Engineering geological environment comprehensive evaluation with intuitionistic fuzzy information

Abstract

Evaluation of engineering geological environment and construction of urban layout compose a multi-factors and multi-levels process. How to choose and use condition of engineering geological environment, protect and control the possible engineering geological problem, reduce the occurrence of geological hazard is very important in urban layout. In this paper, we investigate the engineering geological environment comprehensive evaluation with intuitionistic fuzzy information. Motivated by the ideal of dependent aggregation, we shall propose the dependent intuitionistic fuzzy Hamacher weighted average(DIFHWA) operator, in which the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to those “false” and “biased” ones and then apply this operator to develop an approach for engineering geological environment comprehensive evaluation with intuitionistic fuzzy numbers. Finally, an illustrative example for engineering geological environment comprehensive evaluation is given to verify the developed approach.

Keywords

Intuitionistic fuzzy information operational laws dependent intuitionistic fuzzy Hamacher weighted average(DIFHWA) operator engineering geological environment comprehensive evaluation

1 Introduction

The groundwater and infiltration of rain and water is one of the most important factors that result in the highway geology disaster and the highway water damage, the construction of highway will not only meantime result in variety or break of groundwater and the earth’s surface water environment, but also influence the ecological environment, condition of living and production. The water seepage mechanism is the theoretical foundation that carries on highway waterproof and drainage design, influence evaluation and environmental protection design of groundwater and the earth’s surface water environment. The research of water seepage mechanism of highway is necessary very much. The water seepage mechanism of highway is the overlapping research realm of the highway engineering technique and the hydrogeology, the rock mechanics, the soil mechanics, the groundwater dynamics, it is science to inquire the groundwater flow and distribution regulation in highway engineering, to guide reasonably waterproof and drainage of the highway engineering, to protect highway engineering and groundwater environment in the construction and service activity of highway engineering. It involves the problems of highway engineering technique, groundwater storage, the seepage calculation, conduction and drainage of groundwater, protection of groundwater, etc. In the highway engineering, the water will make that roadbed become wet and soft, the groundwater water pressure enlarge, the strength of the roadbed and pavement be lower, then causes roadbed to sink, slope to freeze, expand, landslide and collapse, glide...etc, even make the whole roadbed to glide. The humidity that enters the bituminous pavement structure layer will wet the grain of inorganic bond, cause that the strength of the pavement structure layer be lower, the car of heavy load causes high-speed water current to scour of the pavement structure layer. When the temperature lowers to freeze, the pavement structure layer will be frost upheaval, making the bituminous pavement structure layer appear peeling off, loose and with pit pond etc. When the cement concrete pavement is at repeat pressure of heavy load vehicle, the water pressure in the cement concrete pavement will be great, the pavement clearance expand quickly, then the tiny grain of the joint neighborhood will be soften, the cement concrete pavement will spurt silt, cutting will take place under the cement concrete pavement, finally they cause cracking, broking joints, splitting and etc of the cement concrete pavement. The geologic disaster will take place, when the condition of groundwater or the moisture is changed in the special soil. The groundwater makes the country rock of the highway tunnel to dissolve, sour and soften, then lowers strength of the country rock. The groundwater not only influences stability and construction of the tunnel, but also may bring hidden safe dangers. The groundwater, infiltrating rain and water will worse highway seriously, lower the service quality of the highway engineering, increase the cost of maintenance of the highway engineering. The character and seepage path of the groundwater may be influenced and broken in the highway construction and service, it make in water shortage or water harm, the pollution of groundwater, and influence water environment, normal production and life of peripheral residents.There is a little research in water seepage mechanism of highway, the existing related research is the conduction and drainage at the earth’s surface water, the simple calculation of the saturated seepage, the design and construction of waterproof and drainage at the direct observation experience, there is no or a few research on influence of the storage and conduction of groundwater with the highway engineering, on the seepage regulation of rain infiltration in the highway engineering structure.

