Towards Interval Type-3 Intuitionistic Fuzzy Sets and Systems

Abstract

In this work, several types of intuitionistic fuzzy sets, inspired by Type-2 and Type-3 concepts, are introduced. In particular, the newly proposed interval Type-3 intuitionistic sets are very interesting as they extend the opportunities of both interval Type-3 fuzzy sets and intuitionistic sets when capturing specific forms of uncertainty. A comparative study of interval Type-3 with respect to intuitionistic fuzzy is presented. Based on this comparison, a novel concept of an interval Type-3 intuitionistic fuzzy set is put forward to enhance the capabilities of modeling uncertainty with respect to the individual Type-3 and intuitionistic concepts. Basically, the secondary and tertiary membership functions are added to the intuitionistic fuzzy sets to build an interval Type-3 intuitionistic fuzzy set. An illustrative example dealing with controlling the imaging system of televisions is provided to envision the potential applicability and advantages of interval Type-3 intuitionistic fuzzy sets in real problems. For this application, the intuitionistic Type-3 approach shows the potential to outperform previous approaches in controlling this system.

1. Introduction

Initially, when Zadeh first put forward fuzzy sets (FSs) [1], which are now called Type-1 fuzzy sets, his idea was oriented towards enhancing the capabilities for managing the existing real-world partial truths, and with his theory, a high number of decision-making (DM) situations and other problems (such as control, pattern recognition, etc.) could be easily modeled, whereas with traditional logic, they could not be modeled [2,3]. This initiated a new era in DM theory based on FSs that has been developing since its beginning. Later, Zadeh also proposed interval Type-2 fuzzy sets (IT2FSs) [4,5,6,7], and later still, he arrived at a more powerful expression of FSs, the general Type-2 fuzzy sets (GT2FSs) [8,9,10,11], which have been more thoroughly evaluated by Mendel and his group since the year 2000. Another proposal based on FSs is intuitionistic fuzzy sets (IFSs) [12,13,14], proposed by Krassimir Atanassov, which model uncertainty by using membership and nonmembership functions, and which have been shown to model, in a better way, other kinds of uncertainty. More recently, interval Type-3 fuzzy sets [15,16,17,18] have been proposed and applied to different problems [19,20,21,22,23,24,25]. Previously, a combination of Type-2 with intuitionistic fuzzy sets was proposed with relatively successful application [26].

Now, in this work, a hybridization of Type-3 with intuitionistic fuzzy sets is proposed to obtain a new concept with enhanced modeling capabilities. The core idea of this article is to combine the advantages of both types of FSs in modeling the existing uncertainty in real-world situations. We believe that intuitionistic fuzzy is able to model certain kinds of real-world uncertainty because of its defining concepts, while Type-2 and Type-3 fuzzy are able to model other kinds of uncertainty, and as a consequence, combining intuitionistic with Type-3 helps in achieving a more powerful model of uncertainty. In addition, this will fill a gap in the existing research on fuzzy logic theory and applications.

The main contribution is the novel concept of interval Type-3 intuitionistic FS (IT3IFS) that is put forward to enhance the capabilities of modeling uncertainty of individual Type-3 and intuitionistic concepts. The concept of IT3IFS has not been previously proposed in the literature, and in this sense, this fact shows the level of innovation of the work presented in this article. In addition, based on this new concept, the definitions of functions, relations, implications, and models can be constructed for IT3IFS. However, in this paper, we are only offering some preliminary concepts and an illustrative example to show the potential of this new concept. We plan in the future to develop more theoretical constructs and algorithms and to consider more applications of Type-3.

The article is structured as follows: Section 2 offers the definitions of Type-1 and Type-2 FSs. Section 3 reviews the concepts of intuitionistic FSs and their combination with Type-2 fuzzy theory. Section 4 offers new concepts related to interval Type-3 intuitionistic fuzzy. Section 5 offers an illustrative example of the application of interval Type-3 intuitionistic with encouraging results. Section 6 outlines the conclusions.

