Research and evaluation on comprehensive obstacle-avoiding behavior for unmanned vehicles based on the interval neutrosophic number multiple attribute group decision making

Abstract

With the advent of the information age, the development direction of automobiles has gradually changed, both from the domestic and foreign policy support attitude, or from the actual actions of the automotive industry and scientific research institutes’ continuous efforts, it is not difficult to see that driverless vehicle. At this time, the testing and evaluation of the intelligent behavior of driverless vehicles is particularly important. It is particularly important not only to regulate the intelligent behavior of unmanned vehicles, but also to promote the key It can not only regulate the intelligent behavior of unmanned vehicles, but also promote the improvement of key technologies of unmanned vehicles and the research and development of driver assistance systems. The evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is often considered as a multi-attribute group decision making (MAGDM) problem. In this paper, the EDAS method is extended to the interval neutrosophic sets (INSs) setting to deal with MAGDM and the computational steps for all designs are listed. Then, the criteria importance through intercriteria correlation (CRITIC) is defined to obtain the attribute’s weight. Finally, the evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is given to demonstrate the interval neutrosophic number EDAS (INN-EDAS) model and some good comparative analysis is done to demonstrate the advantages of INN-EDAS.

Keywords

Multi-attribute group decision making (MAGDM)interval neutrosophic sets (INSs)EDAS method comprehensive obstacle-avoiding behavior unmanned vehicles

1 Introduction

Decision-making is a basic human thought activity. With the help of certain scientific methods, decision-making experts sort out several alternatives and choose the best one to achieve people’s expected goals [1 –3]. During the society development, the rapid development of science & technology and information technology, the problems to be solved are becoming more and more diverse [4 –6]. In the past, people used a single criterion to make decisions [7 –9]. Complexity requires decision-making activities under multiple irreplaceable criteria, and the MADM emerges as the times require [10 –14]. MADM has a wide range of real applications in society, economy and enterprise [15 –17]. The MAGDM is the decision research direction of the connection between MADM and group decision making (GDM) [18 –20]. Therefore, the studies of MAGDM have practical significance and high practical value[21 –25]. The intuitionistic fuzzy sets(IFSs) [26] was used in solving MAGDM decision problems. The IFSs are more flexible than traditional fuzzy sets (IFSs) [27 –31]. Smarandache [32] devised the neutrosophic sets (NSs). Ye [33 –35] devised many similarity measures for SVNSs. The Bonferroni mean (BM) operator was devised through Liu and Wang [36]. Liu et al. [37] connected Hamacher with NSs. Ye [38] defined MADM with probability under INSs. Liu and Wang [39] devised INPOWA fused operator. Zhao et al. [40] devised generalized weighted aggregation decision operator with INSs. Ye [41] devised INWEA operator and DINWEA operator. Broumi and Smarandache [42] devised correlation coefficients under defined INSs. Zhang et al. [43] devised the INNWA and INNWG operators under INSs. Ye and Jun [44] devised the MADM through confidence level under INSs.

In recent years, with the rapid development of computer technology and sensor technology, automotive products gradually tend to be intelligent, and now the most cutting-edge technology can make the car reach a truly driverless [45 –47], that is, unmanned vehicles in any situation can sense the surrounding environment, and complete the corresponding judgment, decision-making, implementation and other processes, completely without the control of the driver [48 –50]. In terms of strategic context, research on unmanned vehicles in developed countries such as the United States, Germany, and the United Kingdom began in the 1970s. The DARPA Ground Challenge, funded and supported by the U.S. Department of Defense Advanced Research Projects Agency (DARPA: Defense Advanced Research Projects Agency), was first conducted in 2004 [51] with $1 million in funding and became the world’s first long-distance challenge for unmanned vehicles, with the ultimate goal of having one-third of U.S. military vehicles unmanned by 2015. Unmanned vehicles have now been approved by California legislation and may be used to transport company employees to and from work in the future [52]. “The Innovate UK agency announced in December 2014 that it was undertaking a pilot project for unmanned vehicles in towns and cities after the UK Treasury published its autumn financial report, which received a total investment of £19 million. From the industry background, the main domestic and foreign car manufacturers are currently involved in the field of unmanned vehicle technology. in September 2014, BMW and Baidu formally established a partnership, is expected to achieve the next three years, unmanned vehicles in China’s complex road driving technology breakthroughs, before, BMW independent research and development of unmanned vehicles 5 series, the technology is very mature. Audi recently showed a unmanned concept car RS7 in Germany with a speed of 305 km/h, which is currently the fastest unmanned vehicle in the world. Mercedes-Benz also launched the new S-class unmanned vehicle, although the unmanned technology is not quite mature, but the driver assistance system on board is more complete [53]. Ford released its first unmanned vehicle in 2014, demonstrating its achievements in unmanned technology research and development in the past 10 years [54]. Google started its unmanned vehicle research project in 2010 and has so far achieved a record of 1 million kilometers driven by unmanned vehicles and obtained a public road test permit issued by the U.S. government of California [55]. The research and development of domestic unmanned vehicles is still in its infancy, including FAW Group’s unmanned vehicle HQ3, which incorporates more than 20 years of research results on Chinese automotive autonomous driving technology and mainly adopts intelligent transportation technology and the most advanced active safety technology [56 –58]. In addition, domestic automakers have also started to invest in the research and development of unmanned technology [59 –61].

The evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is often considered as a MAGDM problem. In this paper, the traditional EDAS method [62 –68] is extended to the interval neutrosophic sets (INSs) setting to deal with MAGDM and the computational steps for all designs are listed. Then, the traditional CRITIC method [69] is defined to obtain the attribute’s weight under INSs. Finally, the evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is given to demonstrate the interval neutrosophic number EDAS (INN-EDAS) model and some good comparative analysis is done to demonstrate the advantages of INN-EDAS.

In order to do so, the reminder of this paper is given. The INNSs is introduced in Sec. 2. The INN-EDAS is devised for MAGDM in Sec. 3. The evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is given to show the INN-EDAS and some comparative analyses are also devised in section 4. At last, the satisfied conclusion analysis is drawn in Sec. 5.

2 Preliminaries

Smarandache [70] gave the definitions of neutrosophic sets (NSs).

Definition 1 [70]. Let X be a space of points (objects) with a generic element in fix set X, denoted by x. A neutrosophic sets (NSs) A in X is characterized by a truth-membership function T_A (x), an indeterminacy-membership I_A (x) and a falsity-membership function F_A (x). The functions T_A (x), I_A (x) and F_A (x) are real standard or nonstandard subsets of , that’s, and . There is no restriction on the sum of T_A (x), I_A (x) and F_A (x), so 0^- ⩽ sup T_A (x) + sup I_A (x) + sup F_A (x) ⩽ 3⁺.

Wang et al. [71] defined the given SVNSs

Definition 2 [71]. The SVNSs A in Y is defined:

$YA = {(y, AT (y), AI (y), AF (y)) | y \in Y}$ (1) with defined truth-membership AT (y), defined indeterminacy-membership AI (y) and defined falsity-membership AF (y), AT (y) , AI (y) , AF (y) ∈ [0, 1], 0 ⩽ ATy + AI (y) + AF (y) ⩽ 3. The SVNN is expressed as YA = (AT, AI, AF), AT, AI, AF ∈ [01], 0 ⩽ AT + AI + AF ⩽ 3.

Wang et al. [72] built the INSs

Definition 3[72]. Let X be an object along with denoted by x. An INSs A in X is characterized:

$\tilde{A} = {(x, {TT}_{\tilde{A}} (x), {II}_{\tilde{A}} (x), {FF}_{\tilde{A}} (x)) | x \in X}$ (2) where the truth-membership ${TT}_{\tilde{A}} (x)$ , indeterminacy-membership ${II}_{\tilde{A}} (x)$ and falsity-membership ${FF}_{\tilde{A}} (x)$ , ${TT}_{\tilde{A}} (x) \subseteq [0, 1], I_{\tilde{A}} (x) \subseteq [0, 1]$ and ${FF}_{\tilde{A}} (x) \subseteq [0, 1]$ . And the sum of ${TT}_{\tilde{A}} (x)$ , ${II}_{\tilde{A}} (x)$ and ${FF}_{\tilde{A}} (x)$ satisfies $0 ⩽ sup {TT}_{\tilde{A}} (x) + sup {II}_{\tilde{A}} (x) + sup {FF}_{\tilde{A}} (x) ⩽ 3$ .

