The research and application of intuitionistic fuzzy decision making

Abstract

This paper studies intuitionistic fuzzy (IF) decision making problems using an integrated approach. Firstly, an IF induced generalized ordered weighted averaging distance (IFIGOWAD) operator is introduced, that covers numerous IF aggregations distance operators. Then, two more generalized operators named IF quasi induced OWAD (Quasi-IFIOWAD) and IF induced generalized hybrid average distance (IFIGHAD) operator are presented. Furthermore, a new method using above operators is introduced to IF decision making problem and online trade systems. Finally, two real cases are present to show the effect of the method.

Keywords

Hybrid average distance distance measure IOWA operator trade systems

1 Introduction

The induced ordered weighted averaging (IOWA) operator [1], is an effective operator, which aggregates values according to their associated order-inducing variables. For 20 years research, the IOWA has constantly been focused all over the world. It has been widely applied in various kinds of areas, including management, economics and many other fields [2 –6].

So far, numerous extensions of the IOWA operator have been studied. One of interesting extension is the induced aggregation distance measures, has gain much attention, such as the IOWA distance (IOWAD) operator [2], and the Euclidean IOWA operator (IEOWAD) [7]. On the peer work of these two operators, a more generalized form, called the induced generalized OWA distance (IGOWAD) has been presented [8], which is an integrated model with the induced operator, generalized mean and distance measures. The IGOWAD operator covers the OWAD, IOWAD and IEOWAD operators, etc.

Usually, the prerequisite for the use of IGOWAD operator means the aggregation data is determined and can be expressed in exact numerical terms. However, in the actual problem, the preferences of attribute values given by decision makers always contain vague and uncertain information, which renders the IGOWAD operator no longer applicable. The IFS, described by Atanassov [9], is an available way dealing with such fuzzy information, which has been widely used in numerous practical fields [10 –16]. Thus it is interesting to study the application of the IGOWAD operator in IF situation, which is the precisely the motivation for this article. For doing so, we will develop the IFIGOWAD operator, which unifies the main advantages of the IGOWAD and IFS. Thus, the IFIGOWAD operator actually extend the IOWA operator to measure the distance of IF information [17]. The IFIGOWAD is further extended by using a hybrid weighted approach, obtaining the IFIGHAD operator [18].

The following section is arranged as: some basic theory is introduced in Section 2. Then, the IFIGOWAD operator and IFIGHAD operator are presented in Section 3. In Section 4, the application of the developed operator in actual problems is studied. In Section 5 and Section 6, an online trade system based on the developed operator is presented. Finally, in Section 7, we will summarize the paper, and put forward the prospect of future research.

2 Preliminaries

Compared to OWA operator [17, 19], the input data is reordered based on induced-order variables in the IOWA operator, but only their values [20 –22]. The definition of the IOWA operator is given:

Definition 1 [1]. An IOWA operator is a mapping: Rⁿ × Rⁿ → R associated with weight vector $W = {w_{j}}_{j = 1}^{n}$ satisfying $\sum_{j = 1}^{n} w_{j} = 1$ such that: $IOWA (〈 l_{1}, x_{1} 〉, 〈 l_{2}, x_{2} 〉, . . ., 〈 l_{n}, x_{n} 〉) = \sum_{j = 1}^{n} w_{j} y_{j}$ (1) where y_j is x_i associated with the j-th largest l_i, l_i is the induced- order variable.

The IGOWAD operator is composed by the generalized mean, the inducing variables and the OWA operator [19]. Let X ={ x₁, x₂, . . . , x_n } and Y ={ y₁, y₂, . . . , y_n } be two real sets, then

Definition 2 [8]. An IGOWAD operator associated with a weight $W = {w_{j}}_{j = 1}^{n}$ satisfying $\sum_{j = 1}^{n} w_{j} = 1$ is defined as following formulas: $f ((l_{1}, x_{1}, y_{1}), . . ., (l_{n}, x_{n}, y_{n})) = {(\sum_{j = 1}^{n} w_{j} d_{j}^{λ})}^{1 / λ}$ (2) where d_j is the |x_i - y_i| associated with the j-th largest l_i, l_i is the induced- order variable, |x_i - y_i| is the individual distances between x_i and y_i, λ is a parameter satisfying λ ∈ (- ∞ , + ∞). Especially, if λ = 1, then we get the IOWAD, and if λ = 2, then the IEOWAD operator [7].

