Fuzzy Logic and Arithmetical Hierarchy,II

A very simple many-valued predicate calculus is presented; a completeness theorem is proved and the arithmetical complexity of some notions concerning provability is determined.     

飞行错觉水平评定方法的初步研究

本文从飞行错觉发生的类型和频率出发,尝试对飞行员在实际飞行中所产生的错觉水平或空间定向能力做出基本的评定。本研究采用区间模糊统计的方法,对飞行错觉的类型（倾斜错觉、俯仰错觉、方位错觉、反旋转错觉和倒飞错觉）和频率（从无、偶尔、时有、经常、总是）做了经验的赋值工作,分别计算出了这些模糊概念（除从无外）的心理量表值和模糊度。同时我们认为,飞行错觉水平是频率与类型的函数,其数学表达式为：,并将这一表达式作为评定飞行员飞行错觉水平的基本模型。     

On Revising Fuzzy Belief Bases

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy logics, we show how the idea of rational change from “crisp” base revision, as embodied by the idea of partial meet (base) revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy base revision and illustrate how the operation works in several important special instances of the framework. We also axiomatise the related operation of partial meet fuzzy base contraction.This paper is an extended version of a paper presented at the Nineteenth Conference on Uncertainty in Arti.cial Intelligence (UAI’03).     

A Fuzzy Goal Programming Formulation with Multiple Target Levels

The essential activity of a manager is decision making, which is becoming more and more complex, mainly in the multi‐criteria problems. Multi‐choice goal programming (MCGP) is considered as a robust tool in operational research to solve this type of problem. However, in real world problems, determining precise targets for the goals is a difficult task. To deal with such situation, Tabrizi introduced and used in 2012 the concept of membership functions in the MCGP model in order to model the targets fuzziness of each goal. In their model, they considered just only one type of functions (triangular form), which does not reflect adequately the decision maker's preferences that are considered as an essential element for modelling the goal's fuzziness. Their model is called Fuzzy MCGP. In this paper, new ideas are presented to reformulate MCGP model to tackle all types of functions by introducing the (decision maker's) preferences. The concept of indifference thresholds is used in the new formulation for characterizing the imprecision and the preferences associated with all types of the goals. The proposed formulation provides useful insight about the solution of a new class of problems. A numerical example is given to demonstrate the validity and strength of the new formulation. Copyright © 2013 John Wiley & Sons, Ltd.     

判断与决策研究纵观:基于模糊痕迹理论的视角(英文)

模糊痕迹理论是用于解释记忆、判断与决策的综合性理论,该理论的提出和发展主要基于对信息存储、表征、提取和加工过程的研究。本文首先介绍了模糊痕迹理论的基本原则,在此基础上重点讨论了其要义(gist)如何发挥核心作用,使得模糊痕迹理论有别于其他传统的决策模型。该理论将高级直觉与原始冲动性进行了区分,并且预测决策误差来源于判断与决策的各种不同成分,如背景知识、信息表征、提取和加工过程等。模糊痕迹理论不仅可以解释诸如框架效应、合取谬误等传统决策与判断文献中常讨论的误差现象,同时基于该理论的研究还得到了一些与传统决策理论相悖的新发现。此外,对脑与行为如何发育性变化的研究为我们了解成人的认知过程提供了至关重要的新视角,这些对脑与行为的发育性研究和对特殊人群的研究结果也都支持了模糊痕迹理论对要义加工依赖的预测。     

Mathematical concepts for analyzing ambiguous situations

Abstract

We examine some mathematical tools for dealing with ambiguous situations. The main tool is the use of non-standard logic with truth-values in what is called a locale. This approach is related to fuzzy set theory, which we briefly discuss. We also consider probabilistic concepts. We include specific examples and describe the way a researcher can set up a suitable locale to analyse a concrete situation.     

On the Standard and Rational Completeness of some Axiomatic Extensions of the Monoidal T-norm Logic

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics.     

Embedding Logics into Product Logic

We construct a faithful interpretation of ukasiewicz's logic in product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable.We prove a completeness theorem for product logic extended by a unary connective of Baaz [1]. We show that Gödel's logic is a sublogic of this extended product logic.We also prove NP-completeness of the set of propositional formulas satisfiable in product logic (resp. in Gödel's logic).