2. Type-1 and Type-2 FSs

Here, the basic terminology of Type-1 and Type-2 FSs is presented in a summarized way.

A Type-1 FS, called A, represented by µ(x), where x∈X, is expressed as

A = {〈x, µ(x)〉 | x∈X},

(1)

where µ(x): X→[0,1]. In this equation, µ(x) is the membership function (MF) that provides a membership degree to each x. Nowadays, it is well-known that Type-1 fuzzy sets cannot represent uncertainty; these sets are only able to represent vagueness, and for this reason Type-2 FSs were proposed [4].

A Type-2 FS, called A′, is represented by the MF µ(x, u) [5,6]. An alternative formulation for A′ is

A′ = {〈x, µ(x, u)〉 | x∈X, u ∈J_x},

(2)

where J_x is a subset of [0,1], x has a primary MF, and u has a secondary MF. This is what is known as a general Type-2 FS. The MF of a Type-2 FS is a 3D function (see Figure 1), with the primary variable x in the axis x, the secondary variable u in the axis y, and the value of MF, $\mu \left(x,u\right)$, in the axis z. In the case that the secondary MF u is fixed to 1 for all x, then we will have an interval Type-2 FS. In the case that u is a Type-1 FS, then A′ is called a general Type-2 FS.

To explain the example shown in Figure 1 in more detail, the formulation and parameterization of IT2 MFs and T2 MFs are presented. In this case, we have Gaussian MFs.

For the IT2 MF, called GausssScaleIntervalType2MF, with Gaussian $FOU$:

The upper MF (UMF) is characterized with parameters $\left[{\sigma }_l,m,{\sigma }_r\right]$, and the lower MF (LMF) with $s$ (LowerScale) and $\mathcal{\ell }$ (LowerLag). The structure of the parameters of the IT2 MF, ${\tilde{\mu }}_A\left(x\right)$, is defined as $params=\left\{\left\{\left[{\sigma }_l,m,{\sigma }_r\right]\right\},s,\left[{\mathcal{\ell }}_1,{\mathcal{\ell }}_2\right]\right\}$. The following equations describe the IT2 MF, ${\tilde{\mu }}_A\left(x\right)=\left[\underset{\_}{u}\left(x\right),\overline{u}\left(x\right)\right]=GausssScaleIntervalType2MF\left(x,params\right):$

$$\overline{u}\left(x\right)=\left\{\begin{array}{cc}exp\left[-\frac{1}{2}{\left(\frac{x-m}{{\sigma }_l}\right)}^2\right]& x\le m\\ exp\left[-\frac{1}{2}{\left(\frac{x-m}{{\sigma }_r}\right)}^2\right]& x>m\end{array}\right.$$

(3)

$$v\left(x\right)=\left\{\begin{array}{cc}exp\left[-\frac{1}{2}{\left(\frac{x-m}{{\sigma }_l^{*}}\right)}^2\right]& x\le m\\ exp\left[-\frac{1}{2}{\left(\frac{x-m}{{\sigma }_r^{*}}\right)}^2\right]& x>m\end{array}\right.$$

(4)

$$\underset{\_}{u}\left(x\right)=s·v\left(x\right)$$

(5)

where m is the mean, ${\sigma }_l^{*}={\sigma }_l \sqrt{\frac{\ln \left({\mathcal{\ell }}_1\right)}{\ln \left(\epsilon \right)}}$, ${\sigma }_r^{*}={\sigma }_r \sqrt{\frac{\ln \left({\mathcal{\ell }}_2\right)}{\ln \left(\epsilon \right)}}$, and $\epsilon$ is an epsilon of the machine. If ${\mathcal{\ell }}_1=0$, then ${\sigma }_l^{*}={\sigma }_l$. In the same way, if ${\mathcal{\ell }}_2=0$, then ${\sigma }_r^{*}={\sigma }_r$.

