Group intelligence-based decision making and its applications to traditional chinese medical dysphagia rehabilitation treatment

Abstract

At present, multi-attribute group decision making (MAGDM) researches are concerned with obtaining the alternatives’ ranking order based on the gathered group fuzzy preference matrix, as a result, it suffers from the group experts’ strong subjectivity fatigue without approaches to obtain and use the group intelligence. This paper proposes a new definition of group intelligence based on sub-attribute’s weight coefficients and expected intervals of the MAGDM. Group intelligence generating methods are provided as well. Additionally, a kind of group intelligence-based decision approach is introduced that can aid in reducing subjective fatigue in humans. In particular, a test function and a kind of medical MAGDM problem addressing Traditional Chinese medical (TCM) dysphagia rehabilitation treatment are employed to verify the correctness and feasibility of the proposed methods.

Keywords

Group intelligence generating multi-attribute group decision making (MAGDM)traditional Chinese medicine (TCM)

1 Introduction

Currently, MAGDM [33, 34] approaches are more concerned with the decision-making results than the method employed to obtain and use the group intelligence based on the sub-attribute’s weight coefficients and expected intervals of MADM problems. Practically, traditional MAGDM methods require every expert to give his preferred judgment preference for each decision-making alternative in order to obtain the alternatives’ ranking order; however, it is important to note that these preferences are influenced by the experts’ strong subjectivity and fatigue.Therefore, it is necessary to gain further insight into group intelligence, which will lay a solid foundation for group intelligence generating techniques.

MAGDM problems [8 , 24] are employed in many complex decision making areas [7 , 16]. Additionally, the expert’s judgment preferences are always complex, and as a result, there have been many studies conducted on group experts’ judgment preferences gathering mechanisms [22, 25]. For example, the new determination model [2, 30] was proposed to obtain the weights of different attributes and the group consistency index. Additionally, methods on calculating the fuzzy decision matrix in the fuzzy environments were introduced [11 , 38]. To describe preferences in the MAGDM, linguistic preference [17], interval preference matrices [3, 9], and intuitionistic fuzzy preference [4] have been discussed in regards to their impact on decision-making results. In addition, to obtain the group experts’ preference, many operators have been proposed [12, 18]. However, most of these studies focused on providing methods for solving MAGDM problems without addressing the characteristics of their sub-attributes (each sub-attribute’s weight coefficient and expected interval). Furthermore, traditional MAGDM studies require each expert to give his preferred judgment preference (such as, a utility vector, ordering relationship value vectors, etc.) for each decision-making alternative [19]. Meanwhile, the gathered group fuzzy preferences matrix cannot describe the group intelligence of the specific MAGDM problem visually, it suffers from the group intelligence’s definition, and its generating approaches aid computers in making an automatic decision.

One such MAGDM problem is the rehabilitation treatment of dysphagia. Dysphagia refers to a dysfunction that occurs when food is transported from the mouth to the stomach. This dysfunction of the lower jaw, lips, tongue, throat, and esophagus can cause serious consequences, such as aspiration pneumonia and asphyxia. The anatomical structures of dysphagia are shown in Fig. 1.

Based on the dysphagia diagnostic results (the mouth period, tongue period, pharynx period, and larynx period) [20, 21], dysphagia rehabilitation treatment [13, 29] usually incorporates TCM techniques [1 , 32] (acupuncture, massage, muscle physiotherapy, etc.) to promote muscle function (soft palate, epiglottis capacity, tongue, etc.) and to stimulate the swallowing nervous system (Fengfu acupoint, Lian Quan acupoint, Yifeng acupoint, etc.). Practically, dysphagia rehabilitation programs involve multiple treatment objectives (multiple muscle and nervous systems) as well as a variety of therapeutic attributes (acupuncture, massage, muscle physiotherapy, etc.); however, it is difficult to quantify the relationship between each treatment objective and therapeutic attribute. Therefore, the dysphagia rehabilitation treatment is a kind of MAGDM problem. Additionally, to ensure the safety and effectiveness of rehabilitation, the current treatment program drafting needs doctor groups to discuss all treatment alternatives for each patient. Furthermore, it is very difficult to build and learn the rehabilitation experts’ treatment decision-making intelligence, where the scientific basis of the treatment decision-making should be improved. Therefore, it is necessary to build a quantitative model of the group intelligence and propose its generating methods. Such a case can greatly benefit from an improved interactive generating method for group intelligence.

In regards to some decision processes, especially for TCM clinical problems without a structured description of the objective function, group experts are often required to provide experience and to assist with the decision making. Therefore, it is particularly important to provide group intelligence generating methods and decision strategies based on group intelligence. With this motivation, based on either the characteristics of the sub-attributes or the weight coefficient and expected interval of each sub-attribute in the MAGDM problems, a new definition of group intelligence is proposed to demonstrate the generating process of group intelligence in this paper. In addition, a group intelligence generating algorithm and a group intelligence-based decision making approach are introduced, which can help gradually learn [23, 24] essentials in a group’s decision intelligence, reduce human subjective fatigue, as well as make the decisions more scientific and objective.

In this study, firstly, we proposes the definition and generating methods of group preferences in Section 2, which are followed by the group intelligence-based decision making approach. Secondly, the applications consisting of test functions and traditional Chinese medicine (TCM) dysphagia rehabilitation treatment issues are provided in Section 3. Furthermore, the performance of the proposed methods is discussed in Section 4. In the end, the conclusions and the future perspectives are shown in Section 5.

2 Group intelligence generating methods

Tradition MADM methods often base the decision solution on utility function and probability approaches. However, the mathematical descriptions of an individual person’s preferred forms judgment preference are always complexes, which include utility vectors and so on [19]. The fuzzy MADM approach is always used to solve MAGDM problems.

