On the Expected Value of Fuzzy Events

2015 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 57-74 ◽  
Author(s):  
Erich Peter Klement ◽  
Radko Mesiar
Keyword(s):  
Boundary Conditions ◽  
Expected Value ◽  
Set Functions ◽  
Expected Values

Generalizing a first approach by L. A. ZADEH (J. Math. Anal. Appl. 23, 1968), expected values of fuzzy events are studied which are (up to standard boundary conditions) only required to be monotone. They can be seen as an extension of capacities, i.e., monotone set functions satisfying standard boundary conditions. Some of these expected values can be characterized axiomatically, others are based on some distinguished integrals (Choquet, Sugeno, Shilkret, universal, and decomposition integral).

scholarly journals Reward Value Coding Distinct From Risk Attitude-Related Uncertainty Coding in Human Reward Systems

2007 ◽  
Vol 97 (2) ◽  
pp. 1621-1632 ◽  
Author(s):  
Philippe N. Tobler ◽  
John P. O'Doherty ◽  
Raymond J. Dolan ◽  
Wolfram Schultz
Keyword(s):  
Risk Aversion ◽  
Risk Attitude ◽  
Mean Value ◽  
Expected Value ◽  
Individual Risk ◽  
Functional Magnetic Resonance ◽  
Coding Regions ◽  
Monetary Rewards ◽  
Expected Values ◽  
Value Coding

When deciding between different options, individuals are guided by the expected (mean) value of the different outcomes and by the associated degrees of uncertainty. We used functional magnetic resonance imaging to identify brain activations coding the key decision parameters of expected value (magnitude and probability) separately from uncertainty (statistical variance) of monetary rewards. Participants discriminated behaviorally between stimuli associated with different expected values and uncertainty. Stimuli associated with higher expected values elicited monotonically increasing activations in distinct regions of the striatum, irrespective of different combinations of magnitude and probability. Stimuli associated with higher uncertainty (variance) elicited increasing activations in the lateral orbitofrontal cortex. Uncertainty-related activations covaried with individual risk aversion in lateral orbitofrontal regions and risk-seeking in more medial areas. Furthermore, activations in expected value-coding regions in prefrontal cortex covaried differentially with uncertainty depending on risk attitudes of individual participants, suggesting that separate prefrontal regions are involved in risk aversion and seeking. These data demonstrate the distinct coding in key reward structures of the two basic and crucial decision parameters, expected value, and uncertainty.

scholarly journals Neural population dynamics underlying expected value computation

2020 ◽  
Author(s):  
Hiroshi Yamada ◽  
Yuri Imaizumi ◽  
Masayuki Matsumoto
Keyword(s):  
Ventral Striatum ◽  
Temporal Dynamics ◽  
Dorsal Striatum ◽  
Expected Value ◽  
Economic Behavior ◽  
Neural Dynamics ◽  
Neural Population ◽  
Integrative Process ◽  
Expected Values ◽  
The Brain

AbstractComputation of expected values, i.e., probability times magnitude, seems to be a dynamic integrative process performed in the brain for efficient economic behavior. However, neural dynamics underlying this computation remain largely unknown. We examined (1) whether four core reward-related regions detect and integrate the probability and magnitude cued by numerical symbols and (2) whether these regions have distinct dynamics in the integrative process. Extractions of mechanistic structure of neural population signal demonstrated that expected-value signals simultaneously arose in central part of orbitofrontal cortex (cOFC, area 13m) and ventral striatum (VS). These expected-value signals were incredibly stable in contrast to weak and/or fluctuated signals in dorsal striatum and medial OFC. Notably, temporal dynamics of these stable expected-value signals were unambiguously distinct: sharp and gradual signal evolutions in cOFC and VS, respectively. These intimate dynamics suggest that cOFC and VS compute the expected-values with unique time constants, as distinct, partially overlapping processes.

scholarly journals Performance Analysis Based on Experimental Data of Backpressure Steam Turbine for Cogeneration in Saturated Steam Applications

2021 ◽  
Vol 31 (2) ◽  
pp. 274-292
Author(s):  
Guilherme Vescovi ◽  
Gabriel Grazziotin ◽  
Tales Souza ◽  
Jorge Guillen ◽  
Ge Quan
Keyword(s):  
Experimental Data ◽  
Performance Analysis ◽  
Boundary Conditions ◽  
Empirical Data ◽  
Saturated Steam ◽  
Effective Efficiency ◽  
Validation Procedure ◽  
Key Variables ◽  
Expected Values ◽  
Turbine Model

Abstract This paper aims to validate the performance capabilities of a Pressure Reducing Turbine (PRT) with respect to initial predictions based on analytic calculations. The designed equipment was installed in a beverage facility, located in Brazil. The validation procedure consists of analyzing the data collected in several periods of PRT’s operation, accessed remotely via an online server. The analysis of empirical data identifies the behavior of two key variables: generated power and effective efficiency. However, the observed boundary conditions differed significantly from expected values, forcing the turbine to operate in off-design conditions. The turbine model was hence refined and used to predict the PRT’s performance in such conditions. Results showed satisfactory accuracy for both power and efficiency predictions.

