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2answers
48 views

How to solve this fuzzy logic inference problem?

I'm having trouble solving an exercise involving fuzzy logic. It basically says something like that (pardon me if I made some mistake, I'm basing only on my poor memory) John goes to park if it is ...
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: ...
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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 ...
1
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0answers
29 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
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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
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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
1answer
276 views

Troubles figuring out how to calculate the centroid for a defuzzification process

I am trying to implement a fuzzy logic system, but am having serious issues finding the centroid for the defuzzification process. This is what my output sets look like: My reference source gives ...
0
votes
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 ...
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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 ...
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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 ...
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
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1answer
58 views

Set Theory Symbols

I get easily confused when it comes to the symbol based terminology in Set Theory. Could someone please elaborate on what the following expressions mean? It would really help me out. $S_1$ = ...
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 ...
0
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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 ...
2
votes
1answer
51 views

Linear fuzzy system

I need help if any one can help me How to define a crisp number or crisp system? Whats the difference between crisp number and fuzzy number? And if there is any references.
2
votes
1answer
104 views

Reference help for “fuzzy mathematics”

I want to study Fuzzy Sets and Fuzzy logic self. For that what would be better book to start from basic?
1
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1answer
843 views

Ranked Preference Matching Algorithm

first dropping the link that will serve as reference: NRMP Residency Matching I have a sort of side project (nothing riding on it, computational performance not an issue, so feel free to go wild, I ...
2
votes
3answers
148 views

Simplifying Equivalences in Łukasiewicz Logic

I am working on an inference system for infinite valued Łukasiewicz logic, using standard MV-algebras. As a pre-processing step, I would like to perform (non-exhaustive) simplification of formulae. ...
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votes
2answers
174 views

What kinds of maths to learn for understanding dynamical systems in cognitive science?

A current trend in cognitive science is to view the mind as a dynamical system (e.g., Continuity of Mind by Spivey, in which cognition is understood as a "continuous and often recurrent trajectory ...
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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 ...
1
vote
1answer
36 views

How to implement fuzzy minimum function via fuzzy maximum

I know that I can represent fuzzy max via power function(i need it in neural network) i.e. def max(p:Double)(a:Double,b:Double) = pow(pow(a,p) + pow(b,p) , 1/p) // assumption a >=0 and b >=0 ...
3
votes
1answer
532 views

Fuzzy C Means mathematics tutorial [closed]

Hello I am looking for help on understanding the maths of Fuzzy C Means as explained here: Fuzzy C Means I was hoping for a broken down explantion of the actual math. I have tryed googling for ...
2
votes
1answer
241 views

Is Fuzzy Logic Needed? [closed]

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 ...
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1answer
2k views

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 ...
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1answer
126 views

Fuzzy logical and integer programming

Is there any way of formulating linear/non-linear programming problems in terms of YES, NO, and MAYBE instead of just $0-1$ programming?
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4answers
814 views

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 ...
0
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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 ...
0
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1answer
283 views

Can someone explain definition of operation $\rightarrow$

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 ...
1
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1answer
181 views

Representing non-fuzzy memberships

I'm trying to model an input for a FIS in Matlab, unlike other inputs this value is a boolean Yes / No Do I use two membership functions that do not overlap but cover the entire domain e.g NO (0 - ...
0
votes
2answers
682 views

What is the difference between Centroid of area and Bisector of area?

We got this fuzzy course in the university, there was a problem which it's result led to multiple overlapping fuzzy values. in order to conclude a value out of that there was different approaches ...
-1
votes
1answer
195 views

Applying fuzzy logic to determine the degree to which a project is complete

I have a Project made up of tasks. Each task has an estimated completion percentage. I realise I could treat each tasks completion percentage as a representation of the degree of membership to the ...
2
votes
1answer
271 views

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 ...
10
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1answer
664 views

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?
1
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1answer
112 views

Possibilistic clustering- what exectly is $\eta$ and how to calculate it

I'm curently studing the topic of Possibilistic shell clustering and I have a hard time with understanding the concept of variable $\eta$. Can somebody in simpe words explain me what exectly this ...
3
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1answer
523 views

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 http://www.springerlink.com/content/654wl9u5mcj7qtva/ On page 479 it is claimed that "It suffices to show ...
4
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1answer
353 views

Lukasiewicz Logic Tautology

Suppose a statement form $\varphi$ always has value T or U. Show $\varphi$ is a classical tautology.
3
votes
1answer
161 views

Help needed on method to use for anomaly detection in Computer Science

I think people here could guide me in solving a problem related to anomaly detection. The term anomaly here refers to some undesired event occurring in the system like a virus infection. I could get ...
3
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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): ...
4
votes
1answer
368 views

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 ...