The fuzzy MAGDM methods tend to focus on the selection of alternatives, ordering, and evaluation issues based on a group fuzzy preferences matrix, which is incapable of obtaining weight coefficients and expected intervals of the sub-attributes. In contrast to group fuzzy preferences matrix, a definition of group intelligence is proposed to describe an alternative to the sub-attribute weight coefficient and expected interval in MAGDM problems. Therefore, the group intelligence generating algorithm is designed under the Genetic Algorithms (GA) framework.

2.1 Background of fuzzy MAGDM methods [12, 19]

In traditional fuzzy MAGDM methods, it is important to convert the person’s different complex judgment preferences into the fuzzy complementary judgment matrix $p^{k} = (p_{ij}^{k})_{n \times n}$ , where $p_{ij}^{k} + p_{ji}^{k} = 1$ , and k is the number of decision-makers. The fuzzy complementary judgment matrices are gathered into the group fuzzy preferences matrix $P^{*} = {(p}_{ij}^{*})_{n \times n}$ . Additionally, based on the gathered group fuzzy preferences matrix, the key step for obtaining the ranking order of the alternatives is shown as follows:

In order to create a new document, do the following:

Set k decision-makers, ξ sub-attributes corresponding to each alternative and n alternatives in MAGDM problems. In addition, u^k is the utility vector, o^k is the ordering relationship value vector, and A^k is the reciprocal judgment matrix. Additionally, ω_l (l ∈ K) is designed as the lth decision-maker’s ordered weight averaging (OWA) operator weight, and $ω_{q}^{*}$ (q ∈ N) is designed as the qth alternative’s OWA operator weight vector.

(1) Conversion methods translate experts’ complex judgment preference of a preferred form [19] to a fuzzy complementary judgment matrix p^k.

(a) The utility vector u^k = $(u_{1}^{k}$ , $u_{2}^{k}$ , ⋯ $u_{n}^{k})^{T}$ (where, $u_{i}^{k}$ ∈ (0, 1) , $\sum_{i = 1}^{k}$ $u_{i}^{k}$ = 1) presents the orders of alternatives, which can be converted to a fuzzycomplementary judgment matrix, where $p_{ij}^{k}$ is the expert’s preference that alternative x_i is betterthan x_j: $p_{ij}^{k} = {\begin{matrix} \begin{matrix} \frac{u_{i}^{k}}{u_{i}^{k} + u_{j}^{k}}, & (u_{i}^{k}, u_{j}^{k}) \neq (0, 0) \end{matrix} \\ \begin{matrix} 0.5, & (u_{i}^{k}, u_{j}^{k}) = (0, 0) \end{matrix} \end{matrix}$ (1)

(b) The ordering relationship value vector $o^{k} = (o_{1}^{k}, o_{2}^{k}, \dots o_{n}^{k})^{T}$ (where $o_{i}^{k} \in K$ ) can be converted to a fuzzy complementary judgment matrix: $p_{ij}^{k} = 0.5 [1 + (o_{j}^{k} - o_{i}^{k}) / (n - 1)]$ (2)

(c) The reciprocal judgment matrix $A^{k} = (a_{ij}^{k})_{n \times n}$ can be converted into a fuzzy complementary judgment matrix to achieve unification: $p_{ij}^{k} = 0.5 + {log}_{c} a_{ij}^{k}$ (3)

Where, φ′ is the maximum possible scaling value of the reciprocal judgment matrix [19]. In particular, the scaling value is 9 in this paper; thus, c = 81.

(2) This section details gathering judgment preferences to the group fuzzy preferences matrix.

(a) The ordered weight averaging (OWA) operator [24] is described in the following.

Firstly, Q (γ) is the fuzzy quantification operator defined by Equation 4. $Q (γ) = {\begin{matrix} \begin{matrix} 0, γ < α \end{matrix} \\ \begin{matrix} \frac{γ - α}{β - α}, α \leq γ \leq β \end{matrix} \\ \begin{matrix} 1, γ > β \end{matrix} \end{matrix}$ (4)

Where, 0 < γ ≤ 1, (α, β) is designed as the decision principle of “majority,” “half at least,” or “as much as possible,” which corresponds to (0.3, 0.8), (0, 0.5), and (0.5, 1), respectively.

Secondly, the OWA operator weight that denotes the lth decision-maker’s weight is expressed as: $ω_{l} = Q (\frac{l}{k}) - Q [(l - 1) / k], l \in K$ (5)

Additionally, the OWA operator weight is constrained by β = 1.

(b) The gathered group fuzzy preferences matrix is described in the following.

We designed the group fuzzy preferences matrix P^* as ${(p}_{ij}^{*})_{n \times n}$ .

Based on the OWA operator weight vector, $p_{ij}^{*}$ denotes the superior degree that the ith alternative is better than the jth alternative in the group judgment, expressed as: $p_{ij}^{*} = φ (p_{ij}^{1}, p_{ij}^{2}, \dots p_{ij}^{k}) = \sum_{l = 1}^{k} ω_{l} b_{ij}^{l}, i, j \in N$ (6) Where, $b_{ij}^{l}$ is the ranked lth element in set ${\begin{matrix} p_{ij}^{1}, & p_{ij}^{2}, & \dots & p_{ij}^{k} \end{matrix}}$ .

(3) This section details the ranking order of the alternative.

(a) The weight vector of the OWA operator for the qth alternative is calculated as follows.

Based on Equation (5), the qth alternative’s OWA operator weight vector is obtained. $ω_{q}^{*} = Q (\frac{q}{n}) - Q [(q - 1) / n], q \in N$ (7)

(b) The superior degree indicating that the ithalternative is more excellent than the other alternatives, is expressed as: $d_{i} = φ (p_{ij}^{*}, j = 1, 2, \dots, n) = \sum_{q = 1}^{n} ω_{q}^{*} c_{i}^{q}, i \in K$ (8)

where $c_{i}^{q}$ is the ranked qth element in set { $p_{ij}^{*}$ | j = 1, 2, ⋯, n}.