The IGOWAD operator is assumed to deal with exact numbers. However, there is always a significant amount of vague or imprecise information in real-world situations, which makes the IGOWAD is no longer suitable. Atanassov [9] presented the theory of IFS, which is described by an IF numbers (IFNs) [10 , 23–25]. The IFN can be used to describe vague or imprecise information in everyday life, reflecting the real-world situations more accurately. In next section, we shall study the application of IGOWAD operator in IF environment and present the IFIGOWAD operator [26 –30].

3 Induced intuitionistic fuzzy generalized aggregation distance operators

We first review some basic concepts about the IFS.

Definition 3 [9]. Let a set A ={ a₁, a₂, . . . , a_n } be fixed, if $I = {〈 a, μ_{I} (a), v_{I} (a) 〉 | a \in A}$ (3) then the set I is called an IFS in A, where the functions μ_B: A → [0, 1] and v_B: A → [0, 1] determine the membership degree and non-membership degree of the element a ∈ A, respectively, and 0 ⩽ μ_I (a) + v_I (a) ⩽1, for all a ∈ A. For convenience, we call α = (μ_α, v_α) an IFN [11].

Let α = (μ_α, v_α) , α₁ = (μ_{α
₁}, v_{α
₁}) and α₂ = (μ_{α
₂}, v_{α
₂}) be three IFNs, their operations and relations are defined as follows [10]:

(1) α₁ + α₂ = (μ_{α
₁} + μ_{α
₂} - μ_{α
₁} · μ_{α
₂}, v_{α
₁} · v_{α
₂})

(2) $λ α = (1 - (1 - μ_{α})^{λ}, v_{α}^{λ})$ , λ > 0.

The distance between the IFNs α₁ = (μ_{α
₁}, v_{α
₁}) and α₂ = (μ_{α
₂}, v_{α
₂}) is given as follows:

Definition 4 [10]. For two IFNs α₁ = (μ_{α
₁}, v_{α
₁}) and α₂ = (μ_{α
₂}, v_{α
₂}), then their distance are defined as follows: $d (α_{1}, α_{2}) = \frac{1}{2} (| μ_{α_{1}} - μ_{α_{2}} | + | v_{α_{1}} - v_{α_{2}} |)$ (4)

Based on the IGOWAD operator and the laws of intuitionistic fuzzy set, now we can develop the IFIGOWAD operator. Let M = (α₁, α₂, . . . , α_n) and N = (β₁, β₂, . . . , β_n) be two sets of IFNs, then we have the following definition.

Definition 5. An IFIGOWAD operator associated with weight vector $W = {w_{j}}_{j = 1}^{n}$ with $\sum_{j = 1}^{n} w_{j} = 1$ is defined as: $\begin{matrix} IFIGOWAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) \\ \begin{matrix} \end{matrix} = {(\sum_{j = 1}^{n} w_{j} d_{j}^{λ})}^{1 / λ} \end{matrix}$ (5) where d_j is |α_i - β_i| value according to the jth largest l_i, |α_i - β_i| is the individual distance between the IFNs α_i and β_i, λ is a parameter satisfying λ ∈ (- ∞ , + ∞).

A simple example is illustrated to show the aggregation process based on the IFIGOWAD operator.

