线性支持向量顺序回归机的原始问题的解集分析

本文主要对线性支持向量顺序回归机进行理论研究.对其相应原始问题解的存在性唯一性问题进行细致的分析,指明其解集的确切结构,并给出由对偶问题的解求出原始问题的解集的具体步骤.从而为建立理论上完备的线性支持向量顺序回归机提供了依据.     

Latent scale linear models for multivariate ordinal responses and analysis by the method of weighted least squares

Summary A multivariate latent scale linear model is defined for multivariate ordered categorical responses and inference procedures based on the weighted least squares method are developed. Several applications of the model are suggested and illustrated through an analysis of real data. Asymptotic properties of the weighted least squares method are examined and some consequences of misspecification of the model are also discussed.     

The generation of a social welfare function under ordinal preferences

Against the background of recent impossibility theorems, the paper establishes a number of rules for the formation of social preferences to ensure the generation of a Bergson-Samuelson social welfare function of the desired ‘individualistic’ form. It demonstrates that such welfare functions can indeed exist under conditions of simply ordinality of individual preferences and a lack of interpersonal comparability, for the general n-person case with only weak restrictions upon individual preferences. A valuable tool of social welfare theory for the single-profile case is therefore restored under a wide set of conditions. By examining Kemp and Ng's justification for their A3 condition in this context, we are able also to highlight a number of key differences between the conditions satisfied by many political constitutions and the requirements for achieving the positive existence of a Bergson-Samuelson social welfare function. In particular the paper focusses here on the weighting systems on individual preferences that are consistent with generating an individualistic welfare function and examines the information content of individual ordinal preferences which must be utilized if the desired welfare function is to result.     

Concordant outranking with multiple criteria of ordinal significance

In this paper we address the problem of aggregating outranking statements from multiple preference criteria of ordinal significance. The concept of ordinal concordance of a global outranking situation is defined and an operational test for its presence is developed. Finally, we propose a new kind of robustness analysis for global outranking statements integrating classical dominance, ordinal and classical majority concordance in a same ordinal valued logical framework.Received: March 2004, Revised: October 2004, MSC classification: 90B50, 06A06, 03C80     

A polarized partition relation for cardinals of countable cofinality

We prove that if and , then

for all . This polarized partition relation holds if for every partition either there are and with or there are and with .

     

On the Slowly Well Orderedness of εo

For α < ε₀, N_α denotes the number of occurrences of ω in the Cantor normal form of α with the base ω. For a binary number-theoretic function f let B(K; f) denote the length n of the longest descending chain (α₀, …, α_n–1) of ordinals <ε₀ such that for all i < n, Nα_i ≤ f (K, i). Simpson [2] called ε₀ as slowly well ordered when B (K; f) is totally defined for f (K; i) = K · (i+ 1). Let |n| denote the binary length of the natural number n, and |n|_k the k-times iterate of the logarithmic function |n|. For a unary function h let L(K; h) denote the function B (K; h₀(K; i)) with h₀(K, i) = K + |i| · |i|_h(i). In this note we show, inspired from Weiermann [4], that, under a reasonable condition on h, the functionL (K; h) is primitive recursive in the inverse h^–1 and vice versa.     

Delays, Recurrence and Ordinals

We apply set-theoretical ideas to an iteration problem of dynamicalsystems. Among other results, we prove that these iterationsnever stabilise later than the first uncountable ordinal; forevery countable ordinal we give examples in Baire space andin Cantor space of an iteration that stabilises exactly at thatordinal; we give an example of an iteration with recursive datawhich stabilises exactly at the first non-recursive ordinal;and we find new examples of complete analytic sets simply definablefrom concepts of recurrence. 2000 Mathematics Subject Classification:primary 03E15, 37B20, 54H05; secondary 37B10, 37E15.     

Intuitionistic Fuzzy Synthetic Measure on the Basis of Survey Responses and Aggregated Ordinal Data

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.