Equation 8 yields the ranking result of the ithalternative.

(c) The group consistency deviation index is defined as: $D (ω) = \sum_{i = 1}^{n} \sum_{j = 1}^{n} [\sum_{k = 1}^{m} c_{k} | ω_{i}^{*} - p_{ij}^{* k} (ω_{i}^{*} + ω_{j}^{*}) |]$ (9)

Where, c_k corresponds to the authority of each expert. For simplification, c_k = 1/k in this paper.

2.2 Group intelligence generating algorithm

In order to thoroughly explore the sub-attribute characteristics (sub-attribute weight coefficient and expected interval) in fuzzy MAGDM, a new definition of group intelligence is proposed. Further, in order to reduce expert subjective fatigue in the decision making process, we designed group intelligence generating algorithms, which embeds learning metrics into the decision process. Furthermore, we provide the complex analysis of the algorithms.

(1) Group intelligence generating

Definition 1. In regard to MAGDM problems, group intelligence is described as a three-dimensional vector that consists of the sub-attribute weight coefficient and the expected interval and is expressed as: $Intelligence = {v_{ξ}^{max}, v_{ξ}^{min}, λ_{ξ}}$ (10)

where $v_{ξ}^{max} = φ (\begin{matrix} v_{1}^{max}, & v_{2}^{max}, & \dots & v_{ξ}^{max} \end{matrix}) {, v}_{ξ}^{min} = φ (\begin{matrix} v_{1}^{min}, & v_{2}^{min}, & \dots & v_{ξ}^{min} \end{matrix})$ correspond to each sub-attribute’s expected interval vector (the interval’s upper and lower limits); λ_ξ = = φ (λ₁, λ₂ … λ_ξ) corresponds to each sub-attribute’s priority vector (weight coefficient); and ξ is the number of sub-attributes.

Definition 2. In regards to the group intelligence generating in the MAGDM problems, the decision satisfaction index is expressed as: $I_{j} = \frac{D_{1 j}}{D_{2 j}}$ (11) $D_{1 j} = \sqrt{\sum_{i = 1}^{ξ} λ_{i} \cdot [υ_{ji} - υ_{i}^{min}]^{2}}$ (12)

where Equation (12) represents the Euclidean distance between all of the actual and upper limit values of the jth decision alternative’s sub-attributes, υ_ji corresponds to the value of the jth decision alternative’s ith sub-attribute, υ_i represents the decision alternative value corresponding to the article attributes. $D_{2 j} = \sqrt{\sum_{i = 1}^{ξ} λ_{i} \cdot [υ_{i}^{max} - υ_{i}^{min}]^{2}}$ (13)

where Equation (13) represents the Euclidean distance between all of the upper and lower limit values of the jth decision alternative’s sub-attributes, $υ_{i}^{min}$ is the ith sub-attribute’s expected lower limit value, $υ_{i}^{max}$ is the ith sub-attribute’s expected upper limit value, λ_i corresponds to the ith sub-attribute’s weight coefficient, and i is the number of sub-attributes.

According to Equation (8), the group intelligence generating problems can be converted into a kind of optimization statement, and they can bedescribed by:

$\begin{matrix} \begin{matrix} min & \sum_{j = 1}^{n} (I_{j} - d_{j})^{2} \end{matrix} \\ \begin{matrix} s . t . & I_{j} = \frac{D_{1 j}}{D_{2 j}} \end{matrix} \end{matrix}$ (14)

where I_j is the jth decision alternative’s satisfaction degree, d_j is the superior degree index that is indicated in Equation (8), and j is the number of decision alternatives. The expected upper limit value $υ_{i}^{max}$ and the expected lower limit value $υ_{i}^{min}$ are unknown parameters, and i is the number of sub-attributes. Simultaneously, $\sum_{j = 1}^{ξ} λ_{j} = 1$ .

Key components of the group intelligence generating methods are described as follows: (a) Obtain every expert’s judgment preference (such as u^k, o^k, A^k) of the MAGDM problems. (b) Gather complex experts’ judgment preferences into a group fuzzy preferences matrix (P^*). (c) Obtain the consistency deviation (D (ω)). If D (ω) meets the requirements, continue to the step (d); otherwise, return to step (a). (d) Identify each sub-attribute’s weight coefficients (λ_ξ) and the expected value vector ( $v_{ξ}^{max} {, v}_{ξ}^{min}$ ) based on a binary-encoded Genetic Algorithms (GA). In this step, the fitness function of GA [23] is the objective function in Equation (14). The initial population is represented by staff experience, and the convergence condition is the iterative generations.

The flowchart of group intelligence generating algorithm in regards to MAGDM problems is shown in Fig. 2.

2.3 Complexity research on the group intelligence generating algorithms

Based on Fig. 2, parameters of group intelligence can be identified by GA. Therefore, the complexity analysis for the proposed group intelligence generating algorithms is demonstrated in detail.

1) Time complexity analysis:

The elements of vector λ_ξ and $v_{ξ}^{max} {, v}_{ξ}^{min}$ are parameters to be optimized. Firstly, we specify the parameters of the GA as follows. t is described as the number of evolutionary generations (we set t = 10). χ (t) is designed as the population of the tth generation. ℓ denotes the population size (we set ℓ=40). q corresponds to the chromosome’s length, and the individual in the population was coded by the binary-encoded method. In addition, σ_c is designed as the crossover rate (we set σ_c = 0.9). σ_m is designed as the mutation rate (we set σ_m = 0.9). Ψ is designed as the fitness function (Equation (14)). Thus, the basic statements involved in the algorithms can be summarized as follows. In addition, π indicates the time performance.