Engineering geological environment evaluation is an important work. Properly determine suitable land use not only is a foundation of various special topic planning but also has important influence on city allocation plan and economic development. Engineering geological environment evaluation relation to naturalism, economy, environment, engineering etc and various factors have variant influence degree. Presently, most of cities in China use method of qualitative analysis in engineering geological environment evaluation and this method has many shortcomings, such as need great investigation workload, difficultly unified standards, lowly spatialization accuracy, quantitative study is not easy and with great subjectivity in city planning. The various aspect problems in city construction are more and more complex with cities’ scale and up-to-dateness continuously growing. The requirements of accuracy on engineering geological environment evaluation are higher and higher and classical method of qualitative analysis is unable to meet the challenge of city planning and proper exploitation and utilization of land resources. A scientific and accurate method of engineering geological environment evaluation is necessary. The problems of engineering geological environment comprehensive evaluation with intuitionistic fuzzy information is the multiple attribute decision making problems [1 –12]. In this paper, we investigate the multiple attribute decision making for engineering geological environment comprehensive evaluation with intuitionistic fuzzy information. Motivated by the ideal of dependent aggregation, we shall propose the dependent intuitionistic fuzzy Hamacher weighted average (DIFHWA) operator, in which the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to those “false” and “biased” ones and then apply this operator to develop an approach for engineering geological environment comprehensive evaluation with intuitionistic fuzzy numbers. Finally, an illustrative example for engineering geological environment comprehensive evaluation is given to verify the developed approach.

In order to do so, the remainder of this paper is set out as follows. In the next section, we introduce some concepts of the intuitionistic fuzzy sets. In Section 3, we develop the dependent intuitionistic fuzzy Hamacher weighted average(DIFHWA) operator. In Section 4, we apply the dependent intuitionistic fuzzy Hamacher weighted average(DIFHWA) operator to deal with multiple attribute decision making for engineering geological environment comprehensive evaluation with intuitionistic fuzzy information. In Section 5, an illustrative example for engineering geological environment comprehensive evaluation is given. In Section 6 we conclude the paper and give some remarks.

2 Preliminaries

In the following, we introduce some basic concepts related to IFS.

Definition 1. [13, 14] An IFS A in X is given by $A = {〈 x, μ_{A} (x), ν_{A} (x) 〉 | x \in X}$ (1)

where μ_A : X → [0, 1] and ν_A : X → [0, 1], with the condition 0 ≤ μ_A (x) + ν_A (x) ≤ 1, ∀ x ∈ X.

Definition 2. [15] Let $\tilde{a} = (μ, ν)$ be an intuitionistic fuzzy number, a score function S of an intuitionistic fuzzy value can be represented as follows: $S (\tilde{a}) = μ - ν, S (\tilde{a}) \in [- 1, 1] .$ (2)

Definition 3. [16] Let $\tilde{a} = (μ, ν)$ be an intuitionistic fuzzy number, an accuracy function H of an intuitionistic fuzzy value can be represented as follows: $H (\tilde{a}) = μ + ν, H (\tilde{a}) \in [0, 1] .$ (3)

Xu [17] give an order relation between two intuitionistic fuzzy values.

Definition 4. Let ${\tilde{a}}_{1} = (μ_{1}, ν_{1})$ and ${\tilde{a}}_{2} = (μ_{2}, ν_{2})$ be two intuitionistic fuzzy values, $s ({\tilde{a}}_{1}) = μ_{1} - ν_{1}$ and $s ({\tilde{a}}_{2}) = μ_{2} - ν_{2}$ be the scores of $\tilde{a}$ and $\tilde{b}$ , respectively, and let $H ({\tilde{a}}_{1}) = μ_{1} + ν_{1}$ and $H ({\tilde{a}}_{2}) = μ_{2} + ν_{2}$ be the accuracy degrees of $\tilde{a}$ and $\tilde{b}$ , respectively, then if $S (\tilde{a}) < S (\tilde{b})$ , then $\tilde{a}$ is smaller than $\tilde{b}$ , denoted by $\tilde{a} < \tilde{b}$ ; if $S (\tilde{a}) = S (\tilde{b})$ , then

(1) if $H (\tilde{a}) = H (\tilde{b})$ , then $\tilde{a}$ and $\tilde{b}$ represent the same information, denoted by $\tilde{a} = \tilde{b}$ ; (2) if $H (\tilde{a}) < H (\tilde{b})$ , $\tilde{a}$ is smaller than $\tilde{b}$ , denoted by $\tilde{a} < \tilde{b}$ .

