Quantity of information; Comparison between information systems: 1. Non-fuzzy states

In statistical theory, experiments or probabilistic information systems are supposed to be informative, since they reduce the amount of uncertainty associated with the states of nature. For the case that the available information systems are vague (fuzzy information systems), H. Tanaka, T. Okuda and K. Asai have proven, using the ‘measure of information’ as provided by ‘entropy’, that the fuzzy information systems are informative too.Now, we wish to state and to study a criterion in order to compare fuzzy information systems by the ‘quantity of information of a fuzzy information system’ (defined by Tanaka et al.).In this first paper we consider the situation where we require information about the original state space (non-fuzzy state space).The second paper will deal with the situation where we require only information on certain vague states (fuzzy states).     

Quantity of information; comparison between information systems: 2. Fuzzy states

In statistical theory, experiments or probabilistic information systems are supposed to be informative, since they reduce the amount of uncertainty associated with the states of nature. For the case that the available information systems are vague (fuzzy information systems), H. Tanaka, T. Okuda and K. Asai have proven, using the ‘measure of information’ as provided by ‘entropy’, that the fuzzy information systems are informative too.Now, we wish to state and to study a criterion in order to compare fuzzy information systems by the ‘quantity of information of a fuzzy information system’ (defined by Tanaka et al.).In the first paper we considered the situation where we require information about the original state space (non-fuzzy state space).This second paper deals with the situation where we require only information on certain vague states (fuzzy states).     

The fuzzy decision problem: An approach to the point estimation problem with fuzzy information

This paper is devoted to the extension of the Bayesian method for the point estimation, when the available information is ‘vague’.In the nonfuzzy case, the parametric estimation can be approached as a particularization in the statistical decision problem. This motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem (defined by Tanaka, Okuda and Asia).In this way, concepts in the fuzzy decision problem are first ‘expressed’ in the estimation terminology. Then, on the basis of these concepts, we shall introduce some notions and state some interesting results. Finally, several illustrative examples will be exposed.     

On coordination of supply chain based on information asymmetry of effort level and fuzzy market environment

The agent’s private information contributes greatly to a person to make principal decision in the supply of a chain coordination. Therefore, it is a great issue for him to design an effective incentive mechanism in order to get the true information from the agent in his principle making. Assuming that the demand depend upon an agent’s effort level and the fuzzy market condition, the author in this paper researches and analyzes the principle-agent problem under fuzzy information asymmetry condition by using the theory of principal-agent as well as incentive mechanism.     

On the loss of information due to fuzziness in experimental observations

The absence of exactness in the observation of the outcomes of a random experiment always entails a loss of information about the experimental distribution. This intuitive assertion will be formally proved in this paper by using a mathematical model involving the notions of fuzzy information and fuzzy information system (as intended by Tanaka, Okuda and Asai) and Zadeh's probabilistic definition. On the basis of this model we are first going to consider a family of measures of information enclosing some well-known measures, such as those defined by Kagan, Kullback-Leibler and Matusita, and then to establish methods for removing the loss of information due to fuzziness by increasing suitably the number of experimental observations.     

Generalized best choice problem based on the information economics approach

We consider the problem of choosing the ‘best choice’ among a certain number of objects that are presented to a decision-maker in sequential order. Such a sequential selection problem is commonly referred to as the ‘best choice problem’, and its optimal stopping rule has been obtained either via the dynamic programming approach or via the Markovian approach. Based on the theory of information economics, we propose in the paper the third approach to a generalized version of the best choice problem that is intuitively more appealing. Various types of the best choice problem, such as (1) the classical secretary problem, (2) no information group interview problem, and (3) full information best choice problem with a random walk process, are shown to be special cases of the generalized best choice problem. The modelling framework of information economics has potential for building theory that ultimately would produce practical stopping rules.     

The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information

This paper is devoted to the problems of testing statistical hypotheses about an experiment, when the available information from its sampling is `vague'. When the information supplied by the experimental sampling is exact, the problems of testing statistical hypotheses about the experiment can be regarded as a particular statistical decision problem. In addition, decision procedures may be used in problems of testing hypotheses.In a similar manner, the problem of testing statistical hypotheses about an experiment when the available sample information is vague, is approached in this paper as a particular fuzzy decision problem (as defined by Tanaka, Okuda and Asai). This approach assumes that the previous information about the experiment can be expressed by means of certain conditional probabilistic information, whereas the present information about it can be expressed by means of fuzzy information. The preceding framework allows us to extend the notion of risk function and some nonfuzzy decision procedures to the fuzzy case, and particularize them to the problem of testing.Finally, several illustrative examples are presented.     