Based on the GA, set the initializing parameters (σ_c, σ_m, t, Ψ);

{t = 0;

give the initiating population χ (t); // initiating population randomly (λ_ξ and $v_{ξ}^{max} {, v}_{ξ}^{min}$ (ξ is the number of sub-attributes) in the Equation (10));

obtain the multi-objective fitness index;

for (j = 1; j < t+1; j++)

{

execute the selection operations;

execute the crossover operations;

execute the mutation operations;

achieve chromosome groups;

// calculating the fitness index (Equation (12)) of the next generation;

}

According to statements ➂–➅, the time complexity of the algorithms is π [t × (ℓ × q)].

2) Space complexity analysis:

Space complexity refers to the cost of the storage space in computers when the algorithm is executing. In this sense, the space complexity of a group intelligence generating algorithm is π (ℓ × q).

2.4 Group intelligence-based MADM methods

Based on group intelligence generating algorithms, group intelligence-based decision making methods automatically calculate each overall value of alternatives through linear programming. The key step of the decision-making process is as follows:

(1) The decision-making matrix is expressed as: $\tilde{G} = {({\tilde{g}}_{i j})}_{n \times m}$ (15)

Where, g_ij is the ith sub-attribute value of the jth alternative.

(2) Based on harmonious parameters $v_{ξ}^{max}, v_{ξ}^{min}$ (Equation 10), as described in Equation 14, the standard matrix is written as: $\tilde{F} = {({\tilde{f}}_{i j})}_{n \times m}$ (16)

Where, it is a normalized processing procedure and can be written as: $f_{ij} = (g_{ij} - v_{i}^{min}) / (v_{i}^{max} - v_{i}^{min})$ .

(3) Thus, the comprehensive alternative value of z_j is expressed as: $z_{j} = \sum_{i = 1}^{ξ} f_{ji} λ_{i}$ (17)

Where, λ_i (i = 1, 2, ⋯ ξ) is described as the ith sub-attribute’s weight in λ_ξ (Equation 10).

3 Case studies

3.1 Test functions

The quality of our technique was measured by comparing the results from traditional fuzzy MAGDM approaches [19] to results from the proposed methods. Unlike the traditional fuzzy MAGDM approaches, the proposed method allows experts to only give their judgment preference for parts of the alternatives and have the computer calculate the ranking results of all the alternatives, in order to reduce the human’s subjectivity fatigue.

Consider a MAGDM problem that consists of four decision-makers and five decision-making alternatives, with each alternative containing three sub-attributes {δ₁, δ₂, ⋯ δ₃ } tabulated out in Table 1.

The decision-makers wish obtain the best alternative whose each sub-attribute’s value is as large as possible. In addition, the expected sub-attribute values are (5,8,2). The group consistency deviation index is constrained by D (ω) ≤ 2.0 (Equation (9)).

(1) Traditional fuzzy MAGDM [19]

In this experiment, in order to generate the group fuzzy preferences matrix, each of the 4 decision-makers are assigned a fuzzy complementary judgment matrix, represented as P¹, P², P³, and P⁴: $p^{1} = [\begin{matrix} 0.5 & 0.2 & 0.2 & 0.1 & 1 \\ 0.8 & 0.5 & 0.8 & 0.8 & 1 \\ 0.8 & 0.2 & 0.5 & 0.7 & 1 \\ 0.9 & 0.2 & 0.3 & 0.5 & 1 \\ 0 & 0 & 0 & 0 & 0.5 \end{matrix}]$ $p^{2} = [\begin{matrix} 0.5 & 0.3 & 0.25 & 0.2 & 1 \\ 0.7 & 0.5 & 0.6 & 0.4 & 1 \\ 0.75 & 0.4 & 0.5 & 0.5 & 1 \\ 0.8 & 0.6 & 0.5 & 0.5 & 1 \\ 0 & 0 & 0 & 0 & 0.5 \end{matrix}]$ $p^{3} = [\begin{matrix} 0.5 & 0.4 & 0.7 & 0.4 & 1 \\ 0.6 & 0.5 & 0.5 & 0.6 & 1 \\ 0.3 & 0.5 & 0.5 & 0.65 & 1 \\ 0.6 & 0.4 & 0.35 & 0.5 & 1 \\ 0 & 0 & 0 & 0 & 0.5 \end{matrix}]$ $p^{4} = [\begin{matrix} 0.5 & 0.4 & 0.6 & 0.3 & 1 \\ 0.6 & 0.5 & 0.6 & 0.5 & 1 \\ 0.4 & 0.4 & 0.5 & 0.6 & 1 \\ 0.7 & 0.5 & 0.4 & 0.5 & 1 \\ 0 & 0 & 0 & 0 & 0.5 \end{matrix}]$

(a) Computing the OWA operator.

The OWA operator is obtained under the “majority” principle (0.3, 0.8). According to Equation (5), the OWA operator weight is obtained by: $\begin{matrix} ω_{1} = Q (\frac{1}{4}) - Q [\frac{1 - 1}{4}] \\ = Q (\frac{1}{4}) - Q (0) = 0 - 0 = 0 \\ ⋮ \\ ω_{1} = (0.0000 0.4000 0.5000 0.1000) \end{matrix}$

(b) Gathering the group fuzzy preferences matrix.

According to Equations (6–10), the following are obtained: the superior degree index and the group consistency deviation index d = (0.4600 0.6320 0.6000 0.6020 0.0000), D = 0.4059 < 2.00, and the alternative ranking order of (2, 4, 3, 1, 5).

