Mathematics Stack Exchange
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Questions tagged [fuzzy-logic]

Fuzzy logic is a form of many-valued logic that deals with approximate, rather than fixed and exact reasoning.

Fuzzy logic is a form of many-valued logic that deals with approximate, rather than fixed and exact reasoning. Reference: Wikipedia.

Compared to traditional binary logic (where variables may take on true or false values), fuzzy logic variables may have a truth value that ranges in degree between 0 and 1.

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Is there anything deep about Fuzzy sets/Fuzzy logic?

I keep coming across the term "fuzzy". I browsed around a bit and read a few articles.. It seems to me that there's absolutely nothing deep or foundational about fuzzy set theory or fuzzy logic. I know they are practically useful in robotics, ..etc.…
aelguindy
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Fuzzy logic and topos theory

Why doesn't one develop fuzzy logic by extending topos theory, by simply extending the subobject classifier $\Omega$ to the unit interval [0,1]? Have people done that?
Yan King Yin
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Fuzzy logic vs probability

In reading about fuzzy logic it says that fuzzy logic is different from probability. Can some one please explain how these two differ. How can this be explained to a person with no mathematical background. Please explain the difference of fuzzy…
sam_rox
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Is Fuzzy Set/Measure Theory an Active Area for Research?

I came across the notion of a fuzzy set the other day and since then, I've been reading about fuzzy measures and the Sugeno/Choquet integrals. While I certainly do not claim to have fully wrapped my mind around it by any means, there is something…
AnalysisStudent
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What references should I follow if I want to learn more about semantic entailment in multi-valued logics?

I am simply curious about this subject, and would like to learn more about it. I am an undergraduate student and in our studies we've always tackled classical logic and simply mentioned that other "logics" exist. As such I would like to be pointed…
Threnody
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Is Fuzzy Logic Needed?

I had a very big doubt in my mind about Fuzzyness. When statistics is answering all the questions, which we see generally in Fuzzy theory. Then why one SHOULD learn Fuzzy Theory. Or is there any gap in statistics, I mean: Is there any problems …
KRRG-BITS
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What is the difference between mamdani and sugeno in fuzzy logic?

I realise that the difference lies in the way the defuzzification happens but I don't fully understand it. I've read some papers comparing the outputs from the two models but I'm still not really sure how they are different.
Luke
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Structure of a fuzzy subspace

Let $V$ be a vector space over a field $F$ and let $f$ be a function from $V$ to the interval $I:=[0,1]$ satisfying the condition that for any $a \in I$ the set $V_a:=\{v \in V | f(v) \ge a\}$ is a subspace of $V$. Then I believe that there exists…
tom_a2
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Is there a logic with quantifier "almost always".

I would like to describe a reasoning with quantifier "almost always". For example, if probability of $Z$ is above $95$%, I would like to say that $Z$ is "almost always true". Is there a modal or fuzzy logic with such a quantifier? If not, is it even…
Marina
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Lukasiewicz Logic Tautology

Suppose a statement form $\varphi$ always has value T or U. Show $\varphi$ is a classical tautology.
user6848
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Definition of functions based on "fuzzy" truth table

I'm stuck on this problem: I have a "truth-table" (well, I don't know if it can be called truth table, if there aren't true/false values only): string | a | b --------------------- x | 1 | 0 z | 1 | 0 xx | 1 | 1 xz | …
Martin Janiczek
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Fuzzy Logic vs Logic

well i was wondering if, there s a way in which one could compare these two theories on the ground that which one will provide more accurate answers to a given problem. Fuzzy logic always focuses on analysing between 0 and 1 and logic only dolls…
Rahul
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Study material for fuzzy logic

Can you please suggest some good study material on fuzzy logic. any good books, articles, video material would be appreciated. I am doing my Master's Diploma in Information Systems, and I need some background in fuzzy logic for it.
Shota Bakuradze
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Fine-grained notions of deduction for fuzzy logic

In the presentations of fuzzy logic that I've seen, $A \vdash B$ is understood as meaning that in any interpretation where $A$ is 1, $B$ is also 1. If we are reasoning meta-theoretically about fuzzy logic, we could make much more complicated…
Nick Thomas
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About the pointwise infimum of a continuous piecewise linear function

I am reading the logic paper "Interpolation in fuzzy logic" by Matthias Baaz and Helmut Veith https://doi.org/10.1007/s001530050151 On page 479 it is claimed that "It suffices to show that continuous piecewise linear functions are closed under…
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