3 Dependent intuitionistic fuzzy Hamacher weighted average (DIFHWA) operator

In this section, we shall introduce the Hamacher operations on intuitionistic fuzzy sets [18] and analyze some desirable properties of these operations. Let the t-norm T and t-conorm S be Hamacher product T” and Hamacher sum S” respectively, then the generalised intersection and union on two IFSs A and B become the Hamacher product (denoted by ${\tilde{a}}_{1} \otimes {\tilde{a}}_{2}$ ) and Hamacher sum (denoted by ${\tilde{a}}_{1} \oplus {\tilde{a}}_{2}$ ) on two IFSs ${\tilde{a}}_{1}$ and ${\tilde{a}}_{2}$ , respectively, as follows. $\begin{matrix} {\tilde{a}}_{1} \oplus {\tilde{a}}_{2} & = & (\frac{μ_{1} + μ_{2} - μ_{1} μ_{2} - (1 - γ) μ_{1} μ_{2}}{1 - (1 - γ) μ_{1} μ_{2}}, \\ \frac{ν_{1} ν_{2}}{γ + (1 - γ) (ν_{1} + ν_{2} - ν_{1} ν_{2})}) \\ λ {\tilde{a}}_{1} & = & (\frac{{(1 + (γ - 1) μ_{1})}^{λ} - {(1 - μ_{1})}^{λ}}{{(1 + (γ - 1) μ_{1})}^{λ} + (γ - 1) {(1 - μ_{1})}^{λ}}, \\ \frac{γ {(ν_{1})}^{λ}}{{(1 + (γ - 1) (1 - ν_{1}))}^{λ} + (γ - 1) {(ν_{1})}^{λ}}) λ > 0 . \end{matrix}$

Definition 5. [18] Let ${\tilde{a}}_{j} = (μ_{j}, ν_{j})$ (j = 1, 2, ⋯ , n) be a collection of Intuitionistic fuzzy numbers, then their aggregated value by using the intuitionistic fuzzy Hamacher weighted averaging (IFHWA) operator is also an IFN, and

$\begin{matrix} {IFHWA}_{ω} ({\tilde{a}}_{1}, {\tilde{a}}_{2}, \dots, {\tilde{a}}_{n}) \\ = {\oplus_{ɛ}}_{j = 1}^{n} (ω_{j} {\tilde{a}}_{j}) \\ = (\frac{\prod_{j = 1}^{n} {(1 + (γ - 1) μ_{j})}^{ω_{j}} - \prod_{j = 1}^{n} {(1 - μ_{j})}^{ω_{j}}}{\prod_{j = 1}^{n} {(1 + (γ - 1) μ_{j})}^{ω_{j}} + (γ - 1) \prod_{j = 1}^{n} {(1 - μ_{j})}^{ω_{j}}}, \\ \frac{γ \prod_{j = 1}^{n} ν_{j}^{ω_{j}}}{\prod_{j = 1}^{n} {(1 + (γ - 1) (1 - ν_{j}))}^{ω_{j}} + (γ - 1) \prod_{j = 1}^{n} ν_{j}^{ω_{j}}}) \end{matrix}$ (4)

where ω = (ω₁, ω₂, ⋯ , ω_n) ^T be the weight vector of ${\tilde{a}}_{j} (j = 1, 2, \dots, n)$ , and ω_j > 0, $\sum_{j = 1}^{n} ω_{j} = 1$ .

Definition 6. Let ${\tilde{a}}_{j} = (μ_{j}, ν_{j}) (j = 1, 2, \dots, n)$ be a group of intuitionistic fuzzy numbers, the average value of the score function of ${\tilde{a}}_{j} (j = 1, 2, \dots, n)$ is computed as $s (\tilde{a}) = \frac{\sum_{j = 1}^{n} s ({\tilde{a}}_{j})}{n}$ (5)

Definition 7. Let ${\tilde{a}}_{1} = (μ_{1}, ν_{1})$ and ${\tilde{a}}_{2} = (μ_{2}, ν_{2})$ be two intuitionistic fuzzy numbers, then the Hamming distance between ${\tilde{a}}_{1} = (μ_{1}, ν_{1})$ and ${\tilde{a}}_{2} = (μ_{2}, ν_{2})$ is defined as follows [19]:

$\begin{matrix} d ({\tilde{a}}_{1}, {\tilde{a}}_{2}) d ({\tilde{a}}_{1}, {\tilde{a}}_{2}) \\ = \frac{| μ_{1} - μ_{2} | + | ν_{1} - ν_{2} |}{2} \end{matrix}$ (6)

Definition 8. Let ${\tilde{a}}_{j} = (μ_{j}, ν_{j}) (j = 1, 2, \dots, n)$ be a group of intuitionistic fuzzy numbers, then we call