(2) Group intelligence-based decision making

As compared to the traditional MAGDM approaches, the proposed group intelligence-based decision methods show the convenience and flexibility of the decision process, the group intelligence generating methods towards the same decision problem above are described as follows:

The interval of the unknown group intelligence’s parameters ( $λ_{ξ}, v_{ξ}^{max} {, v}_{ξ}^{min}$ ) are given, which is expressed as:

\begin{matrix} \begin{matrix} {\begin{matrix} 0.2 \leq λ_{1} \leq 0.3 \\ 0.6 \leq λ_{2} \leq 0.7 \\ 0.05 \leq λ_{3} \leq 0.2 \end{matrix}, & {\begin{matrix} 6.5 \leq v_{1}^{max} \leq 7.5 \\ 6.0 \leq v_{2}^{max} \leq 7.0 \\ 2.0 \leq v_{3}^{max} \leq 2.6 \end{matrix}, \\ {\begin{matrix} 3.0 \leq v_{1}^{min} \leq 4.0 \\ 2.0 \leq v_{2}^{min} \leq 3.0 \\ 0.8 \leq v_{3}^{min} \leq 1.2 \end{matrix} \end{matrix} \end{matrix}

(18)

(b) Without requiring the decision-makers to evaluate all five alternatives, the fuzzy complementary preference matrices for the first three alternatives are provided by the four decision makers, which are expressed as: $p 1 = [\begin{matrix} 0.5 0.24 0.24 \\ 0.76 0.5 0.76 \\ 0.76 0.24 0.5 \end{matrix}]$ $p 2 = [\begin{matrix} 0.5 & 0.35 & 0.2 \\ 0.65 & 0.5 & 0.55 \\ 0.8 & 0.45 & 0.5 \end{matrix}]$ $p 3 = [\begin{matrix} 0.5 & 0.45 & 0.62 \\ 0.55 & 0.5 & 0.58 \\ 0.38 & 0.42 & 0.5 \end{matrix}]$ $p 4 = [\begin{matrix} 0.5 & 0.27 & 0.65 \\ 0.73 & 0.5 & 0.6 \\ 0.35 & 0.4 & 0.5 \end{matrix}]$

(d) According to Equation (10), the group consistency deviation index is obtained:

D = 0.2048 < 2.00

Additionally, the group intelligence generating problem can be into a kind of optimization statement (Equation 12).

GA are used to identify the parameters of group intelligence, such as each sub-attribute’s expected upper and lower limits of interval vector $v_{ξ}^{max}, v_{ξ}^{min}$ and sub-attribute’s weight vector λ_ξ of the group intelligence in Equation (10), where ζ = 3.

The fitness function is:

$min \sum_{j = 1}^{3} {(\frac{\sqrt{\sum_{i = 1}^{3} λ_{i} \cdot [υ_{ji} - υ_{i}^{min}]^{2}}}{\sqrt{\sum_{i = 1}^{3} λ_{i} \cdot [υ_{i}^{max} - υ_{i}^{min}]^{2}}} - d_{j})}^{2}$ (20)

where d_j (j = 1, 2, 3) is shown in Equation (19).

There are nine unknown parameters ( $[v_{1}^{max}$ , $v_{2}^{max}$ , $v_{3}^{max}$ , $v_{1}^{min}$ , $v_{2}^{min}$ , $v_{3}^{min}$ , λ₁, λ₂, λ₃]) that need to be identified by the GA. We set the specific parameters (10 generations and 40 individual species coded by the binary encoded method), and the initial individual species are set based on Equation (18) randomly. We then obtain the weight vector of the sub-attributes (0.22, 0.69, 0.09)

Figures 3–5 represent the parameter evolution curves corresponding to parameters λ_ξ, $v_{ξ}^{max}$ , $v_{ξ}^{min}$ of the group intelligence in ten generations.

Finally, the group intelligence is obtained, expressed as: ${\begin{matrix} \begin{matrix} λ_{1} = 0.22 ν_{1}^{min} = 3.51 ν_{1}^{max} = 7.23 \end{matrix} \\ \begin{matrix} λ_{2} = 0.69 ν_{2}^{min} = 2.66 ν_{2}^{max} = 6.27 \end{matrix} \\ \begin{matrix} λ_{3} = 0.09 ν_{3}^{min} = 1.09 ν_{3}^{max} = 2.43 \end{matrix} \end{matrix}$

Then, based on the proposed MAGDM methods shown in Equations 15–17 in Section 2.3, the satisfaction degree index is obtained for all five alternatives: (0.4256, 0.9832, 0.7372, 0.9516, 0.3032). Therefore, the ranking order of the alternative decisions is determined to be (2, 4, 3, 1, 5), thereby verifying the results obtained by traditional methods.

3.2 Applications in TCM dysphagia rehabilitation treatment

(1) Group Intelligence generating

In regards to a patient with a diagnosis based on the ‘mouth period’, a traditional Chinese swallowing dysfunction rehabilitation medicine problem is considered, consisting of eight expert rehabilitation doctors and ten decision-making alternatives, where each alternative contains five sub-attributes {δ₁, δ₂, ⋯ δ₅ } that correspond to the treatment time (minutes) of physical therapy, muscle massage, medicament-induction, functional training, and acupuncture, respectively. Similarly, the group preference consistency deviation degree is constrained by D (ω) ≤ 2.0.

In addition, we give the optimization interval of the unknown group intelligence’s parameters ( $λ_{ξ}, v_{ξ}^{max} {, v}_{ξ}^{min}$ ), which is expressed as: $\begin{matrix} \begin{matrix} {\begin{matrix} \begin{matrix} 0.30 \leq λ_{1} \leq 0.50 \\ 0.15 \leq λ_{2} \leq 0.25 \\ 0.05 \leq λ_{3} \leq 0.15 \end{matrix} \\ \begin{matrix} 0.10 \leq λ_{4} \leq 0.20 \\ 0.20 \leq λ_{5} \leq 0.30 \end{matrix} \end{matrix}, & {\begin{matrix} \begin{matrix} 4.0 \leq v_{1}^{min} \leq 6.0 \\ 5.5 \leq v_{2}^{min} \leq 7.5 \\ 7.0 \leq v_{3}^{min} \leq 9.0 \end{matrix} \\ \begin{matrix} 6.0 \leq v_{4}^{min} \leq 8.0 \\ 5.0 \leq v_{5}^{min} \leq 7.0 \end{matrix} \end{matrix}, \\ {\begin{matrix} \begin{matrix} 10 \leq v_{1}^{max} \leq 15 \\ 15 \leq v_{2}^{max} \leq 20 \\ 15 \leq v_{3}^{max} \leq 25 \end{matrix} \\ \begin{matrix} 20 \leq v_{4}^{max} \leq 30 \\ 20 \leq v_{5}^{max} \leq 30 \end{matrix} \end{matrix} \end{matrix} \end{matrix}$ (21)

Several decision-making alternatives are provided in Table 2.