The interva neutrosophic number (INN) is expressed as $\tilde{A} = ({TT}_{\tilde{A}}, {II}_{\tilde{A}}, {FF}_{\tilde{A}}) = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ , where ${TT}_{\tilde{A}} \subseteq [01], {II}_{\tilde{A}} \subseteq [01], {FF}_{\tilde{A}} \subseteq [01]$ , and $0 ⩽ {TR}_{\tilde{A}} + {IR}_{\tilde{A}} + {FR}_{\tilde{A}} ⩽ 3$ .

Definition 4 [73]. Let $\tilde{A} = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ , the score value is:

$\begin{matrix} SV (\tilde{A}) \\ = \frac{(2 + {TL}_{\tilde{A}} - {IL}_{\tilde{A}} - {FL}_{\tilde{A}}) + (2 + {TR}_{\tilde{A}} - {IR}_{\tilde{A}} - {FR}_{\tilde{A}})}{6}, \\ SV (\tilde{A}) \in [0, 1] . \end{matrix}$ (3)

Definition 5 [73]. Let $\tilde{A} = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ , the accuracy value is:

$\begin{matrix} AV (\tilde{A}) = & \frac{({TL}_{\tilde{A}} + {TR}_{\tilde{A}}) - ({FL}_{\tilde{A}} + {FR}_{\tilde{A}})}{2}, \\ AV (\tilde{A}) \in [- 1, 1] . \end{matrix}$ (4)

The larger $AV (\tilde{A})$ is, the more $\tilde{A} = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ is.

Huang, Wei and Wei [73] defined the order relation between two INNs.

Definition 6 [73]. Let $\tilde{A} = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ and $\tilde{B} = ([{TL}_{\tilde{B}}, {TR}_{\tilde{B}}], [{IL}_{\tilde{B}}, {IR}_{\tilde{B}}], [{FL}_{\tilde{B}}, {FR}_{\tilde{B}}])$ be two given INNs, let $SV (\tilde{A}) = \frac{(2 + {TL}_{\tilde{A}} - {IL}_{\tilde{A}} - {FL}_{\tilde{A}}) + (2 + {TR}_{\tilde{A}} - {IR}_{\tilde{A}} - {FR}_{\tilde{A}})}{6}$ and $SV (\tilde{B}) = \frac{(2 + {TL}_{\tilde{B}} - {IL}_{\tilde{B}} - {FL}_{\tilde{B}}) + (2 + {TR}_{\tilde{B}} - {IR}_{\tilde{B}} - {FR}_{\tilde{B}})}{6}$ , and let $AV (\tilde{A}) = \frac{({TL}_{\tilde{A}} + {TR}_{\tilde{A}}) - ({FL}_{\tilde{A}} + {FR}_{\tilde{A}})}{2}$ and $AV (\tilde{B}) = \frac{({TL}_{\tilde{B}} + {TR}_{\tilde{B}}) - ({FL}_{\tilde{B}} + {FR}_{\tilde{B}})}{2}$ , respectively, then if $SV (\tilde{A}) < SV (\tilde{B})$ , $\tilde{A} < \tilde{B}$ ; if $SV (\tilde{A}) = SV (\tilde{B})$ , (1)if $HV (\tilde{A}) = HV (\tilde{B})$ , then $\tilde{A} = \tilde{B}$ ; (2) if $HV (\tilde{A}) < HV (\tilde{B})$ , $\tilde{A} < \tilde{B}$ .