Example 1. Let order inducing variable l = (8, 7, 9, 5), U = ((0.8, 0.1) , (0.4, 0.5) , (0.6, 0.2) , (0.2, 0.7)) and V = ((0.5, 0.5) , (0.6, 0.2) , (0.4, 0.4) , (0.1, 0.6)) to be collections of IFSs, then $d (α_{1}, β_{1}) = \frac{1}{2} (| 0.8 - 0.5 | + | 0.1 - 0.5 |) = 0.35,$

Similarly, the rest of IFNs distance are obtained: $d (α_{2}, β_{2}) = 0.25, d (α_{3}, β_{3}) = 0.2, d (α_{4}, β_{4}) = 0.1,$

Record the distances according to order inducing variable:

d₁ = d (α₃, β₃) = 0.2, d₂ = d (α₁, β₁) = 0.35, d₃ = d (α₂, β₂) = 0.25, d₄ = d (α₄, β₄) = 0.1,

Assume the weighting vector is of IFIGHAD is W = (0.30, 0.25, 0.15, 0.25) ^T, and let λ = 2, by Eq. (5), we have the final aggregation result: $\begin{matrix} IFIGOWAD (U, V) = (0.35 \times 0 . 2^{2} + 0.25 \times 0 . 35^{2} \\ + 0.15 \times 0 . 25^{2} + 0.25 \times 0 . 1^{2})^{1 / 2} = 0.238 \end{matrix}$

When the weights of the IFIGOWAD operator is not satisfied the normalized rule, that is if W ≠ 1, then, the IFIGOWAD should be given as:

$\begin{matrix} IFIGOWAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) \\ = {(\frac{1}{W} \sum_{j = 1}^{n} w_{j} d_{j}^{λ})}^{1 / λ} \end{matrix}$ (6)

Nest some attributes of the IFIGOWAD operator is discussed, including the monotonic, commutative, idempotent and bounded. Let be the IFIGOWAD operator, we have the next results:

(1) (Commutativity). $\begin{matrix} IFIGOWAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) = \\ IFIGOWAD (〈 l_{1}, α_{1}^{'}, β_{1}^{'} 〉, . . ., 〈 l_{n}, α_{n}^{'}, β_{n}^{'} 〉) \end{matrix}$ (7) where $(〈 l_{1}, α_{1}^{'}, β_{1}^{'} 〉, . . ., 〈 l_{n}, α_{n}^{'}, β_{n}^{'} 〉)$ is a permutation of the arguments (〈 l₁, α₁, β₁ 〉 , . . . , 〈 l_n, α_n, β_n 〉).

The property can also be viewed as distance measure’ attributes:

(2). (Commutativity). $\begin{matrix} IFIGOWAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) = \\ IFIGOWAD (〈 l_{1}, β_{1}, α_{1} 〉, . . ., 〈 l_{n}, β_{n}, α_{n} 〉) \end{matrix}$ (8)

(3). (Monotonicity). ∀i, if $d (α_{i}, β_{i}) ⩾ d (α_{i}^{'}, β_{i}^{'})$ , then $\begin{matrix} IFIGOWAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) ⩾ \\ IFIGOWAD (〈 l_{1}, α_{1}^{'}, β_{1}^{'} 〉, . . ., 〈 l_{n}, α_{n}^{'}, β_{n}^{'} 〉) \end{matrix}$ (9)

(4). (Boundedness). $\begin{matrix} min_{i} (d (α_{i}, β_{i})) \\ ⩽ IFIGOWAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) \\ ⩽ max_{i} (d (α_{i}, β_{i})) \end{matrix}$ (10)

(5). (Idempotency). ∀i, if d (α_i, β_i) = d, then $IFIGOWAD (〈 l, M, N 〉) = d$ (11)

Theorem 6. (Nonnegativity). $IFIGOWAD (〈 l, M, N_{1} 〉) ⩾ 0$ (12)

Moreover, $IFIGOWAD (〈 l, M, N 〉) = 0$ (13) if α_i = β_i for all i.

The IFIGOWAD operator provides a numerous special cases. Basically, these particular cases can be obtained by assigning difference values for the parameter W and λ.

