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1.
Bart&#x;omiej Jefma&#x;ski Ewa Roszkowska Marta Kusterka-Jefma&#x;ska 《Entropy (Basel, Switzerland)》2021,23(12)
The paper addresses the problem of complex socio-economic phenomena assessment using questionnaire surveys. The data are represented on an ordinal scale; the object assessments may contain positive, negative, no answers, a “difficult to say” or “no opinion” answers. The general framework for Intuitionistic Fuzzy Synthetic Measure (IFSM) based on distances to the pattern object (ideal solution) is used to analyze the survey data. First, Euclidean and Hamming distances are applied in the procedure. Second, two pattern object constructions are proposed in the procedure: one based on maximum values from the survey data, and the second on maximum intuitionistic values. Third, the method for criteria comparison with the Intuitionistic Fuzzy Synthetic Measure is presented. Finally, a case study solving the problem of rank-ordering of the cities in terms of satisfaction from local public administration obtained using different variants of the proposed method is discussed. Additionally, the comparative analysis results using the Intuitionistic Fuzzy Synthetic Measure and the Intuitionistic Fuzzy TOPSIS (IFT) framework are presented. 相似文献
2.
Ewa Roszkowska Bart&#x;omiej Jefma&#x;ski Marta Kusterka-Jefma&#x;ska 《Entropy (Basel, Switzerland)》2022,24(8)
In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig’s method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented. 相似文献
3.
In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form. 相似文献
4.
Aziz Khan Shougi S. Abosuliman Saleem Abdullah Muhammad Ayaz 《Entropy (Basel, Switzerland)》2021,23(4)
Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative. 相似文献
5.
Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy belief entropy to solve the problem based on the relation among IT2 FS, belief structure, and Z-valuations. The interval of membership function can be transformed to interval BPA . Then, and are put into the proposed entropy to calculate the uncertainty from the three aspects of fuzziness, discord, and nonspecificity, respectively, which makes the result more reasonable. Compared with other methods, fuzzy belief entropy is more reasonable because it can measure the uncertainty caused by multielement fuzzy subsets. Furthermore, when the membership function belongs to type-1 fuzzy sets, fuzzy belief entropy degenerates to Shannon entropy. Compared with other methods, several numerical examples are demonstrated that the proposed entropy is feasible and persuasive. 相似文献
6.
Igal Sason 《Entropy (Basel, Switzerland)》2021,23(3)
This paper studies the problem of upper bounding the number of independent sets in a graph, expressed in terms of its degree distribution. For bipartite regular graphs, Kahn (2001) established a tight upper bound using an information-theoretic approach, and he also conjectured an upper bound for general graphs. His conjectured bound was recently proved by Sah et al. (2019), using different techniques not involving information theory. The main contribution of this work is the extension of Kahn’s information-theoretic proof technique to handle irregular bipartite graphs. In particular, when the bipartite graph is regular on one side, but may be irregular on the other, the extended entropy-based proof technique yields the same bound as was conjectured by Kahn (2001) and proved by Sah et al. (2019). 相似文献
7.
Marzena Filipowicz-Chomko Rafa&#x; Mierzwiak Marcin Nowak Ewa Roszkowska Tomasz Wachowicz 《Entropy (Basel, Switzerland)》2021,23(6)
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. 相似文献
8.
In a previous article we presented an argument to obtain (or rather infer) Born’s rule, based on a simple set of axioms named “Contexts, Systems and Modalities\" (CSM). In this approach, there is no “emergence”, but the structure of quantum mechanics can be attributed to an interplay between the quantized number of modalities that is accessible to a quantum system and the continuum of contexts that are required to define these modalities. The strong link of this derivation with Gleason’s theorem was emphasized, with the argument that CSM provides a physical justification for Gleason’s hypotheses. Here, we extend this result by showing that an essential one among these hypotheses—the need of unitary transforms to relate different contexts—can be removed and is better seen as a necessary consequence of Uhlhorn’s theorem. 相似文献
9.