How to treat strict preference information in multicriteria decision analysis

This paper addresses the use of incomplete information on both multi-criteria alternative values and importance weights in evaluating decision alternatives. Incomplete information frequently takes the form of strict inequalities, such as strict orders and strict bounds. En route to prioritizing alternatives, the majority of previous studies have replaced these strict inequalities with weak inequalities, by employing a small positive number. As this replacement closes the feasible region of decision parameters, it circumvents certain troubling questions that arise when utilizing a mathematical programming approach to evaluate alternatives. However, there are no hard and fast rules for selecting the factual small value and, even if the choice is possible, the resultant prioritizations depend profoundly on that choice. The method developed herein addresses and overcomes this drawback, and allows for dominance and potential optimality among alternatives, without selecting any small value for the strict preference information. Given strict information on criterion weights alone, we form a linear program and solve it via a two-stage method. When both alternative values and weights are provided in the form of strict inequalities, we first construct a nonlinear program, transform it into a linear programming equivalent, and finally solve this linear program via the same two-stage method. One application of this methodology to a market entry decision, a salient subject in the area of international marketing, is demonstrated in detail herein.     

Multicriteria sorting using a valued indifference relation under a preference disaggregation paradigm

Most multicriteria decision methods need the definition of a significant amount of preferential information from a decision agent. The preference disaggregation analysis paradigm infers the model’s parameter values from holistic judgments provided by a decision agent. Here, a new method for inferring the parameters of a fuzzy outranking model for multicriteria sorting is proposed. This approach allows us to use most of the preferential information contained in a reference set. The central idea is to characterize the quality of the model by measuring discrepancies and concordances amongst (i) the preference relations derived from the outranking model, and (ii) the preferential information contained in the reference set. The model’s parameters are inferred from a multiobjective optimization problem, according to some additional preferential information from a decision agent. Once the model has been fitted, sorting decisions about new objects are performed by using a fuzzy indifference relation. This proposal performs very well in some examples.     

Fuzzy events and fuzzy logics in classical information systems

Classical information systems are introduced in the framework of measure and integration theory. The measurable characteristic functions are identified with the exact events while the fuzzy events are the real measurable functions whose range is contained in the unit interval. Two orthogonality relations are introduced on fuzzy events, the first linked to the fuzzy logic and the second to the fuzzy structure of partial a Baer¹-ring. The fuzzy logic is then compared with the “empirical” fuzzy logic induced by the classical information system. In this context, quantum logics could be considered as those empirical fuzzy logics in which it is not possible to have preparation procedures which provide physical systems whose “microstate” is always exactly defined.     

毕达哥拉斯群决策方法及其在绿色供应商选取中的应用

针对专家权重未知且属性值为毕达哥拉斯模糊数的多属性群决策问题,基于证据理论和混合加权毕达哥拉斯MSM算子,提出了一种群决策方法。 首先,由决策信息矩阵获取专家的模糊测度,并赋予其相应的权重;其次,基于新构造的混合加权毕达哥拉斯MSM算子对专家所提供的属性信息分别进行集结,得到各个专家的综合评价信息;再次,利用证据合成方法,对专家综合评价信息进行融合,获得候选方案的综合证据信息,进而可知备选方案的信任区间,并据此对候选方案进行优选决策;最后,绿色供应商选取案例的分析与对比验证了方法的可行性与合理性。     

基于模糊测度与累积前景理论的区间二型模糊多准则决策方法

针对准则值为区间二型模糊数且准则间存在关联关系的风险型多准则决策问题, 本文提出一种基于模糊测度理论与累积前景理论的区间二型模糊多准则决策方法。首先, 为全面反映准则间的关联关系, 本文提出Shapley区间二型模糊Choquet积分算子, 并证明该算子的一些性质。其次, 为反映专家行为偏好, 本文定义区间二型模糊前景效应与前景价值函数, 并提出累积前景Shapley区间二型模糊Choquet积分算子。然后, 为确定准则集的模糊测度, 本文建立基于区间二型模糊双向投影与Shapley函数的权重优化模型。在此基础上, 本文给出一种用于解决准则值为区间二型模糊数, 准则间存在关联关系, 专家存在风险偏好以及准则权重部分未知的多准则决策方法。最后, 通过风险投资实例佐证所提出的方法的适用性与科学性。     

Uncertain agency models with multi-dimensional incomplete information based on confidence level

This paper discusses a principal–agent problem with multi-dimensional incomplete information between a principal and an agent. Firstly, how to describe the incomplete information in such agency problem is a challenging issue. This paper characterizes the incomplete information by uncertain variable, because it has been an appropriate tool to depict subjective assessment and model human uncertainty. Secondly, the relevant literature often used expected-utility-maximization to measure the two participators’ goals. However, Ellsberg paradox indicates that expected utility criterion is not always appropriate to be regarded as decision rule. For this reason, this paper presents another decision rule based on confidence level. Instead of expected-utility-maximization, the principal’s aim is to maximize his potential income under the acceptable confidence level, and the agent’s aim depends on whether he has private information about his efforts. According to the agent’s different decision rules, three classes of uncertain agency (UA) models and their respective optimal contracts are presented. Finally, a portfolio selection problem is studied to demonstrate the modeling idea and the viability of the proposed UA models.     

