Article Neutrosophic soft matrices and NSM-decision making

we use neutrosophic matrices when the indeterminacy is presented in the system

As Dr. Said Broumi said, neutrosophic matrices can fully deal with indeterminacy,

while fuzzy matrices cannot deal at all with indeterminacy,

and intuitionistic fuzzy matrices only partially deal with indeterminacy.

Indeterminacy is INDEPENDENT component only in neutrosophic environment,

while in others (fuzzy, intuitionistic fuzzy, etc.) environments, indeterminacy is dependent, or does not exist...

neutrosophic matrices can fully deal with indeterminacy

Neutrosophic Matrices are more reliable, logical and practical for the decision-makers and plays an important role in understanding, modelling and solving the MCDM problems and fully deal with Indeterminacy while other hybrids can't deal with this indeterminacy.

Indeterminacy when present then we use neutrosophic matrices.

Dr. Broumi is right

Deals with independent metric environmental indeterminacy fully +MCDM also.

Logically, indeterminacy function (I) is a complement of the member and non-member functions (T, F). That is, indeterminacy function implicitly exists in intuitionistic fuzzy sets and explicitly exists in neutrosophic sets. It should noted that indeterminacy function takes a value (>0) when available information of phenomenon or problem are incomplete. With respect to the independent and dependent of each other, they must dependent of each other, how do they are independent?! For example, it is not logic that someone expects that A will win with a chance of 40% and will fail with a chance of 70%. But the chances of winning and loss can be respectively: 40% and 50% or 30% and 70% or...(

Indeterminacy (I) is not complement to truth (T) and falsehood (F), since all three components are independent. "I" can be any number in [0, 1], no matter what T and F are equal too.

> For example, it is not logic that someone expects that A will win with a chance of 40% and will fail with a chance of 70%.

Yes, it is possible, if you evaluate the chances from different criteria.

Let A be a soccer team, playing against the team B.

For example, A will have a chance of winning 40% considering the value of its players, but a chance of loosing 70% considering the fact that A will play away from home on the field of B team.

So, first criterion is: value of A team's players;

second criterion: playing at home (which is an advantage), or playing away from home at the adversary field (which is a disadvantage).

Thanks for the clarification @ Florentin Smarandanche

>[ Yes, it is possible, if you evaluate the chances from different criteria. ]

BUT the evaluation system takes into consideration all the criteria, unless this system will be inaccurate, inconsistent,...etc. In the presented example, to determine the chances of winning and loss, the experts give expectations under all criteria (level of player, place of match,..., etc.)

Is it logical to expect the value of T under some conditions and expect the value of F under other conditions?

> Is it logical to expect the value of T under some conditions and expect the value of F under other conditions?

It depends on the application.

If you evaluate a student John in general.

John can be 40% good in mathematics, but 70% bad in linguistics.

Therefore, you cannot have only one condition (one discipline) to judge John, since John studies many disciplines.

Any event/application has to be analysed with respect to all conditions [or as many as possible], not with respect to only one. Some conditions may be positive for the event/application, others negative, and others neutral (or indeterminate) for the event/application -- as in neutrosophy.

For your information, there are cases when the degrees of membership, indeterminacy or nonmembership may be each of them > 1 or < 0, and these are in our real life applications.

See this book and papers below:

The Neutrosophic Set/Logic/Measure/Probability/Statistics etc. were extended to respectively Neutrosophic Over-/Under-/Off- Set, Logic, Measure, Probability, Statistics etc.

F. Smarandache, Neutrosophic Overset, Neutrosophic Underset, and Neutrosophic Offset. Similarly for Neutrosophic Over-/Under-/Off- Logic, Probability, and Statistics, 168 p., Pons Editions, Brussels, Belgium, 2016, http://fs.unm.edu/NeutrosophicOversetUndersetOffset.pdf,

on Cornell University’s website:

https://arxiv.org/ftp/arxiv/papers/1607/1607.00234.pdf

and in France at the international scientific database:

https://hal.archives-ouvertes.fr/hal-01340830

And articles:

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

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

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

An elementary real example, that often occur in our everyday life.

Suppose a worker has the duty to work 40 hours/week.

If he works 40 hours this week, his membership degree is 1.

But many workers work overtime. Assume this worker worked 42 hours this week.

So, it is normal that his degree of membership be greater than somebody who worked only 40 hours.

Thus, his membership degree is 42/40 = 1.05 > 1.

Therefore, neutrosophic component > 1, or sum of neutrosophic components > 1 are REAL and needed in applications.

>[ John can be 40% good in mathematics, but 70% bad in linguistics. ]This what I meant in my previous answer, the evaluation process takes into consideration all influencing factors and the method of calculating the components (For example, T, I, F, in nuetriosophic) depends on the viewpoint of experts in charge of the evaluation. Therefore, if John is 40% good in mathematics does not imply T=0.4. According to this example we obtain the value of T+I+F is smaller or equal to 1 not more than that.

In the second example, you write the membership degree is 1.05 > 1. It seems convincing as a measurement of achievement not a membership degree. However, If we accept this situation, we have two comments: first, Wang et al. (2010) determined the value of each component belongs to [0, 1] and they are named Single valued neutrosophic sets. Here is the question that arises: What are the bounded values of these components with respect to the similar event of that example? Second, in that example how can you calculate the components of I and F for a person whose membership degree is bigger than 1?