Shannon’s entropy is one of the building blocks of information theory and an essential aspect of Machine Learning (ML) methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable alphabet. The unboundedness of Shannon’s entropy over the general class of all distributions on an alphabet prevents its potential utility from being fully realized. To fill the void in the foundation of information theory, Zhang (2020) proposed generalized Shannon’s entropy, which is finitely defined everywhere. The plug-in estimator, adopted in almost all entropy-based ML method packages, is one of the most popular approaches to estimating Shannon’s entropy. The asymptotic distribution for Shannon’s entropy’s plug-in estimator was well studied in the existing literature. This paper studies the asymptotic properties for the plug-in estimator of generalized Shannon’s entropy on countable alphabets. The developed asymptotic properties require no assumptions on the original distribution. The proposed asymptotic properties allow for interval estimation and statistical tests with generalized Shannon’s entropy. 相似文献
10.
The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node’s fugacity in the course of prospective network expansion or shrinking. 相似文献
11.
In this paper, we discuss the decision optimization of tourism projects in Hebei Province, China. To improve the process of analyzing tourism projects, we introduce a model that includes multiple decision makers as subjects based on a standard four-dimensional evaluation system. In order to improve the effectiveness of decision-making results, we will increase the number of decision makers to 40. A novel large-scale group decision-making (LSGDM) algorithm that incorporates the trust–distrust asymmetric relationships between decision makers is proposed. This model contains three main innovations: firstly, in the evaluation of decision makers’ social network relations, the trust–distrust value is introduced as a new carrier, and a weighted directed network and data integration operator are constructed based on the evaluation between decision makers; secondly, an extended Girvan-Newman (GN) algorithm is constructed to cluster the decision makers from this weighted network; thirdly, the interval-valued intuitionistic fuzzy number (IVIFN) is used to evaluate the alternatives, studying the IVIFN’s geometric significance by placing in a rectangular coordinate system. Finally, a new LSGDM model is proposed. Using the development of a cultural tourism project in a township as an example, the effectiveness of the proposed model is illustrated. By comparing the results of our method to those of a LSGDM algorithm that does not incorporate trust relationships, we assess the performance of the new model. 相似文献
12.
Wigner’s friend scenarios involve an Observer, or Observers, measuring a Friend, or Friends, who themselves make quantum measurements. In recent discussions, it has been suggested that quantum mechanics may not always be able to provide a consistent account of a situation involving two Observers and two Friends. We investigate this problem by invoking the basic rules of quantum mechanics as outlined by Feynman in the well-known “Feynman Lectures on Physics”. We show here that these “Feynman rules” constrain the a priori assumptions which can be made in generalised Wigner’s friend scenarios, because the existence of the probabilities of interest ultimately depends on the availability of physical evidence (material records) of the system’s past. With these constraints obeyed, a non-ambiguous and consistent account of all measurement outcomes is obtained for all agents, taking part in various Wigner’s Friend scenarios. 相似文献
13.
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations. 相似文献
14.
Chengli Fan Qiang Fu Yafei Song Yingqi Lu Wei Li Xiaowen Zhu 《Entropy (Basel, Switzerland)》2022,24(12)
Existing missile defense target threat assessment methods ignore the target timing and battlefield changes, leading to low assessment accuracy. In order to overcome this problem, a dynamic multi-time fusion target threat assessment method is proposed. In this method, a new interval valued intuitionistic fuzzy weighted averaging operator is proposed to effectively aggregate multi-source uncertain information; an interval-valued intuitionistic fuzzy entropy based on a cosine function (IVIFECF) is designed to determine the target attribute weight; an improved interval-valued intuitionistic fuzzy number distance measurement model is constructed to improve the discrimination of assessment results. Specifically, first of all, we define new interval-valued intuitionistic fuzzy operation rules based on algebraic operations. We use these rules to provide a new model of interval-valued intuitionistic fuzzy weighted arithmetic averaging (IVIFWAA) and geometric averaging (IVIFWGA) operators, and prove a number of algebraic properties of these operators. Then, considering the subjective and objective weights of the incoming target, a comprehensive weight model of target attributes based on IVIFECF is proposed, and the Poisson distribution method is used to solve the time series weights to process multi-time situation information. On this basis, the IVIFWAA and IVIFWGA operators are used to aggregate the decision information from multiple times and multiple decision makers. Finally, based on the improved TOPSIS method, the interval-valued intuitionistic fuzzy numbers are ordered, and the weighted multi-time fusion target threat assessment result is obtained. Simulation results of comparison show that the proposed method can effectively improve the reliability and accuracy of target threat assessment in missile defense. 相似文献
15.