Remark 1. If λ = 1, then, we have the IFIOWAD operator. $f (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) = \sum_{j = 1}^{n} w_{j} d_{j}$ (14)

Remark 2. If λ = 2, then we have the IF Euclidean IOWAD distance (IFEIOWAD) operator: $f (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) = {(\sum_{j = 1}^{n} w_{j} d_{j}^{2})}^{1 / 2}$ (15)

Remark 3. When λ = -1, the IFIOWHAD: $f (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) = \frac{1}{\sum_{j = 1}^{n} \frac{w_{j}}{d_{j}}}$ (16)

It is interesting to generalize the IFIGOWAD based on the idea of quasi means method as mentioned in Ref. 5, 7, 13. We name this new operator as Quasi-IFIOWAD operator:

Definition 6. A Quasi-IFIOWAD operator associated with weight vector $W = {w_{j}}_{j = 1}^{n}$ satisfying $\sum_{j = 1}^{n} w_{j} = 1$ is defined as:

$\begin{matrix} QIFIOWAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) \\ = g^{- 1} (\sum_{j = 1}^{n} w_{j} g (d_{j})) \end{matrix}$ (17)

Another interesting extension of the IFIGOWAD is based on the hybrid averages. Thus, we get the IFIGHAD operator, which is able to takes into account the experts’ subjective probability and attitude characteristics in the same formulation.

Definition 6. An IFIGHAD operator associated with a weight W satifying 0 ⩽ w_j ⩽ 1 and $\sum_{j = 1}^{n} w_{j} = 1$ is defined as: $\begin{matrix} IFIGHAD (〈 l_{1}, α_{1}, β_{1} 〉, . . ., 〈 l_{n}, α_{n}, β_{n} 〉) \\ = {(\sum_{j = 1}^{n} w_{j} d_{j}^{λ})}^{1 / λ} \end{matrix}$ where d_j is ${\hat{d}}_{i}$ value ( ${\hat{d}}_{i} = n ω_{i} | α_{i} - β_{i} |$ ) of the IFIGHAD pair 〈l_i, α_i, β_i〉 related to the j-th largest l_i, ω = (ω₁, ω₂, . . . , ω_n) is associated with the |α_i - β_i|, with 0 ⩽ ω_i ⩽ 1 and $\sum_{j = 1}^{n} ω_{j} = 1$ , and λ satisfies λ ∈ (- ∞ , + ∞).

It is easy to see that the IFIGHAD reduces to the IFWD when w_i = 1/n, and IFIGOWAD operator if ω_i = 1/n. Note that followed the method described in Ref 18-30, many other families of the IFIGHAD operator can be explored.

4 Illustrative example

Next, we will develop a real-world instance to show the practicality of above method. Suppose that an enterprise intends recruit a new employee for a new position. After analyzing the applicant’ information, all the possible candidates A_i (i = 1, 2, . . . , 5) are assessed from the following five attributes: experience (G₁), skill levels (G₂), knowledge (G₃), motivation (G₄), sense of cooperation (G₅) and other aspects (G₆).

The evaluated values of the five candidates given by experts are shown in Table 1. Note that the decision condition is so complex that the experts would like to express their preference as IFNs.

Table 1
Investments information

G ₁ G ₂ G ₃ G ₄ G ₅ G ₆

A ₁ (0.5,0.4) (0.5,0.3) (0.2,0.6) (0.4,0.4) (0.5,0.4) (0.3,0.5)

A ₂ (0.7,0.3) (0.7,0.3) (0.6,0.2) (0.6,0.2) (0.7,0.2) (0.4,0.5)

A ₃ (0.5,0.4) (0.6,0.4) (0.6,0.2) (0.5,0.3) (0.6,0.3) (0.4,0.4)

A ₄ (0.7,0.2) (0.7,0.2) (0.4,0.2) (0.5,0.2) (0.4,0.4) (0.6,0.3)