(a) In regards to the ten alternatives, the Utility vectors for the eight decision makers are expressed as: $\begin{matrix} u_{1} = [1, 10, 2, 3, 4, 5, 6, 7, 8, 9] \\ u_{2} = [9, 10, 3, 5, 7, 8, 4, 6, 2, 1] \\ u_{3} = [3, 7, 4, 9, 5, 8, 6, 10, 2, 1] \\ u_{4} = [5, 3, 10, 2, 6, 1, 7, 9, 8, 4] \\ u_{5} = [5, 9, 4, 1, 7, 6, 10, 3, 8, 2] \\ u_{6} = [6, 5, 3, 7, 8, 2, 9, 4, 1, 10] \\ u_{7} = [1, 3, 4, 7, 6, 8, 9, 10, 5, 2] \\ u_{8} = [3, 5, 1, 2, 4, 10, 8, 9, 7, 6] \end{matrix}$

(b) Similarly, based on Equation (8), the superior degree index is obtained: $\begin{matrix} d = [0.6239, 0.4733, 0.6511, 0.6083, 0.5156, \\ 0.5000, 0.4217, 0.4209, 0.5561, 0.6317] \end{matrix}$ (22)

D = 1.02 < 2.00

Similarly, the group intelligence generating problem can be into a kind of optimization statement (Equation 12).

The fitness function is; $min \sum_{j = 1}^{10} {(\frac{\sqrt{\sum_{i = 1}^{5} λ_{i} \cdot [υ_{ji} - υ_{i}^{min}]^{2}}}{\sqrt{\sum_{i = 1}^{5} λ_{i} \cdot [υ_{i}^{max} - υ_{i}^{min}]^{2}}} - d_{j})}^{2}$ (23)

where d_j (j = 1, 2, ⋯ 10) is shown in Equation (22).

There are fifteen unknown parameters ( $[v_{1}^{max}$ , $v_{2}^{max}$ , $v_{3}^{max}$ , $v_{4}^{max}$ , $v_{5}^{max}$ , $v_{1}^{min}$ , $v_{2}^{min}$ , $v_{3}^{min}$ , $v_{4}^{min}$ , $v_{5}^{min}$ , λ₁, λ₂, λ₃, λ₄, λ₅]) that need to be identified by the GA. We set the specific parameters (10 generations and 40 individual species coded by the binary encoded method), and the initial individual species are set based on Equation (20) randomly. Figures 6–8 represent the parameter evolution curves corresponding to parameters λ. V^max and v^min of the group intelligence in ten generations, respectively.

Finally, the group preferences are obtained, expressed as: ${\begin{matrix} \begin{matrix} λ_{1} = 0.384 v_{1}^{min} = 4.684 v_{1}^{max} = 13.768 \end{matrix} \\ \begin{matrix} λ_{2} = 0.173 v_{2}^{min} = 7.431 v_{2}^{max} = 18.174 \end{matrix} \\ \begin{matrix} λ_{3} = 0.090 v_{3}^{min} = 6.254 v_{3}^{max} = 21.317 \end{matrix} \\ \begin{matrix} \begin{matrix} λ_{4} = 0.115 v_{4}^{min} = 7.543 v_{4}^{max} = 26.483 \end{matrix} \\ \begin{matrix} λ_{5} = 0.238 v_{5}^{min} = 6.831 v_{5}^{max} = 22.925 \end{matrix} \end{matrix} \end{matrix}$

Therefore, based on the proposed MADM methods (presented by Equations 15–17 in Section 3.2), the ranking order of all ten alternatives is obtained: (3,10,1,4,9,5,6,2,7,8).

(2) Test of Medical Statistics

Thirty samples of the same symptom can be used as convincing statistical data in the medical statistics field [8]. Thirty samples with a diagnosis in the “mouth period” in the Beijing Zhongguancun Hospital physical rehabilitation department were used to verify the correctness of the proposed MADM method.

In this experiment, three expert doctors were employed to give their expert consultation solution based on every patient, while the computer will give its treatment solution based on the proposed MADM method.

Table 3 demonstrates the treatment strategies comparison between the proposed group intelligence-based decision making method and the experts’ consultation (which is expressed in the Appendix). Figure 9 illustrates a comparison of the time in minutes of the five treatment attributes (physical treatment, massage, etc.) between the proposed method and the expert consultation solution.

The consistency index [28] of the diagnosis and treatment is expressed as: $β = 1 - | φ^{'} - φ | / φ$ (24)

where φ′ is the result of the proposed MADM method, φ′ is the result of the expert consultation, |φ′ - φ|/φ is the relative error of the treatment solution, and β ∈ [0 1]. If β = 1, then the results of the proposed MADM method and the expert consultation are completely consistent.

Based on Table 3, it can be concluded that the average consistency index is 0.95 in the comparison between the proposed MADM method and the consultation of doctors.

4 Discussion

In order to reflect the differences between the traditional fuzzy MAGDM and the group intelligence-based decision making methods proposed in this paper, a novel definition of group intelligence was presented. A Genetic Algorithm (GA) was employed to realize the interactive generating algorithms for the group intelligence.

