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0
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2answers
48 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
102 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
82 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
85 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
179 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): ...
1
vote
0answers
30 views

Write down a linear programming problem

I want to replicate a linear programming problem.I have the following information, for the background." A fuzzy regression analysis with only one independent variable X results in the following ...
0
votes
0answers
37 views

Determine set of t-norms verifying a property

As recalled in Scholarpedia, a t-norm $\top(a,b)$ is a function from $\mathbb{R}^{2}$ to $[0,1]$ verifying the following properties: Commutativity: $\top(a,b)=\top(b,a)$ Associativity: ...
0
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0answers
29 views

Multiplication of fuzzy numbers

Can anyone please give me a step by step procedure on how to multiply two fuzzy numbers A and B where ...
0
votes
0answers
16 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
16 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
votes
0answers
32 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
38 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
99 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
58 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 ...