For the general T2 MF, called ScaleGausssGaussT2MF, which is an asymmetric double-sided Gaussian and vertical Gaussian cuts, we have the following description:

The FOU of the ScaleGausssGaussT2MF is characterized by an IT2FS in the plane (x,u) with IT2 MF, $GausssScaleIntervalType2MF$ with parameters $\left[{\sigma }_l,m,{\sigma }_r\right]$ in the UMF and in the LMF, $s$ (LowerScale), and $\mathcal{\ell }$ (LowerLag). The vertical cuts are T1FSs with Gaussian T1 MFs. The structure of the parameters of the T2 MF, $\mu \left(x,u\right)$ are defined as $params=\left\{\left\{\left[{\sigma }_l,m,{\sigma }_r\right]\right\},s,\left[{\mathcal{\ell }}_1,{\mathcal{\ell }}_2\right]\right\}$. The FOU of the T2FS limited by the LMF, $\underset{\_}{u}\left(x\right)$ and UMF, $\overline{u}\left(x\right)$ are evaluated using Equations (3)–(5), which define the IT2 MF, $GausssScaleIntervalType2MF$. The following equations describe the T2 MF, $\mu \left(x,u\right):ScaleGausssGaussT2MF\left(x,u,params\right)$:

$$\delta \left(x\right)=\overline{u}\left(x\right)-\underset{\_}{u}\left(x\right)$$

(6)

$${\sigma }_u=\frac{{\delta }_u}{2\sqrt{3}}+\epsilon$$

(7)

where $\delta \left(x\right)$ is the range of the FOU in x, ${\sigma }_u$ is the radius of uncertainty, and $\epsilon$ is an epsilon of the machine.

The core or apex of the vertical cuts is evaluated using the double-sided Gaussian T1 MF, $p\left(x\right)=gausssmftype1\left(x,\left[{\sigma }_1,m,{\sigma }_2\right]\right)$, described by the following equations:

$${\mu }_l\left(x\right)=exp\left[-\frac{1}{2}{\left(\frac{x-m}{{\sigma }_1}\right)}^2\right]$$

(8)

$${\mu }_r\left(x\right)=exp\left[-\frac{1}{2}{\left(\frac{x-m}{{\sigma }_2}\right)}^2\right]$$

(9)

$$p\left(x\right)={\mu }_l\left(x\right)H\left(x\right)+\left[{\mu }_r\left(x\right)-{\mu }_l\left(x\right)\right]H\left(x-m\right)$$

(10)

where ${\sigma }_1=\left({\sigma }_l^{*}+{\sigma }_l\right)/2$, ${\sigma }_2=\left({\sigma }_r^{*}+{\sigma }_r\right)/2$, ${\sigma }_l^{*}={\sigma }_l \sqrt{\frac{\ln \left({\mathcal{\ell }}_1\right)}{\ln \left(\epsilon \right)}}$, ${\sigma }_r^{*}={\sigma }_r \sqrt{\frac{\ln \left({\mathcal{\ell }}_2\right)}{\ln \left(\epsilon \right)}}$, $H\left(·\right)$ is the Heaviside function, and $p\left(x\right)$ represents the core or apex of the vertical cuts.

For Figure 1, we have the parameter values of m = 5.5, ${\sigma }_1=1, {\sigma }_2=1.5$, s = 0.1, and $\mathcal{\ell }=0.9$.

Currently, there are numerous real applications where Type-2 has outperformed Type-1 in accuracy and/or efficiency [7,11,27,28]. In particular, it has been noticed that, when problems have higher levels of noise, dynamic environments, and nonlinearity, then Type-2 has been able to outperform Type-1 [11,27].

3. Intuitionistic Fuzzy Sets Combined with the Type-2 Concept

In this section, we discuss an approach to combining the intuitionistic and Type-2 concepts. Basically, we use the concept of secondary MFs, coming from Type-2 theory, in the definitions of membership and nonmembership to provide them with enhanced capabilities to handle uncertainty.