A ₅ (0.4,0.3) (0.5,0.2) (0.4,0.5) (0.4,0.6) (0.3,0.4) (0.7,0.2)

	G ₁	G ₂	G ₃	G ₄	G ₅	G ₆
A ₁	(0.5,0.4)	(0.5,0.3)	(0.2,0.6)	(0.4,0.4)	(0.5,0.4)	(0.3,0.5)
A ₂	(0.7,0.3)	(0.7,0.3)	(0.6,0.2)	(0.6,0.2)	(0.7,0.2)	(0.4,0.5)
A ₃	(0.5,0.4)	(0.6,0.4)	(0.6,0.2)	(0.5,0.3)	(0.6,0.3)	(0.4,0.4)
A ₄	(0.7,0.2)	(0.7,0.2)	(0.4,0.2)	(0.5,0.2)	(0.4,0.4)	(0.6,0.3)
A ₅	(0.4,0.3)	(0.5,0.2)	(0.4,0.5)	(0.4,0.6)	(0.3,0.4)	(0.7,0.2)

Based on the previous experience of recruiting and the practical requirements of the job, the enterprise set the standard for an ideal candidate in Table 2.

Table 2

Ideal worker

	G ₁	G ₂	G ₃	G ₄	G ₅	G ₆
P	(0.8,0.1)	(0.9,0)	(0.8,0.1)	(0.9,0.1)	(0.8,0.1)	(1,0)

In order to conduct a detailed analysis of the candidates, the panel calculates the candidate’s attitude characteristics, shown in Table 3.

Table 3

Order-inducing variables

	G ₁	G ₂	G ₃	G ₄	G ₅	G ₆
A ₁	17	13	9	12	10	7
A ₂	12	6	24	17	8	30
A ₃	16	14	12	10	9	8
A ₄	14	17	20	12	16	8
A ₅	15	13	11	17	8	19

Based on the above information, we can utilized the IFIGHAD to aggregate the evaluated values and select a suitable candidate. In this example, without loss of Generality, we select λ = 2 and the weighs related to the IFIGHAD operator is w₁ = w₆ = 0.09, w₂ = w₅ = 0.17, w₃ = w₄ = 0.24, the attribute’s weighting vector is described as ω = (0.12, 0.18, 0.12, 0.26, 0.15, 0.17), then we have $\begin{matrix} IFIGHAD (A_{1}, P) = 0.447, \\ IFIGHAD (A_{2}, P) = 0.262, \\ IFIGHAD (A_{3}, P) = 0.336, \\ IFIGHAD (A_{4}, P) = 0.271, \\ IFIGHAD (A_{5}, P) = 0.414 \end{matrix}$

It is observed that the smaller the distance from the ideal, the better the candidate, so we can rank all of the candidates according to the IFIGHAD (A_i, I) : $A_{2} ≻ A_{4} ≻ A_{3} ≻ A_{5} ≻ A_{1} .$

Thus the most desired candidate is A₂.

5 Case study

The application of the integrated method in trade market is studied by Forex trading. To test the method effect, we use it in the financial field at first. Blessing is a famous Forex EA (Expert Advisor) based on MetaTrader, which can support automated trading. MetaQuotes Language is a high-level language designed for developing technical indicators, trading robots and utility applications, which automate financial trading. Blessing is dedicated to Mike McKeough, a member of the Blessing Development Group. It includes all kinds of trade signals base entry on MA channel, CCI indicator, Bulling Band, Stoch and MACD as shown in Fig. 1.

Fig. 1

Blessing EA setting interface.

Each indicator acts as the experts. So we select the above indicator for test from January 1, 2017 to September 30, 2017, run the EA according to the trading Signals with Automatic Execution on virtual account.

5.1 MA channel as an expert advice

We adopt the M1 period on chart, one the result is shown as Fig. 2:

Fig. 2

Blessing EA trade USD/JPA based on MA channel using M1 Candlestick Charts.

