Estimation of random information sets of multistep systems

The estimation problems for the linear multistep controlled system under mixed perturbations are considered. It is assumed that deterministic perturbations are bounded by convex and compact constraints and random perturbations are Gaussian. Random information sets, called multiestimes for brevity, are defined. In the absence of random components, the introduced multiestimates coincide with information sets in the theory of guaranteed estimation. The multiestimate structure is considered. It is shown that multiestimates can be represented as the sum of a random vector and a deterministic set, which depend on several parameters. In turn, this set of parameters determines uniquely both conditional and unconditional probability of inclusion of the multiestimate in the covering set. Several special cases are analyzed, and the form of the covering set is discussed. A modification of the problem under communication constraints is proposed. This modification takes into account the limited capability of the digital data transfer channel. Relations between the accuracy of multiestimate parameters identification and the length of the transmitted word are obtained. A number of the obtained results are illustrated by examples.     

On the random generation of monotone data sets

Many of the state-of-the-art classification algorithms for data with linearly ordered attribute domains and a linearly ordered label set insist on the monotonicity of the induced classification rule. Training and evaluation of such algorithms requires the availability of sufficiently general monotone data sets. In this short contribution we introduce an algorithm that allows for the (almost) uniform random generation of monotone data sets based on the Markov Chain Monte Carlo method.     

Fuzzy measure identification for criteria coalitions using linguistic information

Modeling interactions between criteria in multiple criteria decision analysis (MCDA) is a complex task. Such complexity arises when there are visible redundancies and synergies among criteria, which traditional MCDA methods cannot deal with. The Choquet integral is a model that has been conceived to deal with these issues, but an appropriate fuzzy measure must be defined. This article shows how to compute a fuzzy measure for criteria coalitions using linguistic information efficiently. Due to the complexity to identify an adequate fuzzy measure when the criteria set cardinality increases, the proposed model reduces the effort to determine the measure of each criteria combination by focusing on relevant interactions. Then, this fuzzy measure is used on Choquet integral to establish the best alternative in a decision-making problem. Finally, a comparison between the arithmetic mean, the OWA operator and the proposed method is presented.     

On the fusion of multi-granularity linguistic label sets in group decision making

Group decision-making problem is a common and crucial human activity. Many times due to inherent uncertainty, exact numbers can be either costly or unnecessary to be applied to express experts’ opinions or preferences. The use of linguistic labels makes expert judgment more reliable and informative for decision-making.     

Extracting linguistic rules from data sets using fuzzy logic and genetic algorithms

Linguistic rules in natural language are useful and consistent with human way of thinking. They are very important in multi-criteria decision making due to their interpretability. In this paper, our discussions concentrate on extracting linguistic rules from data sets. In the end, we firstly analyze how to extract complex linguistic data summaries based on fuzzy logic. Then, we formalize linguistic rules based on complex linguistic data summaries, in which, the degree of confidence of linguistic rules from a data set can be explained by linguistic quantifiers and its linguistic truth from the fuzzy logical point of view. In order to obtain a linguistic rule with a higher degree of linguistic truth, a genetic algorithm is used to optimize the number and parameters of membership functions of linguistic values. Computational results show that the proposed method is an alternative method for extracting linguistic rules with linguistic truth from data sets.     

Similarity evaluation of sets of linguistic summaries

Creating linguistic summaries of data has been a goal of the artificial and computational intelligence communities for many years. Summaries of written text have garnered the most attention. More recently, creating summaries of imagery and other sensed data has become important as a means of compressing large amounts of data and communicating with humans. In this paper, we consider the question of comparing sets of summaries generated from sensed data. In an earlier work, we developed a metric between individual protoform‐based summaries; and here, as a next step, we propose aggregation methods to fuse these individual distances. We provide a case study from eldercare where the goal is to compare different nighttime patterns for change detection. © 2012 Wiley Periodicals, Inc.     

On the estimation of independent binomial random variables using occurrence and sequential information

We re-visit² the age-old problem of estimating the parameters of a distribution from its observations. Traditionally, scientists and statisticians have attempted to obtain strong estimates by ‘extracting’ the information contained in the observations taken as a set. However, generally speaking, the information contained in the sequence in which the observations have appeared, has been ignored—i.e., except to consider dependence information as in the case of Markov models and n-gram statistics. In this paper, we present results which, to the best of our knowledge, are the first reported results, which consider how estimation can be enhanced by utilizing both the information in the observations and in their sequence of appearance. The strategy, known as sequence based estimation (SBE) works as follows. We first quickly allude to the results pertaining to computing the maximum likelihood estimates (MLE) of the data when the samples are taken individually. We then derive the corresponding MLE results when the samples are taken two-at-a-time, and then extend these for the cases when they are processed three-at-a-time, four-at-a-time etc. In each case, we also experimentally demonstrate the convergence of the corresponding estimates. We then suggest various avenues for future research, including those by which these estimates can be fused to yield a superior overall cumulative estimate of the parameter of the distribution, in pattern recognition (PR), and in other internet and compression applications. We believe that our new estimates have great potential for practitioners, especially when the cardinality of the observation set is small.     