You may have T+I+F < 1 if it is incomplete information,

and T+I+F > 1 if it is paraconsistent (conflicting) information.

When T, I, F are in [0, 1], that's call neutrosophic set.

But when T, I, F may be > 1 that's called neutrosophic overset.

So, please read at least a paper I gave you before; otherwise we waste the time.

You'll see that even in the papers' titles it is written "overset", not "set"...

But the discussion is about the reasoning of the values of the components of neutrosophic sets. Especially, how T+F>1 in neutrosophic sets.

Now, regardless of the existence of a practical example to this case.

Did you mean the case T+I+F > 1 occurs if we take the expected values of them from independent (different) sources?

Florentin Smarandache . Is the correct word "Neutrosophic Set" or "Neutrosophic Fuzzy Set"? This set is the generalization of fuzzy set regardless of the reason that the functions T, I and F are defined on a set A under independent environments.`

We better say "single-valued neutrosophic set" when T, I, F are numbers in [0, 1];

but other people said "neutrosophic fuzzy set".

The best is "single-valued neutrosophic set".

If T, I, F are intervals in [0, 1], we call it "interval-valued neutrosophic set".

T + F > 1 or T + I + F > 1 when the components are independent.

Tareq Al-shami I think it is not logical to expect the value of T under some conditions and expect the value of F under other conditions?

Smarandache delivered good answer

Thanks Florentin Smarandache

> I think it is not logical to expect the value of T under some conditions and expect the value of F under other conditions?

It depends on the application.

Let's see a simple example:

Two teams A and B compute against each other.

Andrew is a supporter of team A, while Brenda is a supporter of team B.

The two sources of information, Andrew and Brenda, are independent (they do not communicate with each other).

Andrew bits that his team A will win ( T = 70% ).

But Brenda bits that her team B will win ( F = 60% ).

This is a very frequently met example in our everyday life.

In consequence, it is logical to have T evaluated by a source (Andrew), and F evaluated by another source (Brenda).

Mohammed Jameel : I put that comment (It is logical to expect the value of T under some conditions and expect the value of F under other conditions? ) as an attempt of explaining the case T+F>1.

However, If we accept the validity of this hypothesis (as a football example given by Florentin Smarandache ), we expect that the outputs of such a system are contradictory.

Simply, what compels us to take T from a source different than a source of F?!

If your answer is the type of application, you should give a real application.

In a football example, you can ask the same person to expect T and F and similarly ask the other one. I think it is easy.

Neutrosophic Soft Matrix And Its Application in Solving Group Decision Making Problems from Medical Science

Tanushree Mitra Basu and Shyamal Kumar Mondal

Tareq Al-shami I agree with you that the outputs of such a system are contradictory.

Answer to Tareq Al-shami :

> However, If we accept the validity of this hypothesis (as a football example given by Florentin Smarandache), we expect that the outputs of such a system are contradictory.

The result is not necessarily contradictory, sir, it depends on the sources that provide information.

If we go back to the previous example, you may have, for example, the following

situation:

Andrew bits that his team A will win ( T = 70% ).

But Brenda bits that her team B will win ( F = 20% ).

So now there is no contradiction, since 0.7 + 0.2 < 1.

No matter what very elementary examples I give you, you twist the words...

> If your answer is the type of application, you should give a real application.

There are hundreds or thousands of real applications, sir.

Please READ at least a neutrosophic paper (you did not read any, unfortunately).

Just browse these websites to see thousands of neutrosophic papers and their applications:

http://fs.unm.edu/neutrosophy.htm

and

http://fs.unm.edu/NSS/Articles.htm .

Between 1998-2020 many neutrosophic real applications have been done in:

Artificial Intelligence, Information Systems, Computer Science, Cybernetics, Theory Methods, Mathematical Algebraic Structures, Applied Mathematics, Automation, Control Systems, Big Data, Engineering, Electrical, Electronic, Philosophy, Social Science, Psychology, Biology, Biomedical, Engineering, Medical Informatics, Operational Research, Management Science, Imaging Science, Photographic Technology, Instruments, Instrumentation, Physics, Optics, Economics, Mechanics, Neurosciences, Radiology Nuclear, Medicine, Medical Imaging, Interdisciplinary Applications, Multidisciplinary Sciences etc.

[ Xindong Peng and Jingguo Dai, A bibliometric analysis of neutrosophic set: two decades review from 1998 to 2017, Artificial Intelligence Review, Springer, 18 August 2018.

Open at least this paper to be convinced:

http://fs.unm.edu/BibliometricNeutrosophy.pdf ]

Please respond to me after you READ at least a neutrosophic paper.

It is useful in

Group decision making using neutrosophic soft matrix: An algorithmic approach

The following content may be helpful.

https://www.researchgate.net/publication/261368671_Neutrosophic_soft_matrices_and_NSM-decision_making

Matrices play an important role in computer science and technology. However, the classical matrix theory sometimes fails to solve the problems involving uncertainties, occurring in an im-precise environment. Neutrosophic matrices can be used to handle the computer science problems involving neutrosophic inputs which is an extension of the intuitionistic fuzzy matrix

Neutrosophic Soft Matrix successfully work in Group Decision Making Problems.