Growth: 33.60%

Profit: 336.83 USD

Maximum drawdown: 2%

We adopt the M5 period on chart, one the result is shown as Fig. 3:

Fig. 3

Blessing EA trade USD/JPA based on MA channel using M5 Candlestick Charts.

Growth: 33.65%

Profit: 3665.52 USD

Maximum drawdown: 7%

We adopt the M15 period on chart, one the result is shown as Figs. 4 and 5:

Fig. 4

Blessing EA trade USD/JPA based on MA channel using M15 Candlestick Charts.

Fig. 5

Blessing EA trade USD/JPA based on MA channel using M30 Candlestick Charts.

Profit: -4364.47USD

EA will lose your trading account.

Growth: 3.86%

Profit: 386 USD

Maximum drawdown: 7%

We adopt the H1 period on chart, the result is shown as Fig. 6:

Fig. 6

Blessing EA trade USD/JPA based on MA channel using H1 Candlestick Charts.

Profit: 389.69 USD

We adopt the H4 period on chart, the result is shown as Fig. 7:

Fig. 7

Blessing EA trade USD/JPA based on MA channel using H1 Candlestick Charts.

Growth: 46.31%

Profit: 4631.12 USD

Maximum drawdown: 7%

It shows obviously M1, M5, H4 is suitable the UJ marketing, while M15, M30, H1 will let you down.

5.2 CCI indicator as an expert advice

We adopt the M5 period on chart, one the result is shown as Fig. 8:

Fig. 8

Blessing EA trade USD/JPA based on CCI indicator using H1 Candlestick Charts.

Growth: 38.54%

Profit: 3854.2USD

Maximum drawdown: 7%

5.3 Bulling Band as an expert advice

We adopt the M5 period on chart, one the result is shown as Fig. 9:

Fig. 9

Blessing EA trade USD/JPA based on Bulling Band indicator using M5 Candlestick Charts.

Growth: 49.26%

Profit: 4926.24 USD

Maximum drawdown: 7%

5.4 Stoch as an expert advice

We adopt the M5 period on chart, one the result is shown as Fig. 10:

Fig. 10

Blessing EA trade USD/JPA based on Stoch indicator using M5 Candlestick Charts.

Growth: 56.25%

Profit: 5649.25 USD

Maximum drawdown: 7%

5.5 MACD as an expert advice

We adopt the M5 period on chart, one the result is shown as Fig. 11:

Fig. 11

Blessing EA trade USD/JPA based on Stoch indicator using M5 Candlestick Charts.

Growth: –33.29%

Profit: –3329.98 USD

Maximum drawdown: 11%

Based on the above test results, we can see that the Stoch indicator is the best, while the traditional MACD indicators are not suitable for the current stage of active foreign exchange days trading. So we can give the different weight to the different indicator according to the effect in the current period.

According to developed operators, we setup the trading system using different indicator as experts to enhance the lever for the maximum profit as shown in Fig. 12.

Fig. 12

Trading system based on the developed operator.

6 EA based on the developed operators

According to the case study above, the method of developed induced IF distance operators can be used on capital market. There are a lot of experts (human or machine) in the trading system. We can use their skills to beat the market which needs the decision-making strategy, while the method of induced generalized intuitionistic fuzzy aggregation distance operators gives the useful help (see Fig. 13).

Fig. 13

Different Experts or EA.

In the capital market, investors are mostly loss, fast may be a few days on the burst warehouse, slow may be a few months, but the reasons for the loss is nothing less than the following:

Professional knowledge is not enough which lead to cannot correctly judge the market trend.

Time is not enough energy is not enough: often missed a good opportunity to meet a bad opportunity.

Shigekura transactions: look forward to rapid profit and copy.

Contrarian operation: that will fall will rise, after the rise will fall.

Loss jiacang: no plan with a lucky jiacang, rather than the development of a good jiacang plan.

