Some remarks on axiomatic definition of entropy measure

2017 ◽  
Vol 33 (3) ◽  
pp. 1945-1952 ◽  
Author(s):  
Krzysztof Piasecki
Keyword(s):  
Entropy Measure ◽  
Axiomatic Definition ◽  
Definition Of

scholarly journals A NOVEL FUZZY ENTROPY MEASURE AND ITS APPLICATION IN COVID-19 WITH FUZZY TOPSIS

2021 ◽  
Author(s):  
Razia Sharif
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Multicriteria Decision Making ◽  
Fuzzy Topsis ◽  
Entropy Measure ◽  
Multicriteria Decision ◽  
Axiomatic Definition ◽  
Definition Of ◽  
Topsis Technique

Fuzzy sets (FSs) are an important tool to model uncertainty and vagueness. Entropy is being used to measure the fuzziness within a fuzzy set (FS). These entropies are used to find multicriteria decision-making. For measuring uncertainty with TOPSIS techniques an axiomatic definition of entropy measure for fuzzy sets is also given in this paper. The proposed entropy is provided to satisfy all the axioms. Several numerical examples are presented to compare the proposed entropy measure with existing entropies. The corresponding results show that the newly proposed entropy can be computed easily and give reliable results. Finally, the decision-making algorithm TOPSIS (Techniques of ordered preference similarity to ideal solution) is utilized to solve multicriteria decision-making problems (MCDM) related to daily life. In the current situation, COVID-19 has no proper medical treatment. We use TOPSIS technique to suggest an effective medicine for this pandemic. Numerical results and practical examples show the effectiveness and practical applicability of the proposed entropy.

scholarly journals Quasi-Perfect Stackelberg Equilibrium

2019 ◽  
Vol 33 ◽  
pp. 2117-2124 ◽  
Author(s):  
Alberto Marchesi ◽  
Gabriele Farina ◽  
Christian Kroer ◽  
Nicola Gatti ◽  
Tuomas Sandholm
Keyword(s):  
Broad Class ◽  
Stackelberg Equilibrium ◽  
Correlated Equilibrium ◽  
Equilibrium Concept ◽  
Extensive Form ◽  
Tree Form ◽  
Axiomatic Definition ◽  
Security Games ◽  
Definition Of ◽  
Perfect Equilibria

Equilibrium refinements are important in extensive-form (i.e., tree-form) games, where they amend weaknesses of the Nash equilibrium concept by requiring sequential rationality and other beneficial properties. One of the most attractive refinement concepts is quasi-perfect equilibrium. While quasiperfection has been studied in extensive-form games, it is poorly understood in Stackelberg settings—that is, settings where a leader can commit to a strategy—which are important for modeling, for example, security games. In this paper, we introduce the axiomatic definition of quasi-perfect Stackelberg equilibrium. We develop a broad class of game perturbation schemes that lead to them in the limit. Our class of perturbation schemes strictly generalizes prior perturbation schemes introduced for the computation of (non-Stackelberg) quasi-perfect equilibria. Based on our perturbation schemes, we develop a branch-and-bound algorithm for computing a quasi-perfect Stackelberg equilibrium. It leverages a perturbed variant of the linear program for computing a Stackelberg extensive-form correlated equilibrium. Experiments show that our algorithm can be used to find an approximate quasi-perfect Stackelberg equilibrium in games with thousands of nodes.

scholarly journals DEFORMATION CONDITIONS FOR PSEUDOREPRESENTATIONS

2019 ◽  
Vol 7 ◽  
Author(s):  
PRESTON WAKE ◽  
CARL WANG-ERICKSON
Keyword(s):  
Stability Condition ◽  
Deformation Theory ◽  
Axiomatic Definition ◽  
Galois Deformation ◽  
Definition Of

Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur’s Galois deformation theory for representations with that property. We introduce an axiomatic definition of pseudorepresentations with such a property. Among other things, we show that pseudorepresentations with a property enjoy a good deformation theory, generalizing Ramakrishna’s theory to pseudorepresentations.

scholarly journals Cladistic hypotheses as degree of equivalence relational structures: implications for three-item statements

2021 ◽  
Author(s):  
Valentin Rineau ◽  
Stéphane Prin
Keyword(s):  
Phylogenetic Trees ◽  
Phylogenetic Reconstruction ◽  
Equivalence Relations ◽  
Strong Connection ◽  
Relational Structures ◽  
Degree Of Equivalence ◽  
Axiomatic Definition ◽  
Finite Set ◽  
Definition Of ◽  
Supertree Methods