Arieh Ben-Naim 《Entropy (Basel, Switzerland)》2022,24(11)
In 2015, I wrote a book with the same title as this article. The book’s subtitle is: “What we know and what we do not know.” On the book’s dedication page, I wrote: “This book is dedicated to readers of popular science books who are baffled, perplexed, puzzled, astonished, confused, and discombobulated by reading about Information, Entropy, Life and the Universe.” In the first part of this article, I will present the definitions of two central concepts: the “Shannon measure of information” (SMI), in Information Theory, and “Entropy”, in Thermodynamics. Following these definitions, I will discuss the framework of their applicability. In the second part of the article, I will examine the question of whether living systems and the entire universe are, or are not within the framework of applicability of the concepts of SMI and Entropy. I will show that much of the confusion that exists in the literature arises because of people’s ignorance about the framework of applicability of these concepts. 相似文献
16.
Maxwell’s demon is an entity in a 150-year-old thought experiment that paradoxically appears to violate the second law of thermodynamics by reducing entropy without doing work. It has increasingly practical implications as advances in nanomachinery produce devices that push the thermodynamic limits imposed by the second law. A well-known explanation claiming that information erasure restores second law compliance fails to resolve the paradox because it assumes the second law a priori, and does not predict irreversibility. Instead, a purely mechanical resolution that does not require information theory is presented. The transport fluxes of mass, momentum, and energy involved in the demon’s operation are analyzed and show that they imply “hidden” external work and dissipation. Computing the dissipation leads to a new lower bound on entropy production by the demon. It is strictly positive in all nontrivial cases, providing a more stringent limit than the second law and implying intrinsic thermodynamic irreversibility. The thermodynamic irreversibility is linked with mechanical irreversibility resulting from the spatial asymmetry of the demon’s speed selection criteria, indicating one mechanism by which macroscopic irreversibility may emerge from microscopic dynamics. 相似文献
17.
We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability. 相似文献
18.
We present a hypothetical argument against finite-state processes in statistical language modeling that is based on semantics rather than syntax. In this theoretical model, we suppose that the semantic properties of texts in a natural language could be approximately captured by a recently introduced concept of a perigraphic process. Perigraphic processes are a class of stochastic processes that satisfy a Zipf-law accumulation of a subset of factual knowledge, which is time-independent, compressed, and effectively inferrable from the process. We show that the classes of finite-state processes and of perigraphic processes are disjoint, and we present a new simple example of perigraphic processes over a finite alphabet called Oracle processes. The disjointness result makes use of the Hilberg condition, i.e., the almost sure power-law growth of algorithmic mutual information. Using a strongly consistent estimator of the number of hidden states, we show that finite-state processes do not satisfy the Hilberg condition whereas Oracle processes satisfy the Hilberg condition via the data-processing inequality. We discuss the relevance of these mathematical results for theoretical and computational linguistics. 相似文献
19.
The uncertainty of information is an important issue that must be faced when dealing with decision-making problems. Randomness and fuzziness are the two most common types of uncertainty. In this paper, we propose a multicriteria group decision-making method based on intuitionistic normal cloud and cloud distance entropy. First, the backward cloud generation algorithm for intuitionistic normal clouds is designed to transform the intuitionistic fuzzy decision information given by all experts into an intuitionistic normal cloud matrix to avoid the loss and distortion of information. Second, the distance measurement of the cloud model is introduced into the information entropy theory, and the concept of cloud distance entropy is proposed. Then, the distance measurement for intuitionistic normal clouds based on numerical features is defined and its properties are discussed, based on which the criterion weight determination method under intuitionistic normal cloud information is proposed. In addition, the VIKOR method, which integrates group utility and individual regret, is extended to the intuitionistic normal cloud environment, and thus the ranking results of the alternatives are obtained. Finally, the effectiveness and practicality of the proposed method are demonstrated by two numerical examples. 相似文献
20.