On the information about individual utilities used in social choice

This paper investigates the consequences of the requirement tha a social choice method should convey as much information as possible about the individuals' values. It is first shown that if interpersonal comparisons of utilities are excluded, then the only information about individual values that can be used in the context of social choice is ordinal information. It is then argued that Arrow's independence condition demands that only a part of the information about the individual preferences be used in the social choice. Finally, it is shown that the requirement of maximal information gives strong support to Smith's (1973) ‘separability’ condition. In combination with Smith's result this shows that the choice methods that convey the most information about individual preferences are the ‘generalized point systems’ (also called ‘scoring functions’ or ‘ranking systems’).     

Information acquisition and disclosure by firms in the presence of additional available information

In this paper we analyze a model which addresses two stylized facts which have received little attention in disclosure theory. (a) Information that is acquired for internal decision-making can subsequently be disclosed to outside investors who can use it to update their assessment of the firm’s prospects. Thus, the decision to gather information in the first place does not only depend on the decision value of information. (b) Information disclosed by firms is only one element of the information environment upon which investors can draw. This setting creates an interaction between firms’ information gathering and disclosure decisions as well as alternative sources of information. We identify an equilibrium structure which we call a Countersignaling equilibrium in which only average firms acquire information whereas good and bad firms do not. We show that while several equilibria can coexist, a Countersignaling equilibrium is often the economically most efficient one.     

A mixed theory of information—X: Information functions and information measures

In the probabilistic theory of information, measures of information depend only upon the probabilities of the events, whereas in the nonprobabilistic theory these measures depend only upon the events. In a new, mixed theory of information the measures of information are assumed to depend on both the probabilities and the events. In this paper we consider measures depending upon a n-tuple of events and upon a finite number of n-ary complete, discrete probability distributions and characterize these measures of information only by two properties: by a recursivity condition, which states how the information changes by splitting one event of a system (one outcome of an experiment, market situation etc.) into two events, and by a weak symmetry condition (no regularity condition is assumed). Our result generalizes all recent results on this topic and especially we get from this one theorem a lot of characterization theorems for some well-known (purely probabilistic) information measures like the Shannon entropy, the entropy of degree α, the inaccuracy, the directed divergence, and the information improvement.     

Resampling-based information criteria for best-subset regression

When a linear model is chosen by searching for the best subset among a set of candidate predictors, a fixed penalty such as that imposed by the Akaike information criterion may penalize model complexity inadequately, leading to biased model selection. We study resampling-based information criteria that aim to overcome this problem through improved estimation of the effective model dimension. The first proposed approach builds upon previous work on bootstrap-based model selection. We then propose a more novel approach based on cross-validation. Simulations and analyses of a functional neuroimaging data set illustrate the strong performance of our resampling-based methods, which are implemented in a new R package.     

Comparative statics of a signaling game: An experimental study

In this paper a simple and basic signaling game is studied in an experimental environment. First, we check whether we can replicate some of the findings in the literature concerning equilibrium selection and the use and impact of costly signals. Second, and foremost, the comparative statics implications of the game are studied. The experimental results are related to the predictions of two competing behavioral models: a game model, in which subjects are assumed to behave in line with (refined) sequential equilibrium theory, and a decision model, in which subjects are assumed to behave as non-strategic decision makers. The experimental outcomes replicate the finding in the literature that costly messages are sent more frequently by ‘higher’ sender types (whose information is such that persuasion is also profitable to the responder), and that such messages have an impact on the behavior of the responder. These results are consistent with (versions of) both the game model and the decision model. The comparative statics results, however, clearly point in the direction of the decision model. Play is most strongly affected by ‘own’ payoff parameters, as predicted by the decision model, and less so by opponent's payoff parameters, as predicted by the mixed strategies of the refined sequential equilibrium. Particularly, a decision model in which players are assumed to adapt beliefs about opponents' choice probabilities in response to experience in previous play, appears to succeed best in organizing the data.