On information energy of the image fuzzy sets

Information energy is a measure of useful information obtained from a fuzzy set. This paper investigates the information energy change between the original fuzzy set and the image fuzzy set, through the extension principle. Some methods, by which the information energy of the image fuzzy set can be directly obtained without calculating its membership function, are studied. Useful formulas calculating the information energy of the image of the same shape fuzzy numbers are specifically introduced.     

On the reducibility of sets inside NP to sets with low information content

This paper studies for various natural problems in NP whether they can be reduced to sets with low information content, such as branches, P-selective sets, and membership comparable sets. The problems that are studied include the satisfiability problem, the graph automorphism problem, the undirected graph accessibility problem, the determinant function, and all logspace self-reducible languages. Some of these are complete for complexity classes within NP, but for others an exact complexity theoretic characterization is not known. Reducibility of these problems is studied in a general framework introduced in this paper: prover-verifier protocols with low-complexity provers. It is shown that all these natural problems indeed have such protocols. This fact is used to show, for certain reduction types, that these problems are not reducible to sets with low information content unless their complexity is much less than what it is currently believed to be. The general framework is also used to obtain a new characterization of the complexity class is the class of all logspace self-reducible sets in L^L-sel.     

Sensor control for multi-object state-space estimation using random finite sets

The problem addressed in this paper is information theoretic sensor control for recursive Bayesian multi-object state-space estimation using random finite sets. The proposed algorithm is formulated in the framework of partially observed Markov decision processes where the reward function associated with different sensor actions is computed via the Rényi or alpha divergence between the multi-object prior and the multi-object posterior densities. The proposed algorithm in implemented via the sequential Monte Carlo method. The paper then presents a case study where the problem is to localise an unknown number of sources using a controllable moving sensor which provides range-only detections. Four sensor control reward functions are compared in the study and the proposed scheme is found to perform the best.     

Linguistic models and linguistic modeling

The study is concerned with a linguistic approach to the design of a new category of fuzzy (granular) models. In contrast to numerically driven identification techniques, we concentrate on budding meaningful linguistic labels (granules) in the space of experimental data and forming the ensuing model as a web of associations between such granules. As such models are designed at the level of information granules and generate results in the same granular rather than pure numeric format, we refer to them as linguistic models. Furthermore, as there are no detailed numeric estimation procedures involved in the construction of the linguistic models carried out in this way, their design mode can be viewed as that of a rapid prototyping. The underlying algorithm used in the development of the models utilizes an augmented version of the clustering technique (context-based clustering) that is centered around a notion of linguistic contexts-a collection of fuzzy sets or fuzzy relations defined in the data space (more precisely a space of input variables). The detailed design algorithm is provided and contrasted with the standard modeling approaches commonly encountered in the literature. The usefulness of the linguistic mode of system modeling is discussed and illustrated with the aid of numeric studies including both synthetic data as well as some time series dealing with modeling traffic intensity over a broadband telecommunication network.     

纯语言多属性群决策方法研究

研究了属性权重、属性值以及专家权重均以语言形式给出的纯语言多属性群决策问题．定义了语言评估标度的运算法则，给出了一些基于语言评估标度及其运算法则的新算子，提出了一种纯语言多属性群决策方法．该法不但计算简洁便利，而且能充分地利用已有的语言决策信息．最后将该方法应用于解决供应链管理领域中的战略合作伙伴选择问题．     

Detection of outlier information by the use of linguistic summaries based on classic and interval-valued fuzzy sets

Automatic summary of databases is an important tool in strategic decision-making. This paper presents the application of linguistic summaries to outlier detection in databases containing both text and numeric attributes. The proposed method applies Yager’s standard summary based on interval-valued fuzzy sets. Fuzzy similarity measures are the features which are looked for. Detection of outliers can identify defects, remove impurities from the data, and, most of all, it may provide the basis for decision-making processes. In this paper, we introduce a definition of an outlier based on linguistic summaries. Feasibility of the method is demonstrated on practical examples.     