Definition 7 [74]. Let $\tilde{A} = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ and $\tilde{B} = ([{TL}_{\tilde{B}}, {TR}_{\tilde{B}}], [{IL}_{\tilde{B}}, {IR}_{\tilde{B}}], [{FL}_{\tilde{B}}, {FR}_{\tilde{B}}])$ be two INNs, the basic operations are defined: $\begin{matrix} (1) \tilde{A} \oplus \tilde{B} = (\begin{matrix} ({TL}_{\tilde{A}} + {TL}_{\tilde{B}} - {TL}_{\tilde{A}} {TL}_{\tilde{B}}, {TR}_{\tilde{A}} + {TR}_{\tilde{B}} - {TR}_{\tilde{A}} {TR}_{\tilde{B}}), \\ [{IL}_{\tilde{A}} {IL}_{\tilde{B}}, {IR}_{\tilde{A}} {IR}_{\tilde{B}}], [{FL}_{\tilde{A}} {FL}_{\tilde{B}}, {FR}_{\tilde{A}} {FR}_{\tilde{B}}] \end{matrix}); \\ (2) \tilde{A} \otimes \tilde{B} = (\begin{matrix} [{TL}_{\tilde{A}} {TL}_{\tilde{B}}, {TR}_{\tilde{A}} {TR}_{\tilde{B}}], [{IL}_{\tilde{A}} + {IL}_{\tilde{B}} - {IL}_{\tilde{A}} {IL}_{\tilde{B}}, {IR}_{\tilde{A}} + {IR}_{\tilde{B}} - {IR}_{\tilde{A}} {IR}_{\tilde{B}}], \\ [{FL}_{\tilde{A}} + {FL}_{\tilde{B}} - {FL}_{\tilde{A}} {FL}_{\tilde{B}}, {FR}_{\tilde{A}} + {FR}_{\tilde{B}} - {FR}_{\tilde{A}} {FR}_{\tilde{B}}] \end{matrix}); \\ (3) λ \tilde{A} = ([1 - {(1 - {TL}_{\tilde{A}})}^{λ}, 1 - {(1 - {TR}_{\tilde{A}})}^{λ}], [{({IL}_{\tilde{A}})}^{λ}, {({IR}_{\tilde{A}})}^{λ}], [{({FL}_{\tilde{A}})}^{λ}, {({FR}_{\tilde{A}})}^{λ}]), λ > 0; \\ (4) {(\tilde{A})}^{λ} = ([{({TL}_{\tilde{A}})}^{λ}, {({TR}_{\tilde{A}})}^{λ}], [{({IL}_{\tilde{A}})}^{λ}, {({IR}_{\tilde{A}})}^{λ}], [1 - {(1 - {FL}_{\tilde{A}})}^{λ}, 1 - {(1 - {FR}_{\tilde{A}})}^{λ}]), λ > 0 . \end{matrix}$

Definition 8 [75]. Let $\tilde{A} = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ and $\tilde{B} = ([{TL}_{\tilde{B}}, {TR}_{\tilde{B}}], [{IL}_{\tilde{B}}, {IR}_{\tilde{B}}], [{FL}_{\tilde{B}}, {FR}_{\tilde{B}}])$ , then the normalized Euclidean distance between $\tilde{A} = ([{TL}_{\tilde{A}}, {TR}_{\tilde{A}}], [{IL}_{\tilde{A}}, {IR}_{\tilde{A}}], [{FL}_{\tilde{A}}, {FR}_{\tilde{A}}])$ and $\tilde{B} = ([{TL}_{\tilde{B}}, {TR}_{\tilde{B}}], [{IL}_{\tilde{B}}, {IR}_{\tilde{B}}], [{FL}_{\tilde{B}}, {FR}_{\tilde{B}}])$ is defined:

$\begin{matrix} ED (\tilde{A}, \tilde{B}) = \sqrt{\frac{1}{6} (\begin{matrix} {| {TL}_{\tilde{A}} - {TL}_{\tilde{B}} |}^{2} + {| {TR}_{\tilde{A}} - {TR}_{\tilde{B}} |}^{2} + {| {IL}_{\tilde{A}} - {IL}_{\tilde{B}} |}^{2} + \\ {| {IR}_{\tilde{A}} - {IR}_{\tilde{B}} |}^{2} + {| {FL}_{\tilde{A}} - {FL}_{\tilde{B}} |}^{2} + {| {FR}_{\tilde{A}} - {FR}_{\tilde{B}} |}^{2} \end{matrix})} \end{matrix}$ (5)

3 EDAS method for MAGDM with INNs

The INN-EDAS method is devised for MAGDM. Let YY = { YY₁, YY₂, …, YY_m } be alternatives. Let ZZ ={ ZZ₁, ZZ₂, …, ZZ_n } be attributes, wz = { wz₁, wz₂, …, wz_n } be weight for ZZ_j, where ${wz}_{j} \in [0, 1], \sum_{j = 1}^{n} {wz}_{j} = 1$ . Assume DD = { DD₁, DD₂, …, DD_l } be invited DMs that have weight for dd = { dd₁, dd₂, …, dd_l }, where ${dd}_{k} \in [0, 1], \sum_{k = 1}^{l} {dd}_{k} = 1$ . And ${QQ}^{(k)} = {({qq}_{ij}^{k})}_{m \times n} = {([{TL}_{ij}^{k}, {TR}_{ij}^{k}], [{IL}_{ij}^{k}, {IR}_{ij}^{k}], [{FL}_{ij}^{k}, {FR}_{ij}^{k}])}_{m \times n}$ is the overall INN-matrix. Subsequently, the designed calculating procedures are depicted.