Based on the experiment described in Section 3.1, the traditional fuzzy MAGDM methods sacrifice flexibility and analysis speed by requiring a judgment preference for each alternative. In contrast to traditional approaches, our proposed decision method utilizes only the first three alternatives to generate the group preferences (Figs. 3–5), which can be used to determine the ordering of the remaining two alternatives. With the same decision results, the proposed decision methods (Section 2.4) based on group intelligence generating are capable of gradually learning the group’s judgment preference in decision-making and reducing their subjective fatigue.

In addition, a traditional Chinese medicine rehabilitation treatment problem was designed in Section 3.2. To overcome the traditional Chinese rehabilitation medicine example, wherein expert doctors’ treatment preferences lack quantitative descriptions, the proposed methods were used to obtain a treatment weight and time (Figs. 6–9) of different TCM techniques (i.e., physical therapy, massage, and acupuncture) for a patient with dysphagia.

In the end, the proposed decision methods based on the group intelligence did not decrease the decision accuracy.

5 Conclusions

In order to provide beneficial methods for determining group intelligence in MAGDM, innovative definitions of group intelligence based on the weight coefficient and the expected interval of each sub-attribute were proposed. The group intelligence generating algorithms were explicitly proposed, which embedded learning metrics into the decision process, thus helping reduce subjective fatigue in the humans. In addition, a complexity analysis was presented that helped ensure the accuracy of the MAGDM results. In the end, a test function and a kind of medical MAGDM problem addressing Traditional Chinese medical (TCM) dysphagia rehabilitation treatment were used to verify the correctness and feasibility of the proposed methods.

Nonetheless, it should be acknowledged that this research is rudimentary, and as such, there are some challenges for the algorithm proposed in this paper. For example, (1) a large number of the parameters should be optimized when the number of attributes is excessive; thus, a heavy searching burden is suffered. Therefore, in future work, machine learning methods, such as Principal Component Analysis (PCA) and Deep learning (DL), and so on, can be used to extract the sub-attribute’s feature to optimize the generating process of group intelligence. Additionally, (2) it is very boring that each expert must give his judgment preference, such as a utility vector and so on, in the decision process. Deep research can be conducted on the ‘human’s affective—human’s preference’ mapping approaches based on affect computing methods, and the harmonious of the interaction can be improved.

Footnotes

Appendix

Table 3

Treatment strategies comparison between the proposed method and the experts’ consultation

Patient with	The group intelligence based decision making methods					Consultation of expert doctors
diagnosis	Physical	Muscle	Medicament-	Functional	Acupuncture	Physical	Muscle	Medicament-	Functional	Acupuncture
‘mouth-	therapy	massage	induction	training	(min)	therapy	massage	induction	training	(min)
period’	(min)	(min)	(min)	(min)		(min)	(min)	(min)	(min)
1	12	11	16	19	19	12	12	16	18	19
2	12	12	17	18	18	12	12	17	19	18
3	10	13	15	20	20	11	13	16	19	20
4	11	12	18	15	19	11	13	19	16	17
5	12	14	17	20	18	12	12	17	20	16
6	9.5	12	17	18	18	10	11	17	18	16
7	8.5	15	17	16.5	18	9	13	16	16	18
8	9.5	14	15	19.5	16	10	12	14	20	16
9	9	13	16	16	16	9	13	15	16	15
10	11.5	15	16	18	18	11	14	15	18	16
11	10.5	12	19	18	20	10	12	12	18	20
12	13	10	21	18	20	13	10	20	18	20
13	12.5	11	20	15.5	22	13	10	20	15	22
14	12.5	11	19	17	18	13	10	20	16	16
15	11	14	17	17	18	11	14	15	16	19
16	12	13	16	20	16	12	12	15	20	16
17	11	16	19	21.5	18	10	16	18	20	18
18	10.5	15	19	21	18	11	14	20	20	18
19	9.5	16	20	19.5	20	10	16	20	20	18
20	12	14	17	18	16	12	14	18	18	15
21	9	15	15	17	15	9	16	16	18	15
22	11	14	17	18	16	11	14	18	19	15
23	9.5	12	17	18	18	10	12	18	18	18
24	10	11	15	20.5	16	10	10	15	20	15
25	12.5	16	15	18	16	12	15	15	18	15
26	11.5	11	21	16.5	20	11	10	20	18	20
27	11	15	20	17.5	22	11	14	20	18	22
28	10	12	21	18	20	10	12	20	18	20
29	12.5	12	18	15.5	18	13	12	18	16	18
30	11	15	19	16	18	11	16	20	16	18

Acknowledgments

This study is supported by the Open Research Project under Grant from SKLMCCS (20150103), the Beijing outstanding talent training Project (2015000020124G041), the Fundamental Research Funds for the Central Universities (YS1404) and the National Natural Science Foundation of China (61603023).

The authors Jie Chen and Chong Su contributed equally to this work and should be considered co-first authors.

References

Liu

A.P.

, Jiang

, Zhang

, et al., An integrative approach of linking traditional Chinese medicine pattern classification and biomedicine diagnosis, Journal of Ethnopharmacology141 (2012), 549–556.

Liu

B.S.

, Shen

Y.H.

, Chen

, et al., A two-layer weight determination method for complex multi-attribute large-group decision-making experts in a linguistic environment, Information Fusion23 (2015), 156–165.

Sun

B.Z.

and Ma

W.M.

, An approach to consensus measurement of linguistic preference relations in multi-attribute group decision making and application, Omega51 (2015), 83–92.

Liu

B.S.

, Shen

Y.H.

, Zhang

, et al., An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making, Soft Computing18 (2013), 209–225.

Zhang

, Jiang

, Chen

, et al., Incorporation of traditional Chinese medicine pattern diagnosis in the management of rheumatoid arthritis, European Journal of Integrative Medicine4 (2012), 245–254.

C.J.

, Deng

J.W.

