The hierarchies of knowledge and the mathematics of discovery

Rather than attempting to characterize a relation of confirmation between evidence and theory, epistemology might better consider which methods of forming conjectures from evidence, or of altering beliefs in the light of evidence, are most reliable for getting to the truth. A logical framework for such a study was constructed in the early 1960s by E. Mark Gold and Hilary Putnam. This essay describes some of the results that have been obtained in that framework and their significance for philosophy of science, artificial intelligence, and for normative epistemology when truth is relative.I am indebted to Kevin Kelly for several years of happy conversation from which the perspective and views of this paper grew, for comments on a draft of the paper, and for constructing some of the illustrations. A fellowship from the John Simon Guggenheim Memorial Foundation provided the liberty to write this paper. It was first presented in the Turing Colloquium, 1990.     

Integrating integer programming and probabilistic deduction graphs for probabilistic reasoning

Optimal solutions of several variants of the probabilistic reasoning problem were found by a new technique that integrates integer programming and probabilistic deduction graphs (PDG). PDGs are extended from deduction graphs of the and-type via normal deduction graphs. The foregoing variants to be solved can involve multiple hypotheses and multiple evidences where the former is given and the latter is unknown and being found or vice versa. The relationship among these hypotheses and evidences with possible intermediaries is represented by a causal graph. The proposed method can handle a large causal graph of any type and find an optimal solution by invoking a linear integer programming package. In addition, formulating the reasoning problem to fit integer programming takes a polynomial time. H.-L. Li was visiting the Department of Computer Sciences, University of North Texas in 1988–1989. He is with the Institute of Information Management, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.     

模式识别催化剂生产调优

本文介绍如何将模式识别应用于生产调优,着重讨论了多指标(优化目标)因素的分级,提出了用模糊综合评价度量和依有序聚类最小损失函数准则划类,并相继进行变量与样本筛选、信息压缩、特征提取和模拟仿真获得优区操作条件,实施效果显著。     

一种基于模糊理论的图像边缘提取

讨论了模糊理论在边缘提取中的应用，并给出了一种改进的基于模糊理论的图像边缘检测算法。实验结果表明，与该算法不需要加额外的滤波器或图像降噪预处理。在抗噪性能方面(80％以内的Gaussian噪声和10％以内的椒盐噪声Salt＆Pepper)明显优于其它方法。     

XML schema, tree logic and sheaves automata

XML documents may be roughly described as unranked, ordered trees and it is therefore natural to use tree automata to process or validate them. This idea has already been successfully applied in the context of Document Type Definition (DTD), the simplest standard for defining document validity, but additional work is needed to take into account XML Schema, a more advanced standard, for which regular tree automata are not satisfactory. In this paper, we introduce Sheaves Logic (SL), a new tree logic that extends the syntax of the – recursion-free fragment of – W3C XML Schema Definition Language (WXS). Then, we define a new class of automata for unranked trees that provides decision procedures for the basic questions about SL: model-checking; satisfiability; entailment. The same class of automata is also used to answer basic questions about WXS, including recursive schemas: decidability of type-checking documents; testing the emptiness of schemas; testing that a schema subsumes another one.This work was partially supported by the French government research grant ACI TRALALA and by IST Global Computing Profundis.     

Fixed point theorems on fuzzy normed linear spaces

In this paper, definitions of strongly fuzzy convergent sequence, l-fuzzy weakly convergent sequence and l-fuzzy weakly compact set are given in a fuzzy normed linear space. The concepts of fuzzy normal structure, fuzzy non-expansive mapping, uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non-expansive mappings are proved.     

Using memory and fuzzy rules in a co-operative multi-thread strategy for optimization

In this article, we analyze a co-operative multi-thread search-based optimization strategy, where each solver thread represents a different optimization algorithm (or the same one with different settings), and they are all controlled by a centralized co-ordinator. We also propose the use of memory to keep track of both the state of the individual threads and the obtained solutions. Based on this memory, a very simple fuzzy rule base is used to control the system behavior.We also present the results of three computational experiments. The first of these checks the strategy by comparing it with an independent search strategy and a sequential algorithm, and the superiority of the co-operative scheme is confirmed. The second analyzes how definition of the threads affects the quality of the results, and the importance of there being a balanced set between intensification and diversification is corroborated. The third explores the use of memory with two different fuzzy rules, and the results indicate that the best combination is to use memory together with two rules (solver dependent and solver independent ones) (although this combination should not be activated at the beginning of the search in order to avoid premature convergence).     

A general class of simple majority decision rules based on linguistic opinions

In this paper we have introduced a class of decision rules related to simple majority, by considering individual intensities of preference. These intensities will be shown by means of linguistic labels. In order to compare the amount of opinion obtained by each alternative, we have considered the total ordered monoid generated by the sums of the original labels, according to an addition and an ordering. In this general framework different sets of linguistic labels can be employed and these sets can be represented by means of diverse mathematical objects. Moreover, on these mathematical representations of linguistic labels several orderings can be considered. Thus, flexibility is an important feature of this new class of group decision making procedures. Some examples of putting in practice the simple majority decision rules based on linguistic labels are provided, and the main properties of these voting systems are analyzed. It is worth emphasizing that these properties are satisfied for any total ordered monoid, regardless of the mathematical representation of linguistic labels or the ordering used to compare collective opinions.     

Genetically optimized fuzzy polynomial neural networks with fuzzy set-based polynomial neurons

In this paper, we propose and investigate a new category of neurofuzzy networks—fuzzy polynomial neural networks (FPNN) endowed with fuzzy set-based polynomial neurons (FSPNs) We develop a comprehensive design methodology involving mechanisms of genetic optimization, and genetic algorithms (GAs) in particular. The conventional FPNNs developed so far are based on the mechanisms of self-organization, fuzzy neurocomputing, and evolutionary optimization. The design of the network exploits the FSPNs as well as the extended group method of data handling (GMDH). Let us stress that in the previous development strategies some essential parameters of the networks (such as the number of input variables, the order of the polynomial, the number of membership functions, and a collection of the specific subset of input variables) being available within the network are provided by the designer in advance and kept fixed throughout the overall development process. This restriction may hamper a possibility of developing an optimal architecture of the model. The design proposed in this study addresses this issue. The augmented and genetically developed FPNN (gFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional FPNNs. The GA-based design procedure being applied at each layer of the FPNN leads to the selection of the most suitable nodes (or FSPNs) available within the FPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gFPNN is quantified through experimentation in which we use a number of modeling benchmarks—synthetic and experimental data being commonly used in fuzzy or neurofuzzy modeling. The obtained results demonstrate the superiority of the proposed networks over the models existing in the references.     

On a responsive replenishment system: a fuzzy logic approach

In today's competitive business environment, it is important that customers are able to obtain their preferred items in the shops they visit, particularly for convenience store chains such as 7–Eleven where popular items are expected to be readily available on the shelves of the stores for buyers. To minimize the cost of running such store chains, it is essential that stocks be kept to a minimum and at the same time large varieties of popular items are available for customers. In this respect, the replenishment system needs to be able to cope with the taxing demands of minimal inventory but at the same time keeping large varieties of needed items. This paper proposes a replenishment system which is able to respond to the fluctuating demands of customers and provide a timely supply of needed items in a cost–effective way. The proposed system embraces the principle of fuzzy logic which is able to deal with uncertainties by virtue of its fuzzy rules reasoning mechanism, thereby leveraging the responsiveness of the entire replenishment system for the chain stores. To validate the feasibility of the approach, a case study has been conducted in an emulated environment with promising results.