Step 1. Set up the INN-matrix ${QQ}^{(k)} = {({qq}_{ij}^{k})}_{m \times n}$ and overall INN-matrix QQ = (qq_ij) _m×n by INNWA decision operator.

${QQ}^{(k)} = {[{qq}_{ij}^{k}]}_{m \times n} = [\begin{matrix} {qq}_{11}^{k} & {qq}_{12}^{k} & \dots & {qq}_{1 n}^{k} \\ {qq}_{21}^{k} & {qq}_{22}^{k} & \dots & {qq}_{2 n}^{k} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ {qq}_{m 1}^{k} & {qq}_{m 2}^{k} & \dots & {qq}_{mn}^{k} \end{matrix}]$ (6)

$QQ = {[{qq}_{ij}]}_{m \times n} = [\begin{matrix} {qq}_{11} & {qq}_{12} & \dots & {qq}_{1 n} \\ {qq}_{21} & {qq}_{22} & \dots & {qq}_{2 n} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ {qq}_{m 1} & {qq}_{m 2} & \dots & {qq}_{mn} \end{matrix}]$ (7)

$\begin{matrix} {qq}_{ij} = ([{TL}_{ij}, {TR}_{ij}], [{IL}_{ij}, {IR}_{ij}], [{FL}_{ij}, {FR}_{ij}]) \\ = (\begin{matrix} [1 - \prod_{k = 1}^{l} {(1 - {TL}_{ij}^{k})}^{{dd}_{k}}, 1 - \prod_{k = 1}^{l} {(1 - {TR}_{ij}^{k})}^{{dd}_{k}}], \\ [\prod_{k = 1}^{l} {({IL}_{ij}^{k})}^{{dd}_{k}} \prod_{k = 1}^{l} {({IR}_{ij}^{k})}^{{dd}_{k}}], [\prod_{k = 1}^{l} {({FL}_{ij}^{k})}^{{dd}_{k}}, \prod_{k = 1}^{l} {({FR}_{ij}^{k})}^{{dd}_{k}}] \end{matrix}) \end{matrix}$ (8)

Step 2. Normalize the QQ = (qq_ij) _m×n to NQQ = [nqq_ij] _m×n.

$\begin{matrix} {nqq}_{ij} = ([{NTL}_{ij}, {NTR}_{ij}], [{NIL}_{ij}, {NIR}_{ij}], [{NFL}_{ij}, {NFR}_{ij}]) \\ = {\begin{matrix} ([{TL}_{ij}^{k}, {TR}_{ij}^{k}], [{IL}_{ij}^{k}, {IR}_{ij}^{k}], [{FL}_{ij}^{k}, {FR}_{ij}^{k}]) {ZZ}_{j} is a benefit criterion \\ ([{FL}_{ij}^{k}, {FR}_{ij}^{k}], [{IL}_{ij}^{k}, {IR}_{ij}^{k}], [{TL}_{ij}^{k}, {TR}_{ij}^{k}]) {ZZ}_{j} is a cost criterion \end{matrix} \end{matrix}$ (9)

Step 3. Utilize CRITIC to obtain the given weight.

The CRITIC [69] is used to decide the weights. the calculating procedures is presented [76].

(1) The INN correlation coefficient values (INNCCV) for attributes are obtained.

${INNCCV}_{jt} = \frac{\sum_{i = 1}^{m} (SV ({nqq}_{ij}) - SV ({nqq}_{j})) (SV ({nqq}_{it}) - SV ({nqq}_{t}))}{\sqrt{\sum_{i = 1}^{m} {(SV ({nqq}_{ij}) - SV ({nqq}_{j}))}^{2}} \sqrt{\sum_{i = 1}^{m} {(SV ({nqq}_{it}) - SV ({nqq}_{t}))}^{2}}}, j, t = 1, 2, \dots, n,$ (10) where $SV ({nqq}_{j}) = \frac{1}{m} \sum_{i = 1}^{m} SV ({nqq}_{j})$ ,

$SV ({nqq}_{t}) = \frac{1}{m} \sum_{i = 1}^{m} SV ({nqq}_{it})$ .

(2) Calculate the defined INN standard deviation values (INNSDV).