, Li

, et al., Application of metabolomics on diagnosis and treatment of patients with psoriasis in traditional Chinese medicine, Biochimica et Biophysica Acta18 (2014), 280–288.

Williams

D.M.

and Raynor

H.A.

, Disentangling the effects of choice and intensity on affective response to and preference for self-selected- versus imposed-intensity physical activity, Psychology of Sport and Exercise14 (2013), 767–775.

Cheek

and Rajkumar

, How to present statistics in medical journals, Age and Ageing43 (2014), 306–308.

Liu

, Zhang

W.G.

and Zhang

L.H.

, A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices, Fuzzy Sets and Systems246 (2014), 1–18.

10.

F.C.

, Chung

S.H.

, Cheng

C.Y.

, et al., How to standardize the pulse-taking method of traditional Chinese medicine pulse diagnosis, Computers in Biology and Medicine43 (2013), 342–349.

11.

Xia

H.C.

, Li

D.F.

, Zhou

J.Y.

, et al., Fuzzy LINMAP method for multiattribute decision making under fuzzy environments, Journal of Computer and System Sciences72 (2006), 741–759.

12.

Behret

, Group decision making with intuitionistic fuzzy preference relations, Knowledge-Based Systems70 (2014), 33–43.

13.

Hassan

H.E.

and Aboloyoun

A.I.

, The value of bedside tests in dysphagia evaluation, Egyptian Journal of Ear, Nose, Throat and Allied Sciences15 (2014), 197–203.

14.

Golbeck

and Hansen

, A method for computing political preference among Twitter followers, Social Networks36 (2014), 177–184.

15.

Rezaei

, Best-worst multi-criteria decision-making method, Omega53 (2015), 49–57.

16.

Svobodova

, Sklenicka

, Molnarova

, et al., Does the composition of landscape photographs affect visual preferences? The rule of the Golden Section and the position of the horizon, Journal of Environmental Psychology38 (2014), 143–152.

17.

Qin

J.D.

and Liu

X.W.

, Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment, Information Sciences297 (2015), 293–315.

18.

Lan

J.B.

, Sun

, Chen

Q.M.

, et al., Group decision making based on induced uncertain linguistic OWA operators, Decision Support Systems55 (2013), 296–303.

19.

, Fan

Z.P.

and Jiang

Y.P.

, An optimization approach to multiperson decision making based on different formats of preference information, IEEE Transactions on Systems, Man and Cyberbetics-Part A: Systems and Humans36 (2006), 876–889.

20.

Fields

, Go

J.T.

and Schulze

K.S.

, Pill properties that cause dysphagia and treatment failure, Current Therapeutic Research77 (2015), 79–82.

21.

Huang

K.L.

, Liu

T.Y.

, Huang

Y.C.

, et al., Functional outcome in acute stroke patients with oropharyngeal dysphagia after swallowing therapy, Journal of Stroke and Cerebrovascular Diseases23 (2014), 2547–2553.

22.

Grassi

, Cambria

, Hussain

, et al., Sentic web: A new paradigm for managing social media affective information, Cogn Comput3 (2011), 480–489.

23.

Cai

, He

and Man

, Imbalanced evolving self-organizing learning, Neurocomputing133 (2014), 258–270.

24.

Yager

R.R.

, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man and Cyberbetics18 (1988), 183–190.

25.

Enric

S.N.

, Marcos

F.Z.

and Jiri

, An information analysis of in-air and on-surface trajectories in online handwriting, Cogn Comput4 (2012), 195–205.

26.

Paulo

, Pedro

, Jose

, et al., An expert system for supporting Traditional Chinese Medicine diagnosis and treatment, Procedia Technology16 (2014), 1487–1492.

27.

Volker

, Veronica

, Thomas

, et al., Chinese medicine treatment for menopausal symptoms in the UKhealth service: Is a clinical trial warranted?Maturitas80 (2015), 179–186.

28.

Evan

S.D.

, Cary

C.C.

and Jessica

H.W.

, Accuracy of the eosinophilic esophagitis endoscopic reference score in diagnosis and determining response to treatment, Clinical Gastroenterology and Hepatology14 (2016), 31–39.

29.

Navaneethan

and Eubanks

, Approach to patients with esophageal dysphagia, Surgical Clinics of North America95 (2015), 483–489.

30.

Wang

W.Z.

and Liu

X.W.

, An extended LINMAP method for multi-attribute group decision making under interval-valued intuitionistic fuzzy environment, Procedia Computer Science17 (2013), 490–497.

31.

Wang

X.W.

, Qu

H.B.

, Liu

, et al., A self-learning expert system for diagnosis in traditional Chinese medicine, Expert Systems with Applications26 (2004), 557–566.

32.

Yan

, Wang

W.D.

, Walters

A.S.

, et al., Traditional Chinese medicine herbal preparations in restless legs syndrome (RLS) treatment: A review and probable first description of RLS in, Sleep Medicine Reviews16 (2012), 509–518.

33.

Jiang

Y.P.

and Fan

Z.P.

, Judgment Matrix Based On Decision Theory and Method, Science Press, Beijing, 2008, pp. 163–175.

34.

Z.S.

, Uncertain Multiple Attribute Decision Making Methods and Applications, Tsinghua University Press, Beijing, 2004, pp. 100–150.

35.

Z.S.

and Yager

R.R.

, Dynamic intuitionistic fuzzy multi-attribute decision making, Approximate Reasoning48 (2008), 246–262.

36.

Wang

Z.J.

, Li

K.W.

and Xu

J.H.

, A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information, Expert Systems with Applications38 (2011), 12462–12469.

37.

Z.X.

, Chen

M.Y.

, Xia

G.P.

and Wang

, An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making, Expert Systems with Applications38 (2011), 15286–15295.

38.

Z.S.

and Zhang

X.L.

, Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information, Knowledge-Based Systems52 (2013), 53–64.