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The notion of fuzzy set theory has not so far been districted over medical diagnosis. There are some added applications, for example, in image processing, pattern identification, and many medical devices. In this research article, we introduced a new mediative fuzzy ranking technique as the fuzzy extension in decision making. The proposed mediative fuzzy logic-based technique is more relevant and applicable to incomplete and doubtful situations or some contradictions present in the expert knowledge. The value of the contradictory degree for mediative fuzzy sets used in the extension principle is deﬁned. The proposed mediative fuzzy ranking method is easily implemented in the medical field, and the proposed mediative fuzzy extension-based measured technique is useful to medical experts and doctors in many decision-making situations; the entire work is illustrated with numerical examples. We have also given some future aspects of mediative fuzzy extension in the interpretation of type-2 intuitionistic fuzzy sets.

The successful list of applications of fuzzy set theory [

The similarity measure technique has been widely used in many fields. Other study on similarity measure through interval-valued type-2 intuitionistic fuzzy set [

However, due to the benefit of intuitionistic fuzzy set over the ordinary fuzzy set, intuitionistic fuzzy sets receive a little attention together with its corresponding measured techniques in [

Later in [

There are so many techniques that have been applied in the similarity measurement and ranking between two fuzzy sets or two intuitionistic fuzzy sets.

The well-defined extension principle will also extend over mediative fuzzy sets.

A compositional fuzzy relation between patients with symptoms and symptoms with disease has also been defined over meditative fuzzy sets.

We will define a priority contradictory function for the ranking purpose of two mediative fuzzy sets. The proposed tool will be easy to calculate and can easily be applicable in contradictory situations.

In the present work, we initiated with a comprehensive technique for a mediative fuzzy ranking method based on extension principle for mediative fuzzy set to construct a crisp order from the mediative fuzzy sets. In this paper, we are also giving an alternative approach for the better enhancement of medical diagnosis by using the utility of mediative fuzzy ranking analysis based on extension principle. The work in this present research article is divided into eight sections. In Section

Mediative fuzzy relation involved in medical diagnostic system.

In this section, we present some basic terminologies and the definitions associated with mediative fuzzy sets and the extension of mediative fuzzy sets.

Consider

An intuitionistic fuzzy set

such that

Both

Let

Then, the extension

The mediative fuzzy set [

Let

Then,

Let

The value of contradictory function can be calculated by

For the purpose of our study, we have given a compositional rule for the intuitionistic fuzzy relationship to the diagnostic process as follows:

The algorithm is divided into two parts: part (A) presents the algorithm for intuitionistic fuzzy set which depends upon the membership and non-membership values and part (B) presents the algorithm for mediative fuzzy sets, which is based upon a single contradictory function value.

Step 1: let us consider two intuitionistic fuzzy sets

Step 2: calculate a “priority” function

Step 3: in step 3, we have the following conclusions:

If

If

Step 1: let us consider two mediative fuzzy sets

Step 2: find the “priority” contradictory function

Step 3: after step 2, we have the following conclusions:

If

If

The intuitionistic fuzzy numbers are not comparable. In any intuitionistic fuzzy decision making, we need a comprehensive technique. We adopt an intuitionistic fuzzy ranking method based on extension principle to construct a crisp ordering from intuitionistic fuzzy numbers. In this section, we construct an intuitionistic fuzzy set

If

The mediative fuzzy sets are not comparable. In any mediative fuzzy decision making, we need a comprehensive technique. We adopt a mediative fuzzy ranking method based on extension principle to construct a crisp ordering from mediative fuzzy sets. In this section, we construct a mediative fuzzy set

If

Consider a patient

For each

For

For

We may conclude that, according to the first priority, we have

Consider a patient

For each

For

We extend the idea of mediative fuzzy extension over type-2 intuitionistic fuzzy sets. In this, the membership/nonmembership functions of type-1 mediative fuzzy sets are crisp and the two-dimensional can be taken as in type-1 intuitionistic fuzzy set. So, type-1 intuitionistic fuzzy sets are sufficient for dealing with the uncertainty of the present model of this study. On the one hand, type-2 intuitionistic fuzzy sets are capable of dealing with these uncertainties due to the three-dimensional nature of membership/non-membership functions. So, mediative fuzzy set is not capable to instantly form the uncertainties present in any study. On the other hand, type-2 intuitionistic fuzzy sets have the capability to deal such type of uncertainties due to their membership/non-membership functions which are themselves fuzzy and three-dimensional. So, it gives the three-dimensional degree that provides the added degree of freedom to handle such type of uncertainties. The arithmetic of type-2 intuitionistic fuzzy sets provided the clarity to deal the uncertainty, so everyone should believe in using the type-2 intuitionistic fuzzy extension principle which is the generalization of Zadeh's [

Let

Geometrical representation of type-2 intuitionistic fuzzy extension.

Since proper diagnosis is one of the most essential part

The concept of extension principle over mediative fuzzy set has been introduced; furthermore, a mediative fuzzy ranking-based technique is also described that provides a well ordering of the mediative fuzzy sets.

The given concept may also be used in decision-making for diagnosing the most likely same disease of this category. From the proposed measured technique, we can easily verify the patient symptoms most similar to a particular disease.

In the application section of the research work, for a patient

Furthermore, a new methodology for the interpretation of type-2 intuitionistic fuzzy set has also been discussed. Also

One major advantage of mediative fuzzy logic over intuitionistic fuzzy logic is that, during the comparison process of mediative fuzzy sets, we need only one single value of the contradictory function as an output, which gives an easiest tool to compare two mediative fuzzy sets. In general, to do work with an intuitionistic fuzzy set, we need to consider both the values during the ranking process, i.e., membership degree and non-membership degree, which is quite difficult and time-consuming process. So, the proposed method presents the utility of mediative fuzzy logic over intuitionistic fuzzy logic.

A comparative study is also discussed in Table

A comparative study among the existing approaches and the proposed mediative fuzzy logic-based measurement approach.

Techniques | Tools of measurement | Computational results | Advantages of proposed approach |
---|---|---|---|

Fuzzy logic approach | Truth value based only | For | An ordinary solution, based only on membership value. |

Intuitionistic fuzzy logic approach | Truth/false values based | For | Better solution than fuzzy approach. But slightly tough to understand and hard to calculate and time consuming. |

Mediative fuzzy logic approach | Contradictory value based | For | Sigle value-based solution. Considering the membership, non-membership, hesitation, and contradictory factors, it is easy to compare and compute. Computes each and every aspect of the model. |

On the basis of above, we may conclude that the present research paper describes the utility of mediative fuzzy logic in decision making. The uncertainties present in the membership degree and the non-membership degree of the mediative fuzzy set are described and their use in ranking technique has also been discussed. The given ranking method is effortlessly implemented and has a useful explanation over type-2 intuitionistic fuzzy sets.

We are sharing the source that includes the data that support the findings of our results and conclusion of the manuscript. The technique which we have given can be verified on the data which are available on the following hyperlinks:

The authors declare that they have no conflicts of interest.

The second author is grateful to the University Grant Commission (UGC) for economic assistance.