$\begin{matrix} {INNSDV}_{j} \\ = \sqrt{\frac{1}{m - 1} \sum_{i = 1}^{m} {(SV ({nqq}_{ij}) - SV ({nqq}_{j}))}^{2}} \end{matrix}$ (11) where $SV ({nqq}_{j}) = \frac{1}{m} \sum_{i = 1}^{m} SV ({nqq}_{ij})$ .

(3) Obtain the defined attributes’ weight.

${wz}_{j} = \frac{{INNSDV}_{j} \sum_{t = 1}^{n} (1 - {INNCCV}_{jt})}{\sum_{j = 1}^{n} ({INNSDV}_{j} \sum_{t = 1}^{n} (1 - {INNCCV}_{jt}))}$ (12) where wz_j ∈ [0, 1], $\sum_{j = 1}^{n} {wz}_{j} = 1$ .

Step 4. Obtain the INN average solution (INNAS) for attributes.

$INNAS = {[{INNAS}_{j}]}_{1 \times n} = {[\frac{\sum_{i = 1}^{m} {nqq}_{ij}}{m}]}_{1 \times n}$ (13)

$\begin{matrix} {[{INNAS}_{j}]}_{1 \times n} = {[\frac{\sum_{i = 1}^{m} {nqq}_{ij}}{m}]}_{1 \times n} \\ = (\begin{matrix} [1 - \prod_{i = 1}^{m} {(1 - {NTL}_{ij})}^{\frac{1}{m}}, 1 - \prod_{i = 1}^{m} {(1 - {NTR}_{ij})}^{\frac{1}{m}}], \\ [1 - \prod_{i = 1}^{m} {(1 - {NIL}_{ij})}^{\frac{1}{m}}, 1 - \prod_{i = 1}^{m} {(1 - {NIR}_{ij})}^{\frac{1}{m}}], \\ [1 - \prod_{i = 1}^{m} {(1 - {NFL}_{ij})}^{\frac{1}{m}}, 1 - \prod_{i = 1}^{m} {(1 - {NFR}_{ij})}^{\frac{1}{m}}] \end{matrix}) \end{matrix}$ (14)

Step 5. Obtain the INN positive distance from average (INNPDA) and INN negative distance from average (INNNDA):

$\begin{matrix} {INNPDA}_{ij} = {[{INNPDA}_{ij}]}_{m \times n} \\ = \frac{max (0, (SV ({nqq}_{ij}) - SV ({INNAS}_{j})))}{SV ({INNAS}_{j})}, \end{matrix}$ (15)

$\begin{matrix} {INNNDA}_{ij} = {[{INNNDA}_{ij}]}_{m \times n} \\ = \frac{max (0, (SV ({INNAS}_{j}) - SV ({nqq}_{ij})))}{SV ({INNAS}_{j})}, \end{matrix}$ (16)

Step 6. Obtain the INNSP_i and INNSN_i.

$\begin{matrix} {INNSP}_{i} = \sum_{j = 1}^{n} {zz}_{j} \cdot {INNPDA}_{ij}, \\ {INNNP}_{i} = \sum_{j = 1}^{n} {zz}_{j} \cdot {INNNDA}_{ij} \end{matrix}$ (17)

Step 7. Normalized the INNSP_i and INNSN_i:

$\begin{matrix} {NINNSP}_{i} = \frac{{INNSP}_{i}}{max_{i} ({INNSP}_{i})}, \\ {NINNSN}_{i} = 1 - \frac{{INNSN}_{i}}{max_{i} ({INNSN}_{i})} \end{matrix}$ (18)

Step 8. Obtain the INN appraisal values (INNAV) for each alternative.

${INNAV}_{i} = \frac{1}{2} (NINNSP + {NINNSN}_{i})$ (19)

Step 9. In terms of the INNAV, all the chosen alternatives are ranked. The higher value of INNAV is, the chosen optimal alternative is.

