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Computational transformation between different symbolic representations of BK products of fuzzy relations.

机译：模糊关系的BK乘积的不同符号表示之间的计算转换。

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摘要

Fuzzy relational calculi based on BK products of relations have representational and computational means for handling both concrete numerical representations of relations and symbolic manipulation of relations. BK calculus of relations together with fast fuzzy relational algorithms allows concrete numerical representations of relations to be used extensively in applications. On the other hand, when enriched by relational inequalities like BK Bootstrap or combined with other theories such as generalized morphisms, high level symbolic forms of relations can be used for symbolic manipulation of relations that have been abstracted from numerical representations. Furthermore, symbolic formulas of relations can be handled equationally. Equations over BK-products can characterize relational properties in a universal way.; The research in this dissertation focuses on symbolic manipulations of BK products of fuzzy relations. We have developed as a proof-of-concept an automated tool that works with various representational forms of relations and facilitates transformations among them. Major contribution that this system brings into the field is that, it provides a link between numerical and symbolic representations of relations, which can substantially extend the applicability of fuzzy relations.; The pilot implementation of the tool consists of two systems. At a high level of general fuzzy logic systems, the first system transforms BK-product formulas syntactically between three notational forms: matrix form, set form and predicate form. We have defined for each kind of BK-product representations a tree-type data structure, called a notational tree. All transformations are then carried out by set of transformational algorithms among the notational trees of BK representational forms.; At a lower level of t-norm based residuated logic systems (BL logic), we have developed a second system which is a term rewriting theorem prover/checker that validates and generates proofs for theorems of BK relational calculi. For each given theorem, a derivation tree will first be generated. A matching of any node in that tree with the theorem's conclusion will validate it. We proposed a generate-and-match algorithm based on a breadth-first-search navigation process through theorems' derivation trees which guarantees a loop-free result for any derivable theorem (in a given theory). The original version of this algorithm has been improved further by applying a human-like proof strategy, which we called distance-first-search and optimized distance-first-search algorithms. These optimized versions improve the performance of our system significantly, reducing both number of logical inferences and the CPU's time required. The experiments also showed that proofs in BK calculi are significantly shorter than in predicate calculus of BL logic. Interestingly enough, proofs generated by the tool are the same as those done by hand. This illustrates the successfulness of our human-like strategy.
机译：基于关系的BK乘积的模糊关系计算具有表示和计算手段，用于处理关系的具体数字表示和关系的符号处理。关系的BK演算以及快速的模糊关系算法使关系的具体数字表示形式可以在应用中广泛使用。另一方面，当通过关系不等式（例如BK Bootstrap）来充实或与其他理论（例如广义态射）结合使用时，高级的关系符号形式可以用于从数字表示形式抽象的关系的符号操纵。此外，关系的符号公式可以方程式处理。 BK乘积上的方程可以通用方式描述关系属性。本文的研究集中在模糊关系的BK乘积的符号操纵上。我们已经开发出一种自动工具，以作为概念验证，可以处理各种关系的表示形式并促进它们之间的转换。该系统带给该领域的主要贡献是，它在关系的数字表示和符号表示之间提供了联系，这可以大大扩展模糊关系的适用性。该工具的试验实施包括两个系统。在较高水平的通用模糊逻辑系统中，第一个系统在三种表示形式之间进行句法转换BK-乘积公式：矩阵形式，集合形式和谓词形式。我们为每种BK产品表示形式定义了树型数据结构，称为符号树。然后通过BK表示形式的符号树之间的一组转换算法执行所有转换。在基于t范数的剩余逻辑系统（BL逻辑）的较低级别上，我们已经开发了第二个系统，它是一个术语重写定理证明者/检查者，可以验证和生成BK关系计算定理的证明。对于每个给定定理，首先将生成一个导数树。该树中任何节点与定理结论的匹配将对其进行验证。我们通过定理的推导树基于广度优先搜索的导航过程，提出了一种生成和匹配算法，该算法可确保任何可推定理（在给定的理论中）都不会产生循环。该算法的原始版本通过应用类似于人的证明策略（我们称为距离优先搜索和优化的距离优先搜索算法）得到了进一步改进。这些优化的版本显着提高了我们系统的性能，从而减少了逻辑推理次数和所需的CPU时间。实验还显示，BK结石的证据比BL逻辑的谓词演算的证据短得多。有趣的是，该工具生成的证明与手工完成的证明相同。这说明了我们类似人的策略的成功。

著录项

  • 作者

    Hoang, Ha V.;

  • 作者单位

    The Florida State University.;

  • 授予单位 The Florida State University.;
  • 学科 Computer Science.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 142 p.
  • 总页数 142
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 自动化技术、计算机技术;
  • 关键词

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