Dear prof, can we consider it as a refined neutrosophic system? Indeterminacy I came from the first source and other indeterminacy J from another source, with I+J=0?

Yes, you can refine the Indeterminacy "I" into more sub-indeterminacies, as many as needed into the problem to solve.

You name them: I1, I2, ... .

Mr Florentin Smarandache

We know that the neutrosophic set is a generalization of the opaque set, and fuzzy means inaccurate, ambiguous, and floating. I think if we get to the point where we fuzzy each of the components of a neutrosophic set, then the flexibility and generality of the set in question will increase.

In my opinion, If Indeterminacy I = 0, in the neutrosophic set, then it looks like an Intuiotonic fuzzy set.

What is the definition of opaque set ?

Dear Sir Pattanayak

Earlier I used to think too that, if I=0, then it's most probably an intuitionistic set but I feel that as told by Sir Smarandache , T+F

Dear Sir Jangizehi

I find neutrosophic sets quite interesting but I have not read or heared about opaque sets yet. Could you please recommend something which tells clearly n precisely giving or stating comparison of neutrosophic sets and opaque set for beginners.

O ask you again: what is the definition of opaque set?

Let C be a convex body in the plane. A set B is said to be an opaque set or a barrier for C, if it meets all lines that intersect C.

Note:

A barrier may consist of one or more rectifiable arcs. It does not need to be connected and its portions may lie anywhere in the plane, including the exterior of C.

Regards

Following paper may help for proper understanding regarding Opaque Sets

Dumitrescu, A., & Jiang, M. (2014, June). The opaque square. In Proceedings of the thirtieth annual symposium on Computational geometry (pp. 529-538).

Thanks.

Can you please give me a concrete example of opaque set?

Maybe a geometrical figure of it, etc.

Please send me this paper: Dumitrescu, A., & Jiang, M. (2014, June). The opaque square. In Proceedings of the thirtieth annual symposium on Computational geometry (pp. 529-538).

In addition to above discussion if indeterminacy is negative (say) i.e. I < 0 it results in unstable structure (unstable set) which means solution does not exist (instability and non existance of solution).

Dear Professor

Here is the paper

Thanks for the paper.

Yes, there are cases/applications when indeterminacy is negative, or greater than 1. The set is called: neutrosophic overset (when > 1), neutrosophic underste (when < 0), or neutrosophic offset (when both: some > 1, others < 0).

See these papers and a book:

http://fs.unm.edu/SVNeutrosophicOverset-JMI.pdf

http://fs.unm.edu/IV-Neutrosophic-Overset-Underset-Offset.pdf

http://fs.unm.edu/NeutrosophicOversetUndersetOffset.pdf

Thank you for your replies Sir Rahman, Sir Arshad, and Sir Sameandache. These are some interesting findings and arguments.

Also thank you sharing these above papers.

Regards.

Thanks Florentin Smarandache for refrence papers and books. They are really helpful in understanding the cases when indeterminacy is negative or greater than 1 or both cases

Please have a look at DIF definition.

https://ieeexplore.ieee.org/abstract/document/9015987

In neutrosophy we have: the opposites and , while in between them is .

Therefore, Indeterminacy = .

Please do not take 'ad literam' (literally) the word "indeterminacy" only as something not clear, etc. [as in a language dictionary].

For example, in games "indeterminacy" means "tie game" (neither winning, nor losing).

In physics, for charged particles, you have: positive particle, negative particle, and neutral particle (no charge);

hence "Indeterminacy" = "neutral".

In decision making "indeterminacy: means "pending" (neither taking a decision, nor rejecting a decision).

Again, please do not make the confusion considering "Indeterminacy" as the narrow sense definition from a language dictionary.

Selcuk, your Distributed Indeterminacy Form does the following:

(T, I, F) is reduced to ( T – TI, 0, F – FI ) .

But this transformation does not work if your application has a middle (neutral) term.

1) For example, if your application is about a soccer game, and if you distribute the indeterminacy, you LOSE information, you lose the possibility of saying something about a "tie game" (i.e. you eliminate the degree of "tie game", so your work is incomplete, you give the degree of winning and the degree of defeated, but you say nothing on the degree of tie game).

2) If your application is about decision-making and you distribute the indeterminacy, then you LOSE the degree of "pending" (i.e. you eliminate the "pending" possibility from: accept / pending / reject).

3) Similarly if you have (positive, neutral, negative) particles in physics (you LOSE the "neutral" particles).

Therefore, your approach does not work for triads of the form (, , ).

On the other hand, your DIF (Distributed Indeterminacy Form) is not justified: why do you reduce the T and F the way you do (see above), and not in a different way?

Is DIF just a mathematical artifact?

Distributed Indeterminacy Form (DIF) of a is defined as aDIF = (Ta − TaIa, 0, Fa − FaIa). Here, we distribute indeterminacy effect on truth and falsity. In other words, we decrease the power of truth and falsity in proportion to the magnitude of indeterminacy. Our aim here is to determine how the value of truth and falsity is affected by the degree of growth of indeterminacy.

DIF doesn't ignore Indeterminacy!!!. On the contrary, it is the effect on truth and falsity is taken into account.

While thinking about a phenomenon, I am talking about making a social choice and interpretation on a particular feature of that phenomenon simultaneously in the context of truth, falsity, and indeterminacy.

That's why we focused on truth-maker theory.

https://ieeexplore.ieee.org/abstract/document/9015987