Let X be a given universe; then, the intuitionistic FS defined on X is expressed as

A = {〈x, µ(x), ν(x)〉 | x∈X},

(11)

where µ(x), ν(x) are membership and nonmembership degrees of x ∈X to a given set A in X, 0 ≤ µ(x), ν(x) ≤ 1 and

0 ≤ µ(x) + ν(x) ≤ 1.

(12)

Let us consider the function

π_A(x) = 1 − μ(x) − ν(x).

(13)

In this situation, function π_A determines the degree of uncertainty. The main idea is that the uncertainty in a real-world problem can be represented by this π value.

The inference in intuitionistic systems must deal with the MFs and the nonmembership functions (NMFs). In this situation, it is assumed (as an initial approximation) that the global output of the system is a combination of two systems, one for MFs, and another for NMFs.

The output IFS of an intuitionistic system is computed (as an approximation) as:

IFS = (1 − π)FSµ + πFSν

(14)

where FSµ is the output of a fuzzy system (FS) utilizing MFs (µ), and FSν is the output of a FS utilizing NMFs (ν) [26]. The output of a fuzzy system is calculated with the fuzzy rules, inference method, and input data [26]. In this case, Equation (14) for π = 0 will simplify to the output of a Type-1 system, but for different values of π, the results will change as now we utilize π.

Now, we can consider the generalization of the previous concepts. Let the set X be fixed. The intuitionistic fuzzy multi-dimensional set (IFMDS) A in X, Z₁, Z₂, …, Z_n is an object of the form

A(Z₁, Z₂, …, Z_n) = {〈x, µ(x, z₁, z₂, …, z_n), ν(x, z₁, z₂, …, z_n)〉 | 〈x, z₁, z₂, …, z_n〉 ∈ X × Z₁ × Z₂ … ×Z_n},

where 0 ≤ µ(x, z₁, z₂, …, z_n) and ν(x, z₁, z₂, …, z_n) ≤ 1 are membership and nonmembership degrees, respectively, of 〈x, z₁, z₂, …, z_n 〉 ∈ X × Z₁ × Z₂ × … × Z_n and

0 ≤ µ_A(x, z₁, z₂, …, z_n) + ν_A(x, z₁, z₂, …, z_n) ≤ 1.

Now, with the concepts of IFMDS, a given IF2-dimensional-S (IF2DS) changes to the following expression

A₁ = {〈x, µ(x, u), ν(x, u)〉 | x∈X, u∈J_x},

(15)

where µ(x, u) and ν(x, u) are the membership and nonmembership degrees of x∈X and satisfy the condition

0 ≤ µ(x, u) + ν(x, u) ≤ 1

(16)

In this case, we now have secondary functions for the MFs and NMFs; these sets are viewed as interval Type-2 intuitionistic FSs. Intuitionistic FSs have also found multiple applications in many different areas [29], as has the hybrid of Type-2 intuitionistic FSs [30,31]. We believe that the Type-2 intuitionistic has enhanced capabilities for handling higher uncertainty degrees, and due to this fact, it can outperform other methods in some problems.

4. Proposal for Interval Type-3 Intuitionistic FSs

Now, we extend to Type-3 fuzzy logic the Type-2 intuitionistic concept presented in the previous section.