Heart to play: greed, do not admit mistakes, death does not repent, war, confidence and expansion.

For investors’ weaknesses, EA trading advantage is shown as follow:

6.1 Strong execution force

EA is an intelligent automatic trading program, it can 24 hours to capture the market, accurately determine the opportunity to do admission, open quickly. Just set the relevant parameters, EA program will strictly enforce the trading strategy, sensitive to changes in price changes and trends, to avoid the mistakes of manual transactions.

6.2 Overcome the weakness of human nature

EA programmatic intelligent trading to overcome the interference of artificial trading mentality, do not hesitate, not greedy, do not fear, really do not be proud of complacency, loss is not frustrated and lost, to avoid unnecessary loss of emotional transactions.

6.3 Strict risk control

EA program of intelligent transactions will be many year experience in the management of a set of perfect trading system, the position of the transaction positions, the number of single orders, stop-loss points have been carefully calculated; when the market to determine the correct, Quotes appear reversal, to strictly stop.

6.4 Sustained and stable profitability

EA can integrate many senior traders trading experience and wisdom, 24 hours of continuous trading.

Lately, data mining has had to deal with increasingly complex problems connected with the character of data. It is not the volume of the data, but their imperfection and different forms present the explorers with a multitude of various scenarios. Consequently, preliminary data processing has an important effect in decision making process. At the same time, the development of the software for preliminary data processing based on the method of developed distance operators provides enough tools for work [30]. We gather the signal data form the trading market and select some excellent signals with different weight to distribute the venture. With the developing of the trading market, some signals failure with the new excellent signals generates the signals set following by us should refresh again.

In the future, we will examine and analyze the main and secondary patterns, as well as their application tactics, try to bring closure to studying the patterns occurring when applying combined oscillators and trend-following indicators, give the combined trend-following indicators.

7 Conclusion

In general, we proposed the IF induced aggregation distance operators, named the IFIGOWAD operator. It generalizes the IOWA operator that uses distance measure, intuitionistic fuzzy information and generalized means. It is shown that this operator covers a kind of IF special cases including the IFGMD, the IFOWD and the IFOWAD operator. Moreover, the IFIGHAD operator is present by using the hybrid aggregation. The main feature of this operator is its ability to handle IF distance measures based on WA and OWA operator. We have also studied the application of the developed operators in human resource management and online trade system. The results show that our proposed methods are practical and effective, which provide a more robust formulation for the actual problems. In our next research, we would like to develop the application of this method in other domains.

Footnotes

Acknowledgments

This paper is supported by Zhejiang Wanli College Research and Development Fund & Applied Economics, Zhejiang Basic Public Welfare Research Program (LGF19G020001), Ningbo Natural Fund (No. 2017A610126), Ningbo intelligent team business plan project (Ningbo World Information Technology Development Co., Ltd.), Ningbo leader and top-notch talent and Ningbo Wisdom team project, Ningbo University of Finance & Economics Sciences support project, Ningbo Soft Science Fund (2016A10053), Zhejiang science and technology innovation program for College Students(2020R476008). Ningbo Science and technology innovation Fund (2020Z008), Zhejiang Public Welfare Technology Research Project (LGF20G020002), Humanities and Social Sciences Foundation of the Ministry of Education (20YJC630073).

References

Yager

R.R.

and Filev

D.P.

, Induced ordered weighted averaging operators, IEEE Transactions on Systems, Man and Cybernetics B29 (1999), 141–150.

Merigó

J.M.

and Casanovas

, Decision making with distance measures and induced aggregation operators, &Industrial Engineering60 (2010), 66–76.

Liu

H.C.

, Mao

L.X.

, Zhang

Z.Y.

and Li

, Induced aggregation operators in the VIKOR method and its application in material selection, Applied Mathematical Modelling37 (2013), 6325–6338.

Z.S.

, An overview of methods for determining OWA weights, International Journal of Intelligent Systems20 (2005), 843–865.

Zeng

S.Z.