$\begin{matrix} sim (s ({\tilde{a}}_{j}), s (\tilde{a})) & = & 1 - \frac{d (s ({\tilde{a}}_{j}), s (\tilde{a}))}{\sum_{j = 1}^{n} d (s ({\tilde{a}}_{j}), s (\tilde{a}))}, \\ j & = & 1, 2, \dots, n . \end{matrix}$ (7)

the degree of similarity between the intuitionistic fuzzy values $s ({\tilde{a}}_{j})$ and the mean $s (\tilde{a})$

In real-life situations, the intuitionistic fuzzy numbers ${\tilde{a}}_{j} = (μ_{j}, ν_{j}) (j = 1, 2, \dots, n)$ usually take the form of a collection of n preference values provided by n different individuals. Some individuals may assign unduly high or unduly low preference values to their preferred or repugnant objects. In such a case, we shall assign very low weights to these “false” or “biased” opinions, that is to say, the closer a preference value (argument) is to the mid one(s), the more the weight [20, 21]. As a result, based on (7), we define the IFHWA operator weights as $w_{j} = \frac{sim (s ({\tilde{a}}_{j}), s (\tilde{a}))}{\sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))}, j = 1, 2, \dots, n$ (8)

Obviously, w_j ≥ 0, j = 1, 2, ⋯ , n and $\sum_{j = 1}^{n} w_{j} = 1$ .

Especially, if $s ({\tilde{a}}_{j}) = s (\tilde{a})$ , for all i, j = 1, 2, ⋯ , n, then by (8), we have $w_{j} = \frac{1}{n}$ , for all j = 1, 2, ⋯ , n.

By (4), we have

$\begin{matrix} IFHWA ({\tilde{a}}_{1}, {\tilde{a}}_{2}, \dots, {\tilde{a}}_{n}) \\ = \oplus_{j = 1}^{n} (\frac{sim (s ({\tilde{a}}_{j}), s (\tilde{a}))}{\sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))} {\tilde{a}}_{j}) \\ = (\frac{\prod_{j = 1}^{n} {(1 + (γ - 1) μ_{j})}^{sim (s ({\tilde{a}}_{j}), s (\tilde{a})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))} - \prod_{j = 1}^{n} {(1 - μ_{j})}^{sim (s ({\tilde{a}}_{j}), s (\tilde{a})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))}}{\prod_{j = 1}^{n} {(1 + (γ - 1) μ_{j})}^{sim (s ({\tilde{a}}_{j}), s (\tilde{a})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))} + (γ - 1) \prod_{j = 1}^{n} {(1 - μ_{j})}^{sim (s ({\tilde{a}}_{j}), s (\tilde{a})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))}}, \\ \frac{γ \prod_{j = 1}^{n} ν_{j}^{sim (s ({\tilde{a}}_{j}), s (\tilde{a})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))}}{\prod_{j = 1}^{n} {(1 + (γ - 1) (1 - ν_{j}))}^{sim (s ({\tilde{a}}_{j}), s (\tilde{a})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))} + (γ - 1) \prod_{j = 1}^{n} ν_{j}^{sim (s ({\tilde{a}}_{j}), s (\tilde{a})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{j}), s (\tilde{a}))}}) \end{matrix}$ (9)

We call (9) a dependent intuitionistic fuzzy Hamacher weighted average (DIFHWA) operator.

4 Model for comprehensive evaluation with intuitionistic fuzzy information

In this section, we shall apply DIFHWA operator to the comprehensive evaluation problems with intuitionistic fuzzy numbers. Let A ={ A₁, A₂, ⋯ , A_m } be a discrete set of alternatives, and G ={ G₁, G₂, ⋯ , G_n } be the set of attributes. Suppose that $\tilde{R} = {({\tilde{r}}_{ij})}_{n \times m} = {(μ_{ij}, ν_{ij})}_{n \times m}$ is the intuitionistic fuzzy evaluation matrix, μ_ij ⊂ [0, 1], ν_ij ⊂ [0, 1], μ_ij + ν_ij ≤ 1, i = 1, 2, ⋯ , m, j = 1, 2, ⋯ , n,

In the following, we apply the DIFHWA operator to comprehensive evaluation problem with intuitionistic fuzzy information. The method involves the following steps:

