Kripke Frame with Graded Accessibility and Fuzzy Possible World Semantics

A possible world structure consist of a set W of possible worlds and an accessibility relation R. We take a partial function r(·,·) to the unit interval [0, 1] instead of R and obtain a Kripke frame with graded accessibility r Intuitively, r(x, y) can be regarded as the reliability factor of y from x We deal with multimodal logics corresponding to Kripke frames with graded accessibility in a fairly general setting. This setting provides us with a framework for fuzzy possible world semantics. The basic propositional multimodal logic gK (grated K) is defined syntactically. We prove that gK is sound and complete with respect to this semantics. We discuss some extensions of gK including logics of similarity relations and of fuzzy orderings. We present a modified filtration method and prove that gK and its extensions introduced here are decidable.     

飞行员情境认知的模糊综合评判

借用环境科学中环境质量评价的概念和方法,建立了飞行员情境认知的多级模糊综合评判模型,并用该模型对飞行员的情境认知进行了综合评判。研究表明,用模糊综合评判方法评价飞行员的情境认知可以提供真实、全面的飞行认知信息,为飞行员的训练有效性及安全性提供可靠依据。     

Two-Way Regularized Fuzzy Clustering of Multiple Correspondence Analysis

Multiple correspondence analysis (MCA) is a useful tool for investigating the interrelationships among dummy-coded categorical variables. MCA has been combined with clustering methods to examine whether there exist heterogeneous subclusters of a population, which exhibit cluster-level heterogeneity. These combined approaches aim to classify either observations only (one-way clustering of MCA) or both observations and variable categories (two-way clustering of MCA). The latter approach is favored because its solutions are easier to interpret by providing explicitly which subgroup of observations is associated with which subset of variable categories. Nonetheless, the two-way approach has been built on hard classification that assumes observations and/or variable categories to belong to only one cluster. To relax this assumption, we propose two-way fuzzy clustering of MCA. Specifically, we combine MCA with fuzzy k-means simultaneously to classify a subgroup of observations and a subset of variable categories into a common cluster, while allowing both observations and variable categories to belong partially to multiple clusters. Importantly, we adopt regularized fuzzy k-means, thereby enabling us to decide the degree of fuzziness in cluster memberships automatically. We evaluate the performance of the proposed approach through the analysis of simulated and real data, in comparison with existing two-way clustering approaches.     

The Gist of Delay of Gratification: Understanding and Predicting Problem Behaviors

Delay of gratification captures elements of temptation and self‐denial that characterize real‐life problems with money and other problem behaviors such as unhealthy risk taking. According to fuzzy‐trace theory, decision makers mentally represent social values such as delay of gratification in a coarse but meaningful form of memory called “gist.” Applying this theory, we developed a gist measure of delay of gratification that does not involve quantitative trade‐offs (as delay discounting does) and hypothesize that this construct explains unique variance beyond sensation seeking and inhibition in accounting for problem behaviors. Across four studies, we examine this Delay‐of‐gratification Gist Scale by using principal components analyses and evaluating convergent and divergent validity with other potentially related scales such as Future Orientation, Propensity to Plan, Time Perspectives Inventory, Spendthrift‐Tightwad, Sensation Seeking, Cognitive Reflection, Barratt Impulsiveness, and the Monetary Choice Questionnaire (delay discounting). The new 12‐item measure captured a single dimension of delay of gratification, correlated as predicted with other scales, but accounted for unique variance in predicting such outcomes as overdrawing bank accounts, substance abuse, and overall subjective well‐being. Results support a theoretical distinction between reward‐related approach motivation, including sensation seeking, and inhibitory faculties, including cognitive reflection. However, individuals' agreement with the qualitative gist of delay of gratification, as expressed in many cultural traditions, could not be reduced to such dualist distinctions nor to quantitative conceptions of delay discounting, shedding light on mechanisms of self‐control and risk taking. Copyright © 2016 John Wiley & Sons, Ltd.     

Vagueness and Blurry Sets

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S ₁ to the effect that Bob is bald is x true, for x in [0,1], there should be a further statement S ₂ which tells us how true S ₁ is, and so on – that is, it accommodates higher-order vagueness – without resorting to the claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic – as opposed to the semantics – of vague discourse is classical. I model the extension of a vague predicate P as a blurry set, this being a function which assigns a degree of membership or degree function to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence 0.3,0.2, for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature.     

Fuzzy Logic Programming and Fuzzy Control

We show that it is possible to base fuzzy control on fuzzy logic programming. Indeed, we observe that the class of fuzzy Herbrand interpretations gives a semantics for fuzzy programs and we show that the fuzzy function associated with a fuzzy system of IF-THEN rules is the fuzzy Herbrand interpretation associated with a suitable fuzzy program.