, An extension of OWAD operator and its application to uncertain multiple-attribute group decision-making, Cybernetics and Systems47 (2016), 363–375.

Z.S.

and Xia

, Induced generalized intuitionistic fuzzy operators, Knowledge-Based Systems24 (2010), 197–209.

Merigó

J.M.

and Casanovas

, Induced aggregation operators in the Euclidean distance and its appplication in financia decision making, Expert Systems with Applications38 (2011), 7603–7608.

Merigó

J.M.

and Casanovas

, A new minkowski distancebased on induced aggregation operators, Journal of Computational Intelligence Systems4 (2011), 123–133.

Atanassov

, Intuitionistic fuzzy sets, Fuzzy Sets and Systems20 (1986), 87–96.

10.

Z.S.

, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems15 (2007), 1179–1187.

11.

Wan amd

S.P.

and Dong

J.Y.

, A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making, Journal of Computer and System Sciences80 (2014), 237–256.

12.

Z.S.

, A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making, and Negotiation19 (2010), 57–76.

13.

Zeng

S.Z.

, Su

W.H.

and Zhang

C.H.

, Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making, Technological and Economic Development of Economy22 (2016), 177–193.

14.

D.J.

and Liao

H.C.

, Visualization and quantitative research on intuitionistic fuzzy studies, &Fuzzy Systems30 (2016), 3653–3663.

15.

Büyüközkan

and Göçer

, Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem, Applied Soft Computing52 (2017), 1222–1238.

16.

D. J.

, Softmax function based intuitionistic fuzzy multi-criteria decision making and applications, Operational Research16 (2016), 327–348.

17.

Yager

R.R.

, On ordered weighted averaging aggregation operators in multicriteria decision making, on Systems, Man and Cybernetics B18 (1988), 183–190.

18.

, Zeng

, Pan

and Zheng

, A method based on induced aggregation operators and distance measures to multiple attribute decision making under 2-tuple linguistic environment, Journal of Computer and System Sciences, 2014.

19.

Zeng

S.Z.

, Chen

J.P.

and Li.

X.S.

, A hybrid method for pythagorean fuzzy multiple-criteria decision making, International Journal of Information Technology & Decision Making, 2015.

20.

Pan

T.J.

and Zheng

L.N.

, IPD-CMMI Model of Embedded Software Engineering under IEC-CDIO Framework, Journal of Software, 2012.

21.

Merigo

J.M.

, Uncertain induced aggregation operators and its application in tourism management, Expert Systems With Applications, 2012.01

22.

X.R.

and Wu

Y.Y.

, Global Research Trends of Intuitionistic Fuzzy Set: A Bibliometric Analysis, Journal of Intelligent Systems, 2017

23.

Zeng

S.Z.

, Wei

and Merigó

J.M.

, Extended induced ordered weighted averaging distance operators and their application to group decision-making, International Journal of Information Technology & Decision Making, 2013.

24.

Zeng

S.Z.

, An Extension of OWAD Operator and Its Application to Uncertain Multiple-Attribute Group Decision-Making, Cybernetics & Systems, 2016.

25.

Chao

S.G.

, A Material Selection Method Based on Double Base Points, Applied Mechanics and Materials, 2014.

26.

Merigó

J.M.

, Casanovas

and Palacios-Marqués

, Linguistic group decision making with induced aggregation operators and probabilistic information, Applied Soft Computing, 2014.

27.

, Zhang

and Zeng

, Uncertain Induced Heavy Aggregation Distance Operator and its Application to Decision Making, Cybernetics & Systems, 2015.

28.

, Induced uncertain linguistic OWA operators applied to group decision making, Information Fusion, 2006.06.

29.

Z.S.

, Multi-person multi-attribute decision making models under intuitionistic fuzzy environment, Fuzzy Optimization and Decision Making, 2007.

30.

Yang

, Induced quasi-arithmetic uncertain linguistic aggregation operator, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2013.