一种逐次逼近方法的形式与选择问题
One Form of Successive Approximation Method and Choice Problem
AI总结：
本文提出主体行为选择模型，基于内部与外部偏好关系，通过逐次逼近方法最小化外部偏好使用，构造逼近形式，并应用于逻辑起源及Lefebvre选择模型的新解释。
摘要：
提出了一个主体行为选择的数学模型。该模型的背景是决定主体行为的两个偏好关系的概念。这两个偏好关系分别是“内部”或主观偏好关系和“外部”或客观偏好关系。第一个（内部）偏好关系由主体状态集合上的某个偏序定义。第二个（外部）偏好关系在状态集合上由从状态集合到另一个偏序集合的映射定义。该映射将被称为评价映射（函数）。我们研究外部偏好最大化的过程，其方式尽可能少地使用外部偏好。相反，主体可以不受任何限制地使用内部偏好。最大化过程的复杂性取决于这些偏好之间的不一致程度。为了解决该问题，我们应用某种逐次逼近方法。在评价映射的术语中，该方法作用于将映射分解为若干标准运算和“简单”映射的叠加（详见下文）。以这种方式获得的叠加称为逼近形式。我们构造了几种这样的形式并给出了两个应用。其中一个涉及逻辑的假设性起源。另一个应用为Lefebvre的著名人类选择模型提供了新的解释。该解释似乎提出了一种不同于Lefebvre本人所提出的论证。
英文摘要：
A mathematical model of Subject behaviour choice is proposed. The background of the model is the concept of two preference relations determining Subject behaviour. These are an "internal" or subjective preference relation and an "external" or objective preference relation. The first (internal) preference relation is defined by some partial order on a set of states of the Subject. The second (external) preference relation on the state set is defined by a mapping from the state set to another partially ordered set. The mapping will be called evaluation mapping (function). We research the process of external preference maximization in a fashion that uses the external preference as little as possible. On the contrary, Subject may use the internal preference without any restriction. The complexity of a maximization procedure depends on the disagreement between these preferences. To solve the problem we apply some kind of the successive approximations methods. In terms of evaluation mappings this method operates on a decomposition of the mapping into a superposition of several standard operations and "easy" mappings (see the details below). Obtained in such way superpositions are called approximating forms. We construct several such forms and present two applications. One of them is concerned with a hypothetic origin of logic. The other application provides a new interpretation of the well known model of human choice by Lefebvre. The interpretation seems to suggest a justification different from the one proposed by Lefebvre himself.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