Weighted Fuzzy Averages in Fuzzy Environment: Part II. Generalized Weighted Fuzzy Expected Values in Fuzzy Environment

2003 ◽  
Vol 11 (02) ◽  
pp. 159-172 ◽  
Author(s):  
G. Sirbiladze ◽  
A. Sikharulidze
Keyword(s):  
Measure Space ◽  
Expected Value ◽  
Fuzzy Measure ◽  
Weighted Averages ◽  
Fuzzy Environment ◽  
Fuzzy Expected Value ◽  
Interval Extension ◽  
Finite Set ◽  
Expected Values ◽  
Iteration Processes

The weighted fuzzy expected value (WFEV) of the population for a sampling distribution was introduced in 1. In 2 the notion of WFEV is generalized for any fuzzy measure on a finite set (WFEVg). The latter paper also describes the notions of weighted fuzzy expected intervals WFEI and WFEIg which are an interval extension of WFEV and WFEVg, respectively, when due to ''scarce'' data the fuzzy expected value (FEV) 3 does not exist, but the fuzzy expected interval (FEI) 3 does. In this paper, The generalizations GWFEVg and GWFEIg of WFEVg and WFEIg, respectively, are introduced for any fuzzy measure space. Furthermore, the generalized weighted fuzzy expected value is expressed in terms of two monotone expectation (ME)4 values with respect to the Lebesgue measure on [0,1]. The convergence of iteration processes is provided by an appropriate choice of a ''weight'' function. In the interval extension (GWFEIg) the so-called combinatorial interval extension of a function 5 is successfully used, which is clearly illustrated by examples. Several examples of the use of the new weighted averages are discussed. In many cases these averages give better estimations than classical estimators of central tendencies such as mean, median or the fuzzy ''classical'' estimators FEV, FEI and ME.

scholarly journals Information processing in tax decisions: A MouselabWEB study on the Allingham and Sandmo model of income tax evasion

2020 ◽  
Author(s):  
Christoph Kogler ◽  
Jerome Olsen ◽  
Martin Müller ◽  
Erich Kirchler
Keyword(s):  
Tax Evasion ◽  
Information Acquisition ◽  
Income Tax ◽  
Tax Compliance ◽  
Relevant Information ◽  
Expected Value ◽  
Decision Under Uncertainty ◽  
Tax Rate ◽  
Compliance Decisions ◽  
Expected Values

The highly influential Allingham and Sandmo model of income tax evasion framed the decision whether to comply or to evade taxes as a decision under uncertainty, assuming that taxpayers are driven by utility-maximization. Accordingly, they should choose evasion over compliance if it yields a higher expected profit. We test the main assumptions of this model considering both compliance decisions and the process of information acquisition applying MouselabWEB. In an incentivized experiment, 109 participants made 24 compliance decisions with varying information presented for four within-subject factors (income, tax rate, audit probability, and fine level). Additional explicit expected value information was manipulated between-subjects. The results reveal that participants attended to all relevant information, a prerequisite for expected value like calculations. As predicted by the Allingham and Sandmo model, choices were clearly influenced by deterrence parameters. Against the assumptions, these parameters were not integrated adequately, as evasion did not increase with rising expected rate of return. More transitions between information necessary for calculating expected values did not result in higher model conformity, just as presenting explicit information on expected values. We conclude that deterrence information clearly influences tax compliance decisions in our setting, but observed deviations from the model can be attributed to failure to integrate all relevant parameters.

scholarly journals A Note on L-Fuzzy Bags and Their Expected Values

2016 ◽  
Vol 66 (1) ◽  
pp. 73-80
Author(s):  
Fateme Kouchakinejad ◽  
Mashaallah Mashinchi ◽  
Radko Mesiar
Keyword(s):  
Expected Value ◽  
New Concepts ◽  
Expected Values ◽  
Definition Of

Abstract A definition of L-fuzzy bags is introduced and studied. In this approach, according to the concept given by M. Delgado et al. (2009), each bag has two parts: function and summary information. Then, the definition of L-fuzzy bag expected value is introduced. In the case L = [0,1], several integral-based fuzzy bag expected values are prepared. By some examples, the new concepts are illustrated.

Approximate Solutions to Stochastic Dynamic Programs

1997 ◽  
Vol 13 (3) ◽  
pp. 392-405 ◽  
Author(s):  
Steven Stern
Keyword(s):  
Structural Estimation ◽  
Approximate Solutions ◽  
Expected Value ◽  
Stochastic Dynamic ◽  
Approximation Methods ◽  
Distributional Assumption ◽  
Approximation Errors ◽  
Dynamic Programs ◽  
Estimation Problems ◽  
Expected Values

This paper examines the properties of various approximation methods for solving stochastic dynamic programs in structural estimation problems. The problem addressed is evaluating the expected value of the maximum of available choices. The paper shows that approximating this by the maximum of expected values frequently has poor properties. It also shows that choosing a convenient distributional assumptions for the errors and then solving exactly conditional on the distributional assumption leads to small approximation errors even if the distribution is misspecified.

scholarly journals Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 442 ◽  
Author(s):  
Yige Xue ◽  
Yong Deng
Keyword(s):  
Decision Making ◽  
Choquet Integral ◽  
Decision Rules ◽  
Expected Value ◽  
Experimental Results ◽  
Numerical Examples ◽  
Fuzzy Environment ◽  
Proposed Model ◽  
Expected Values ◽  
Function Measure

Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully.

scholarly journals Um Problema de Seleção de Carteiras de Múltiplos Períodos por Média e Variância

2005 ◽  
Vol 3 (1) ◽  
pp. 101
Author(s):  
Oswaldo Luiz do Valle Costa ◽  
Rodrigo De Barros Nabholz
Keyword(s):  
Optimization Problem ◽  
Expected Value ◽  
Expected Values ◽  
Mean Variance

In a recent paper, Li and Ng (2000) considered the multi-period mean variance optimization problem, with investing horizon T, for the case in which only the final variance Var(V(T)) or expected value of the portfolio E(V(T)) are considered in the optimization problem. In this paper we extend their results to the case in which the intermediate expected values E(V(t)) and variances Var(V(t)) for t = 1,,T can also be taken into account in the optimization problem. The main advantage of this technique is that it is possible to control the intermediate behavior of the portfolios return or variance. An example illustrating this situation is presented.

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