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0
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2answers
41 views

Proof of a property of fuzzy extension principle

I'm looking for a proof of the following property of the fuzzy extension principle: $$ B \supseteq f(f^{-1}(B)) $$ ($f: X\rightarrow Y$ is an arbitrary crisp function, and $B$ is a fuzzy set). I ...
2
votes
1answer
30 views

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 ...
1
vote
1answer
99 views

Approximate function from sample data

Let $f\colon\mathbb{R}^n\to\mathbb{R}$ be a function. I don't have function definition. It's described as a fuzzy inference system. I have the inference system and can manipulate sample data for each ...
0
votes
1answer
67 views

How can compose fuzzy rules in 1-D and 2-D?

fuzzy implication function based on the interpretation "A entails B" can be expressed as : $$R_{s}=A \longrightarrow B=\int_{X\times Y} sgn[\mu_{B}(y)-\mu_{A}(x)]/(x,y),$$ or, alternatively, ...
4
votes
0answers
80 views

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 ...
3
votes
0answers
176 views

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): ...
0
votes
0answers
11 views

fuzzy computation

I am completely new to fuzzy set theory and fuzzy logic and maybe i am way off the subject, but I was wondering about the following. Suppose i have a statement: "X is about the same as Y and equal ...
0
votes
0answers
14 views

Maximum likelihood estimation algorithm

I have problem with Gath-Geva algorithm. 1.Choose initial values for h(i|Xj),the probability of selecting i-th cluster givng the j-th feature vector In multivariate case,if I have 144 points(with two ...
0
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0answers
29 views

T-norms with arity 3

I'm working on some 3D vectors with fuzzy values, and I'd like to devise some operations on them. After my brief search, I haven't been able to find any existing work on t-norms with arity n>2. Is ...
0
votes
0answers
35 views

Genre for logic using the unit circle in the complex plane?

Is there a genre for logic, using the unit circle in the complex plane as all possible values for logical statments? Mabye some kind of fuzzy logic? Like this: $\;\forall{S}\in F\quad\left | S \right ...
0
votes
0answers
41 views

Event probability prediction from multiple observations

I am programming some fuzzy logic for an application I'm developing, and I'm not sure how to "combine" multiple fuzzy boolean observations into a guess. Each of my fuzzy boolean observations describes ...
0
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0answers
21 views

Can you recommend a book or resource on L-fuzzy sets?

I'm finding it hard to find good introductory books or articles on the subject of lattice-valued fuzzy set theory. Thanks.
0
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0answers
91 views

a question in soft topology

The definition of soft topology is: My question is, isn't the soft topology in the folowing example lack the intersection and the union of two of it's sets? I mean, shouldn't the sets ...
0
votes
0answers
64 views

Association, $\circ$, of fuzzy ordered ternary semigroup. How can I verify this?

For each $x \in S$, let $A_{x}:= \{(u,v) \in S \times S : x \leq uv \}$. Let $f, g$ be fuzzy subsets of an ordered semigroup $S$, we define binary operation, $\circ$ by $$(f \circ g)(x)= ...
0
votes
0answers
57 views

How to prove Bi-residual theorem (Theorem 1)?

It turns out that most frequently set of truth values comprises the so-called residue lattice in other words L is a partiar order set, which includes maximum element(1) and minimum(0), where each ...