studies.

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Discussing an Expected Utility and Weighted Entropy Framework

Cited by 5 publications

References 33 publications

Combining Expected Utility and Weighted Gini-Simpson Index into a Non-Expected Utility Device

Combining Expected Utility and Weighted Gini-Simpson Index into a Non-Expected Utility Device

Research on the assessment indicators for crime prevention lighting in residential areas based on AHP and Entropy Weight

Discussing Landscape Compositional Scenarios Generated with Maximization of Non-Expected Utility Decision Models Based on Weighted Entropies

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