Step 1. Utilize the evaluation information given in matrix $\tilde{R}$ , and the DIFHWA operator $\begin{matrix} {\tilde{r}}_{i} = (μ_{i}, ν_{i}) = DIFHWA ({\tilde{r}}_{i 1}, {\tilde{r}}_{i 2}, \dots, {\tilde{r}}_{in}) = \oplus_{j = 1}^{n} (\frac{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))}{\sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))} {\tilde{a}}_{ij}) \\ = (\frac{\prod_{j = 1}^{n} {(1 + (γ - 1) μ_{ij})}^{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))} - \prod_{j = 1}^{n} {(1 - μ_{ij})}^{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))}}{\prod_{j = 1}^{n} {(1 + (γ - 1) μ_{ij})}^{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))} + (γ - 1) \prod_{j = 1}^{n} {(1 - μ_{ij})}^{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))}}, \\ \frac{γ \prod_{j = 1}^{n} ν_{ij}^{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))}}{\prod_{j = 1}^{n} {(1 + (γ - 1) (1 - ν_{ij}))}^{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))} + (γ - 1) \prod_{j = 1}^{n} ν_{ij}^{sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i})) / \sum_{j = 1}^{n} sim (s ({\tilde{a}}_{ij}), s ({\tilde{a}}_{i}))}}) \end{matrix}$

Step 2. Calculate the scores $S ({\tilde{r}}_{i}) (i = 1, 2, \dots, m)$ of the collective overall values ${\tilde{r}}_{i} (i = 1, 2, \dots, m)$ to rank all the alternatives A_i (i = 1, 2, ⋯ , m) and then to select the best one(s).

Step 3. Rank all the alternatives A_i (i = 1, 2, ⋯ , m) and select the best one(s) in accordance with $S ({\tilde{r}}_{i})$ and $H ({\tilde{r}}_{i}) (i = 1, 2, \dots, m)$ .

Step 4. End.

5 Numerical example

include the ding172G₁ is the earth’s crust stability; ding173G₂ is the stability of ground surface; ding174G₃ is the stability of foundation soil; ding175G₄ is the surface anti-fouling ability. The five possible engineering projects A_i (i = 1, 2, 3, 4, 5) are to be evaluated using the intuitionistic fuzzy information by the decision maker under the above four attributes, as listed in the following matrix.

$\tilde{R} = [\begin{matrix} (0.5, 0.3) & (0.6, 0.2) & (0.4, 0.6) & (0.3, 0.7) \\ (0.7, 0.2) & (0.7, 0.2) & (0.7, 0.2) & (0.4, 0.5) \\ (0.6, 0.3) & (0.5, 0.3) & (0.5, 0.3) & (0.6, 0.3) \\ (0.8, 0.2) & (0.6, 0.3) & (0.5, 0.4) & (0.4, 0.6) \\ (0.5, 0.2) & (0.4, 0.3) & (0.7, 0.2) & (0.5, 0.3) \end{matrix}]$

In the following, we apply the DIFHWA operator for engineering geological environment comprehensive evaluation with intuitionistic fuzzy information. The method involves the following steps:

Step 1. If we apply the DIFHWA operator to decision making with intuitionistic fuzzy information, we get the weight of DIFHWA operator is: $w = (0.18, 0 . 31, 0 . 25, 0 . 26) .$

Step 2. Utilize the evaluation information given in matrix $\tilde{R}$ , and the DIFHWA operator, we get the values ${\tilde{r}}_{i}$ of the engineering projects A_i (i = 1, 2, ⋯ , 5). $\begin{matrix} {\tilde{r}}_{1} & = & (0.38, 0.42), {\tilde{r}}_{2} = (0.59, 0.21) \\ {\tilde{r}}_{3} & = & (0.47, 0.12), {\tilde{r}}_{4} = (0.38, 0.26) \\ {\tilde{r}}_{5} & = & (0.53, 0.32) \end{matrix}$

Step 3. Calculate the scores $S ({\tilde{r}}_{i}) (i = 1, 2, \dots, 5)$ of the intuitionistic fuzzy information ${\tilde{r}}_{i} (i = 1, 2, \dots, 5)$ $\begin{matrix} S ({\tilde{r}}_{1}) & = & - 0.04, S ({\tilde{r}}_{2}) = 0.38, S ({\tilde{r}}_{3}) = 0.35 \\ S ({\tilde{r}}_{4}) & = & 0.12, S ({\tilde{r}}_{5}) = 0.21 \end{matrix}$

Step 4. Rank all the engineering projects A_i (i = 1, 2, 3, 4, 5) according to the scores $S ({\tilde{r}}_{i})$ of the values ${\tilde{r}}_{i} (i = 1, 2, \dots, 5)$ : A₂ ≻ A₃ ≻ A₅ ≻ A₄ ≻ A₁, and thus the most desirable engineering project is A₂.