A Type-3 fuzzy set (T3FS) [18], denoted by $A^{\left(3\right)}$, is represented by the plot of a trivariate function, called membership function (MF) of $A^{\left(3\right)}$, in the Cartesian product $X\times \left[0,1\right]\times \left[0,1\right]$ in $\left[0,1\right]$, where $X$ is the universe of the primary variable of $A^{\left(3\right)}$, x. The MF of ${\mu }_{A^{\left(3\right)}}$ is formulated by ${\mu }_{A^{\left(3\right)}}\left(x,u,v\right)$ (or ${\mu }_{A^{\left(3\right)}}$ to abbreviate), and it is called a Type-3 membership function (T3 MF) of the T3FS. In other words, more formally,

$$A^{\left(3\right)}=\left\{\left(x,u\left(x\right),v\left(x,u\right),{\mu }_{A^{\left(3\right)}}\left(x,u,v\right)\right) | x\in X, u\in U\subseteq \left[0,1\left],v\in V\subseteq \right[0,1\right]\right\}$$

(17)

where $U$ is the universe for the secondary variable $u$, and $V$ is the universe for tertiary variable $v$. If ${\mu }_{A^{\left(3\right)}}\left(x,u,v\right)=1$ for all $x\in X$, $u\in U$, $v\in V$, then a T3FS, $A^{\left(3\right)}$, is simplified to an interval Type-3 fuzzy set (IT3FS). We illustrate in Figure 2 a sample T3FS.

To explain the IT3FS shown in Figure 2, we provide more details on the mathematical formulation of the IT3 MF used in this example.

The interval Type-3 Gaussian membership function, called ScaleGaussScaleGaussIT3MF, with Gaussian $FOU$, is characterized by two parameters $\left[\sigma ,m\right]$ (UpperParameters) for the UMF, and for the LMF, the parameters $s$ (LowerScale) and $\mathcal{\ell }$ (LowerLag) to form the domain of uncertainty (DOU). The following equations define the IT3 MF, ${\tilde{\mu }}_{A\left(3\right)}\left(x,u\right)$:

$$\overline{u}\left(x\right)=exp\left[-\frac{1}{2}{\left(\frac{x-m}{\sigma }\right)}^2\right]$$

(18)

$$\underset{\_}{u}\left(x\right)=s·exp\left[-\frac{1}{2}{\left(\frac{x-m}{{\sigma }^{*}}\right)}^2\right]$$

(19)

where ${\sigma }^{*}=\sigma \sqrt{\frac{\ln \left(\mathcal{\ell }\right)}{\ln \left(\epsilon \right)}}$, and $\epsilon =0.01$. If $\mathcal{\ell }=0$, then ${\sigma }^{*}=\sigma$. Then, $\overline{u}\left(x\right)$ and $\underset{\_}{u}\left(x\right)$ are the upper and lower limits of the DOU. For plotting Figure 2 we have the parameter values of m = 1.5, σ = 0.12, s = 0.6, and $\mathcal{\ell }=0.4$.

Now, to obtain the interval Type-3 intuitionistic fuzzy set, we introduce the tertiary MF to represent the membership over the secondary MF [15]. The idea is to provide an even better capability for handling uncertainty, which Type-3 has shown individually, to the intuitionistic concept. An interval Type-3 intuitionistic FS can be formulated as:

A = {〈x, µ(x, u, v), ν(x, u, v)〉 | x∈X, u∈J_x, v∈H_x},

(20)

where µ_A(x, u, v) and ν_A(x, u, v) are the membership and nonmembership degrees of x∈X, J_x is the secondary domain, and H_x is the tertiary domain, satisfying the condition

0 ≤ µ(x, u, v) + ν(x, u, v) ≤ 1

(21)

Based on this proposed definition, all the operations of fuzzy sets, relations, and implications can also be extended. In addition, interval Type-3 intuitionistic fuzzy inference systems (IT3IFISs) can be proposed and applied to solve problems in different areas of application. We can also use the following equation (similar to Equation (6)) to approximate the results of the inference in an interval Type-3 intuitionistic:

IT3IFIS = (1 − π)IT3FISµ + πIT3FISν

(22)

At this point, we are relying on the fact that, for IT3FISs, we have previously defined how to calculate the outputs of interval Type-3 fuzzy systems, and their linear combination will allow the computation of the proposed IT3IFIS. We must recall that the output of a fuzzy system is obtained by the inference process performed on the fuzzy rules for specific input values. More details can be found in papers, including [13,14]. Of course, there are many theoretical issues to be considered in this line of research, and we plan to work on some of these in the future, but here, we are just putting forward (for the moment) some initial foundations for this new area of IT3IFSs, and in the following section, we provide an illustrative example with encouraging results. We expect that our research group and other groups around the world will become interested and continue the work in this area.