AbstractThree-item statements, as minimal informative rooted binary phylogenetic trees on three items, are the minimal units of cladistic information. Their importance for phylogenetic reconstruction, consensus and supertree methods relies on both (i) the fact that any cladistic tree can always be decomposed into a set of three-item statements, and (ii) the possibility, at least under some conditions, to build a new cladistic tree by combining all or part of the three-item statements deduced from several prior cladistic trees. In order to formalise such procedures, several k-adic rules of inference, i.e., rules that allow us to deduce at least one new three-item statement from exactly k other ones, have been identified. However, no axiomatic background has been proposed, and it remains unknown if a particular k-adic rule of inference can be reduced to more basic rules. In order to solve this problem, we propose here to define three-item statements in terms of degree of equivalence relations. Given both the axiomatic definition of the latter and their strong connection to hierarchical classifications, we establish a list of the most basic properties for three-item statements. With such an approach, we show that it is possible to combine five three-item statements from basic rules although they are not combinable only from dyadic rules. Such a result suggests that all higher k-adic rules are well reducible to a finite set of simpler rules.

Wavelet-based Entropy Measure for Rate-Distortion Optimization in Image Coding

2010 ◽  
Vol 56 (1) ◽  
pp. 25-32
Author(s):  
J. Garcia-Alvarez ◽  
H. Führ ◽  
G. Castellanos-Domínguez
Keyword(s):  
Image Coding ◽  
Rate Distortion ◽  
Entropy Measure ◽  
Quality Level ◽  
Rate Distortion Optimization ◽  
Information Quantity ◽  
Wavelet Representation ◽  
Wavelet Space ◽  
Definition Of ◽  
Entropy Estimates

Wavelet-based Entropy Measure for Rate-Distortion Optimization in Image CodingA novel method for calculation of the entropy measure in wavelet space is proposed. This perceived-based entropy measure uses a Second Order Model entropy estimator, in which the occurrence of neighbors is considered in formulation. It has the intention to allow the implementation of a more suitable measure in coding processes and a relationship between the metric and the description of perceptual features. This method is used for the Rate-Distortion optimization in order to improve the bit-allocation coding algorithm, demonstrating that the wavelet-based entropy estimates a truncation step close to the target rate. The hypothesis is founded in the effect of distortion on the coefficient allocation. Because entropy measure is a close approximation of the conditional probability of image in multi-resolution space, it provides an adequate representation for the information of aDetailfeature. A definition of Detail-based homogeneity variance criteria is used for the information quantity - wavelet representation space, in order to find the image that fits a given Quality Level criteria. Experimental results are obtained for artificial and natural databases.

A Novel Entropy Measure for Interval-Valued Intuitionistic Fuzzy Set and Its Application to Failure Mode and Effect Analysis

2021 ◽  
pp. 115-134
Author(s):  
Kamal Kumar ◽  
Naveen Mani ◽  
Amit Sharma ◽  
Reeta Bhardwaj
Keyword(s):  
Failure Mode ◽  
Fuzzy Set ◽  
Failure Modes ◽  
Intuitionistic Fuzzy Set ◽  
Entropy Measure ◽  
Effect Analysis ◽  
Intuitionistic Fuzzy ◽  
Safety And Reliability ◽  
Definition Of ◽  
Interval Valued

The failure mode and effect analysis (FMEA) is widely used an effective pre-accident risk assessment tool to identify, eliminate, and assess potential failure modes in different industries for enhancing the safety and reliability of systems, process, services, and products. Therefore, this chapter presents a new approach to rank the failure modes under the interval-valued intuitionistic fuzzy set (IVIFS). For this, a novel measure to measure the fuzziness known as entropy measure is proposed. Some properties and axiom definition of the proposed entropy measure have been presented to show the validity of it. Afterwards, the proposed entropy measure is utilized to obtain the weight of risk factor and developed an approach under the IVIFS environment to determine the risk priority order of failure modes. Finally, a real-life case of FMEA has been discussed to manifest the developed approach, and obtained results are compared with the results obtained by the existing methods for showing the feasibility and validity of the proposed approach.

Sign in / Sign up

Export Citation Format

Share Document