6 Result(s)
within
Mathematics
Applications of Mathematics
Artificial Intelligence
Da Ruan
Chapter
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Chapter
Preliminaries
This chapter aims to recall basic concepts of set theory and abstract algebra including set, relation, isomorphism, lattice, Boolean algebra and soft algebra, which will serve as the base of the remaining chap...
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Chapter
Fuzzy Inference and Fuzzy Control
The major subject of this chapter is fuzzy control, one of the most successful application areas of fuzzy set theory. Nowadays, many fuzzy products are visible in the market. Almost every fuzzy product is rela...
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Chapter
Fuzzy Relations
As known to us, a relation is a subset of the Cartesian product of two sets. A relation is naturally fuzzified while a subset is fuzzified. In fact, whether two objects have a relation is not always easy to de...
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Chapter
A Brief Introduction to Some Pure Mathematical Topics
As known to us, the theory of classical sets is the foundation on which modern mathematics rests. When sets are fuzzified, some traditional pure mathematical branches are accordingly generalized. In this chapt...
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Chapter
Basics of Fuzzy Sets
In this chapter, we focus on the introduction of fundamentals in fuzzy set theory, including some set-theoretic operations and their extensions, the decomposition of a fuzzy set, and mathematical representatio...
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Chapter
Extension Principle and Fuzzy Numbers
In the traditional multi-attribute decision analysis, there is a well-defined problem-solving model–the Simple Additive Weighting (SAW) method. This model can be formulated as follows. Let A1, A2, ..., A ...