5. Illustrative Example

In this section, we illustrate the advantages of using interval Type-3 intuitionistic fuzzy inference systems (IT3IFISs) with a realistic example of controlling the tuning process of the imaging system in televisions. The imaging system of a television and its tuning are described in [32]. More complete details for this example, where we have applied interval Type-3 systems for this problem, can be found in [33]. In this work, readers can find the membership functions that we will adopt in this paper as part of our IT3IFIS, and we will only show in the present paper the nonmembership functions. Previously, we have also solved this problem with Type-2 and Type-1 systems, as can be seen in [32]. Now, in this section, we present the interval Type-3 intuitionistic approach for solving this problem, and at the end, we offer a comparative study with respect to Type-3 and general Type-2, as the latter outperform Type-1 systems.

In this paper, we are only reporting the information on NMFs, as the MFs are presented in detailed fashion in a previous paper [33]. The general architecture is similar to the one presented in [33], but now the fuzzy system is Type-3 intuitionistic (we show this in Figure 3). We have three input variables (voltage, current intensity, and time) and one output variable (image quality). Previously, human experts in production plants manually tuned the imaging systems for televisions, but now, with the fuzzy system approach, the tuning process has been automated, and it is more efficient. Initially, a Type-1 system was developed, and later, a Type-2 system was implemented with better results than those obtained with Type-1. More recently, an interval Type-3 fuzzy approach was proposed in [33], and it outperformed Type-2 and Type-1. Now, in this paper, we show initial and encouraging results, where interval Type-3 intuitionistic is able to outperform interval Type-3 in most of the cases. In Figure 3, we show that the membership and nonmembership parts of Type-3 fuzzy are used to compute the IT3IFIS.

Table 1. Rules of the IT3IFS for control.

	IF	AND	AND	THEN
Number	Voltage	Current	Time	Image Quality
1	High	Adequate	Low	Very Good
2	Adequate	High	Low	Very Good
3	High	High	Low	Regular
4	Low	Adequate	Low	Regular
5	Adequate	Low	Low	Regular
6	Low	Low	Low	Bad
7	Adequate	Adequate	High	Very Good
8	High	Adequate	High	Good
9	Adequate	High	High	Good
10	Adequate	Adequate	High	Regular
11	Low	Adequate	High	Bad
12	Adequate	Adequate	Low	Excellent

summarizes the set of rules for automatically tuning the imaging system in televisions. In

Table 2. Parameterization that was utilized in the NMFs.

Variable	MFs	σ	m
Input 1	Low	1.25	0.05
Input 1	Adequate	1.05	4.95
Input 1	High	1.25	9.95
Input 2	Low	1.25	0.05
Input 2	Adequate	1.05	4.95
Input 2	High	1.25	9.95
Input 3	Low	2.45	0.05
Input 3	High	2.55	9.95
Output	Bad	6.95	0.50
Output	Regular	6.95	25.50
Output	Good	6.95	50.50
Output	Very Good	6.45	75.50
Output	Excellent	4.05	99.50

, the parameter values of the nonmembership functions (NMFs) utilized in the variables are offered. We utilized Mamdani reasoning and Gaussian NMFs. The system was formed by capturing the knowledge of experts in controlling the tuning in real TV manufacturing, and in this form, we arrive at an IT3IFS of 14 rules.

We illustrate the Gaussian NMFs for the output variable of image quality in Figure 4. In Figure 5, we illustrate the voltage input variable. In Figure 6, the current intensity variable is illustrated.