Managing information measures for hesitant fuzzy linguistic term sets and their applications in designing clustering algorithms

Recently, the Hesitant Fuzzy Linguistic Term Sets (HFLTSs) have been widely used to address cognitive complex linguistic information because of its advantage in representing vagueness and hesitation in qualitative decision-making process. Information measures, including distance measure, similarity measure, entropy measure, inclusion measure and correlation measure, are used to characterize the relationships between linguistic elements. Many decision-making theories are based on information measures. Up to now, distance, similarity, entropy and correlation measures have been proposed by scholars but there is no paper focuses on inclusion measure. This paper dedicates to filling this gap and the inclusion measure between HFLTSs are proposed. We discuss the relationships among distance, similarity, inclusion and entropy measures of HFLTSs. Given that clustering algorithm is an important application of information measures but there are few papers related to clustering algorithm based on information measures in the environment of HFLTS, in this paper, we propose two clustering algorithms based on correlation measure and distance measure, respectively. After that, a case study concerning water resource bearing capacity is illustrated to verify the applicability of the proposed clustering algorithms.     

Operators and comparisons of probabilistic linguistic term sets

The probabilistic linguistic term sets (PLTSs) allow experts to express their preferences regarding one linguistic term over another. Nowadays, multicriteria decision-making methods for PLTSs are very popular, and Bai et al’s multicriteria decision-making method based on the possibility degree formula for PLTSs cannot be ranked in some situations. In this paper, we first propose a new possibility degree method for PLTSs and state their properties, and we use this new possibility degree method to solve the drawbacks of Bai et al’s possibility degree method. Second, we propose a probabilistic linguistic weight average (PLWA) and probabilistic linguistic order weight average (PLOWA) operator and state their properties. Then, based on the new possibility degree method and the PLWA (PLOWA) operator, we propose a multicriteria decision-making method based the PLWA (PLOWA) operator. Finally, we utilize an example to illustrate the interrelationships between our method and Bai et al’s method. The result shows that our multicriteria decision-making method is more rational.     

Pictorial information retrieval using the random neural network

A technique is developed based on the use of a neural network model for performing information retrieval in a pictorial information system. The neural network provides autoassociative memory operation and allows the retrieval of stored symbolic images using erroneous or incomplete information as input. The network used is based on an adaptation of the random neural network model featuring positive and negative nodes and symmetrical behavior of positive and negative signals. The network architecture considered has hierarchical structure and allows two-level operation during learning and recall. An experimental software prototype, including an efficient graphical interface, has been implemented and tested. The performance of the system has been investigated through experiments under several schemes concerning storage and reconstruction of patterns. These schemes are either based on properties of the random network or constitute adaptations of known neural network techniques     

Project evaluation method using non-formatted text information based on multi-granular linguistic labels

We propose a novel project evaluation method for non-formatted Chinese text evaluation information. First, the non-formatted Chinese text evaluation information is determined and expressed using extensible markup language and a hypertext preprocessor. Then, the evaluation problem is transformed into a multiple-criteria decision-analysis problem based on multi-granular linguistic labels, including a comprehensive evaluation score for alternatives and an evaluation criteria point score for incomplete items. Next, we propose a weighting model for the criteria based on the minimal difference between the comprehensive evaluation score and the evaluation criterion point score of decision-makers. We establish an estimation model for incomplete evaluation items with the minimal evidence distance of Dempster–Shafer theory using maximal group consistency. In addition, we calculate a weighting for the decision-makers using the similarity of the group. Finally, we present a score modification method for alternatives based on weights of the criteria and the decision-maker. We use a soft science project evaluation and selection to illustrate the application process and feasibility of the proposed method.     

An essay on the linguistic roots of fuzzy sets

This paper mainly tries to show that the membership function of a fuzzy set labeled P does show some intrinsic property related with how P is actually managed in the universe of discourse. Its final goal is to analyze an answer to the question, which intrinsic but simple property allows a function to represent a fuzzy set labeled P? The presented property exhibits that the membership function just ‘measures’ in some scale the extent up to which x is P in language, for all x in the universe of discourse.Such study is done in a form allowing to consider how to represent the ‘collective’ originated by a predicate reflecting a collective noun. As particular cases of what is presented, and when the degrees can be some kinds of numerical subsets, the Zadeh’s fuzzy sets, the interval-valued, the intuitionistic, and the type-2 fuzzy sets, appear as particular cases and to some extent are discussed. A ‘unification’ of all different kinds of fuzzy sets based on a linguistic origin is achieved.     

Strong limit theorems for random sets and fuzzy random sets with slowly varying weights

Theories of random sets and fuzzy random sets are useful concepts which are frequently applied in scientific areas including information science, probability and statistics. In this paper strong limit theorems are derived for random sets and fuzzy random sets with slowly varying weights in separable Banach spaces. Both independent and dependent cases are covered to provide a wide range of applications.