6 Conclusion

Evaluation of engineering geological environment and construction of urban layout compose a multi-factors and multi-levels process. How to choose and use condition of engineering geological environment, protect and control the possible engineering geological problem, reduce the occurrence of geological hazard is very important in urban layout. In this paper, we investigate the engineering geological environment comprehensive evaluation with intuitionistic fuzzy information. Motivated by the ideal of dependent aggregation, we shall propose the dependent intuitionistic fuzzy Hamacher weighted average (DIFHWA) operator, in which the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to those “false” and “biased” ones and then apply this operator to develop an approach for engineering geological environment comprehensive evaluation with intuitionistic fuzzy numbers. Finally, an illustrative example for engineering geological environment comprehensive evaluation is given to verify the developed approach.

Footnotes

Acknowledgments

This research was supported by the National Natural Science Foundation of China(51374112, 51308234); the Program for New Century Excellent Talents in Fujian Province University, China; the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University, China (ZQN-PY112,ZQN-PY311); the Open Research Fund of State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, China(SKLGDUEK1304).

References

Fan

Z.P.

, Feng

, Sun

Y.H.

and Ou

, Evaluating knowledge management capability of organizations: A fuzzy linguistic method, Expert Systems with Applications36(2) (2009), 3346–3354.

Martínez

, Liu

, Ruan

and Yang

J.B.

, Dealing with heterogeneous information in engineering evaluation processes, Information Sciences177(7) (2007), 1533–1542.

Martínez

, Sensory evaluation based on linguistic decision analysis, International Journal of Approximate Reasoning44(2) (2007), 148–164.

Herrera

, Martínez

and Sánchez

P.J.

, Managing non-homogeneous information in group decision making, European Journal of Operational Research166(1) (2005), 115–132.

Herrera

, Herrera-Viedma

and Verdegay

, A linguistic decision process in group decision making, Group Decision and Negotiation5(1) (1996), 165–176.

Wei

G.W.

, Wang

J.M.

and Chen

, Potential optimality and robust optimality in multiattribute decision analysis with incomplete information: A comparative study, DecisionSupport Systems55(3) (2013), 679–684.

Wei

G.W.

, Approaches to interval intuitionistic trapezoidal fuzzy multiple attribute decision making with incomplete weight information, International Journal of Fuzzy Systems17(3) (2015), 484–489.

Wei

G.W.

, Wang

H.J.

, Zhao

X.F.

and Lin

, Hesitant triangular fuzzy information aggregation in multiple attribute decision making, Journal of Intelligent and Fuzzy Systems26(3) (2014), 1201–1209.

Wei

G.W.

, A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information, Expert Systems with Applications37(12) (2010), 7895–7900.

10.

Kim

S.H.

, Choi

S.H.

and Kim

J.K.

, An interactive procedure for multiple attribute group decision making with incomplete information: Range-based approach, European Journal of Operational Research118 (1999), 139–152.

11.

Z.S.

, Induced uncertain linguistic OWA operators applied to group decision making, Information Fusion7 (2006), 231–238.

12.

Z.S.

, An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations, Decision Support Systems41 (2006), 488–499.

13.

Atanassov

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

14.

Atanassov

, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems33 (1989), 37–46.

15.

Chen

S.M.

and Tan

J.M.

, Handling multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets and Systems67(4) (1994), 163–172.

16.

Hong

D.H.

and Choi

C.H.

, Multicriteria fuzzy problems based on vague set theory, Fuzzy Sets and Systems114(3) (2000), 103–113.

17.

Z.S.

, Intuitionistic fuzzy aggregation operators, IEEE Transations on Fuzzy Systems15(6) (2007), 1179–1187.

18.

Huang

J.Y.

, Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making, Journal of Intelligent and Fuzzy Systems27(1) (2014), 505–513.

19.

Z.S.

, Models for multiple attribute decision making with intuitionistic fuzzy information, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems15 (2007), 285–297.

20.

Z.S.

, Dependent uncertain ordered weighted aggregation operators, Information Fusion9(2) (2008), 310–316.

21.

Wei

G.W.

and Zhao

X.F.

, Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making, Expert Systems with Applications39 (2012), 5881–5886.