In Figure 7, the NMFs of the time input variable are illustrated. Lastly, we illustrate two different views of IT3IFS in Figure 8 and Figure 9.

The nonlinear surfaces of Figure 8 and Figure 9 illustrate the way in which the independent variables affect the output variable. For example, in Figure 8 we have a representation of how the current and voltage affect the output (given by the model).

The experimental results for 11 cases are illustrated in

Table 3. Experimental results for 11 real cases (The best results are marked in bold).

Voltage	Current	Time	GT2 Fuzzy (%) [32]	IT3 Fuzzy (%) [33]	Quality with NMFs (%)	IT3IFS [This Work] (%)	Expert Evaluation (%)
9.03	7.47	2.53	39.1266	39.6137	37.1972	39.4928	40.50
5.01	5.02	3.10	86.8751	87.9177	88.5204	87.9478	88.25
4.91	5.10	5.10	51.9168	52.2079	52.6641	52.2297	53.00
8.75	4.95	5.03	57.2788	58.5392	58.7301	58.5487	57.75
5.20	4.85	8.70	48.8429	49.1119	49.6084	49.1367	50.75
2.25	6.33	7.20	24.0734	21.9642	21.2715	21.9295	23.25
5.10	4.99	5.20	50.7942	51.8969	52.3282	51.9184	51.50
6.20	3.17	5.15	50.7333	51.8500	52.3093	51.8729	52.25
5.31	5.21	4.80	54.2964	55.8204	56.6152	55.8601	56.50
3.99	6.25	5.10	51.2754	52.1439	52.5924	52.1663	53.25
5.00	5.00	0.20	91.7652	94.3397	94.6043	94.3529	95.50

, where it should be noticed that the IT3IFS results are near the real data offered by the experts. (For this problem, two experts were considered as these were the available ones in the plant).

From Table 3, it can be seen that image quality of the intuitionistic Type-3 fuzzy approach is closer to the expert values in 7 of the 11 (63%) cases when compared to the plain interval Type-3, which is better in 4 of the 11 cases (best results shown in bold). Also, as the Type-3 fuzzy system was able to outperform our previous work on Type-2 and Type-1, then IT3IFS also outperforms them. We must mention that this application could be solved with Type-1 or any other extension of Type-1 (such as Type-2 and Type-3), but we are illustrating that the hybrid intuitionistic Type-3 fuzzy approach can outperform the previous approaches that have been applied to solve this problem.

6. Conclusions

In this work, the concept of interval Type-3 intuitionistic FS has been proposed. This was proposed as a natural evolution of the previous concept of interval Type-2 intuitionistic, with the goal of enhancing its capabilities for modeling real-world uncertainty. The main idea is that, by using interval Type-3 intuitionistic FSs in decision-making problems, we will be able to produce better results in applications. The main reason is that uncertainty in decision making could potentially be modeled in a better fashion by combining the advantages of interval Type-3 fuzzy and intuitionistic fuzzy concepts as both concepts have individually shown good capabilities in handling real-world uncertainty for different kinds of problems, and their combination could exhibit even better capabilities. We show the possible advantages of IT3IFSs with an illustrative example, which is fuzzy control of the imaging systems in televisions. Simulation results are encouraging, as the IT3IFS is able to outperform interval Type-3 fuzzy in 63% of the cases. In addition, IT3IFS is also able to outperform Type-2 and Type-1 for the same problem. As future work, we plan to develop other corresponding theoretical concepts related to IT3IFSs and later extend them to general Type-3 intuitionistic fuzzy sets. In addition, we plan to consider the optimization of parameters of the IT3IFSs with bio-inspired algorithms for improving results in applications to real problems. Finally, other areas of opportunity for IT3IFSs can be investigated, such as in time-series prediction, monitoring, and others. Even further into the long-term future, we expect to study Type-n fuzzy systems and their optimal design utilizing nature-inspired metaheuristics as more complex real problems could require more powerful uncertainty models.