12 Result(s)
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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 ...
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Chapter
Fuzzy Rules Extraction-Based Linguistic and Numerical Heterogeneous Data Fusion for Intelligent Robotic Control
Autonomous robots, which achieve tasks without human operators, are required in many fields. They have to be intelligent to determine their own motions in unknown environments based on both sensory data (numer...
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Chapter
Approximate Reasoning Based on Lattice-Valued Propositional Logic L vpl
This chapter approaches the theory of approximate reasoning in the “If … then…” type approximate-reasoning mode based on the lattice-valued proposition logic L vpl . T...
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Chapter
Novel Neural Algorithms for Solving Fuzzy Relation Equations
Due to the difficulty in a given system of using neural networks to solve fuzzy relation equations, the best learning rate sometimes cannot be decided easily and strict theoretical analyses on convergence of a...
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Chapter
Fuzzy Logic Applications in Nuclear Industry
Fuzzy logic applications in nuclear industry present a tremendous challenge. The main reason for this is the public awareness of the risks of nuclear industry and the very strict safety regulations in force fo...
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Chapter
Information Diffusion Principle and Application in Fuzzy Neuron
In this paper, we demonstrate that the fuzziness of fuzzy information can come not only from the measuring scale, but also from the incompleteness of sample knowledge. Fundamentally, by develo** the method o...
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Chapter
On Transitivity of Fuzzy Preference Relations in Ranking Fuzzy Numbers
In this paper, we first carry out further investigations into relations between several existing transitivity-related notions in ranking alternatives or fuzzy numbers. Then we pay attention to the discussion o...