4 Numerical example and comparative analysis

4.1 Numerical example

As a comprehensive intelligent system integrating perception, decision-making and control technologies, unmanned vehicles have been attracting many scholars to devote themselves to their scientific research in recent years [77 –79]. Whether it is theoretical analysis, virtual experimental research or actual road testing, intelligent behavior as the performance of the intelligence level of unmanned vehicles is analyzed in different ways and gradually formed into a system, and with the development of technology, the evaluation of unmanned vehicles With the development of technology, the intelligent behavior of unmanned vehicles is not only limited to the general judgment, but also requires the evaluation of it in a definite quantity [80, 81]. Scholars from Nanyang Technological University developed a vehicle following simulation test system to control the distance and relative angle between the front and rear vehicles by establishing a complex two-vehicle kinematic model, and the vehicle dynamics model they established was through the Simulink module of MATLAB software, and the model was more accurate, which enabled a high tracking accuracy to be achieved in the final test [82]. Toyota of Japan has also conducted research in this area, using a multi-vehicle GPS-guided vehicle to conduct research on vehicle adaptive cruise, driving in cruise mode when there is no vehicle in front of it, and intelligently adjusting the speed and workshop distance to follow the vehicle when there is a vehicle in front of it to achieve a better following effect [83]. The German INTERSAFE project is dedicated to the study of the collision problem of vehicle interaction, and the collision coefficient between the vehicle and other vehicles is estimated by means of communication and the vehicle installed with an alert system, and the driver is reminded to brake or move forward using the method of indicator lights, which makes the collision coefficient of the vehicle greatly reduced [84]. The European PROMETHEUS project used machine vision and radar technology to analyze the lane keeping and automatic obstacle avoidance behaviors of intelligent vehicles, to identify the factors that affect these two types of behaviors, and to establish the relationships that exist between the factors, leading to the development of lane keeping systems and automatic obstacle avoidance assistance systems [85]. TNO Automotive Technologies used four experimental intelligent vehicles to design vehicle distance control algorithms, tested the speed and vehicle distance control of multiple vehicles in the LIDAR-only case and in the communication case, respectively, and analyzed the lane change behavior of intelligent vehicles under the influence of multi-vehicle interaction, drawing many control conclusions with practical application [86]. The French National Institute of Automation has solved the problem of vehicle interaction influence by studying different types of intelligent vehicles, using the Cycab platform as a basis for workshop communication as well as designing path planning algorithms so as to achieve the reproduction of multi-vehicle interaction traffic scenarios [87]. The LAFR project uses computer vision to locate the position of surrounding vehicles in the image, thus ensuring that lane changes are made with the surrounding vehicles maintaining a safe distance, empowering intelligent vehicle map construction, and getting feature points of surrounding vehicles to further detect their speedometer trajectory changes to provide more considerations for safe lane changes. The evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is viewed as the MAGDM. In this section, the evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is provided through SVNN-EDAS method. There are five participating teams of unmanned vehicles YY_i (i = 1, 2, 3, 4, 5). In order to select the best participating teams of unmanned vehicles, the competition organizers invite three experts DD = { DD₁, DD₂, DD₃ } (whose weight dd = (0 . 30, 0 . 40, 0 . 30) to assess the comprehensive obstacle-avoiding behavior for unmanned vehicles. All invited experts depict their assessment with four defined attributes: ding172 ZZ₁ is exercising speed (The exercising speed is characterized by travel time, acceleration degree to characterize); ding173 ZZ₂ is the driving intelligence (The driving intelligence is characterized by vehicle off-range, turn signal on, and obstacle vehicle recognition); ding174 ZZ₃ is safety of driving (The safety of driving is characterized by relative distance and relative speed); ding175 ZZ₄ is smoothness of driving (The smoothness of driving is characterized by steering wheel angle variance, speed variance). To obtain the optimal participating teams of unmanned vehicles, the defined procedures are given.

Step 1. Build the INN-matrix ${QQ}^{(k)} = {({qq}_{ij}^{k})}_{5 \times 4}$ (Tables 2 –4) based on Table 1. The overall INN-matrix is calculated in Table 5.

Table 1
Linguistic scale

Linguistic terms INNs

Exceedingly Terrible-YET ([0.05,0.2], [0.6,0.7], [0.75,0.9])

Very Terrible-YVT ([0.15,0.3], [0.5,0.6], [0.65,0.8])

Terrible-YT ([0.25,0.4], [0.4,0.5], [0.55,0.7])

Medium-YM ([0.4,0.6], [0.1,0.2], [0.4,0.6])

Well-YW ([0.45,0.6], [0.3,0.4], [0.25,0.5])

Very Well-YVW ([0.65,0.8], [0.5,0.6], [0.15,0.3])

Exceedingly Well-YEW ([0.75,0.9], [0.6,0.7], [0.05,0.2])

Linguistic terms	INNs
Exceedingly Terrible-YET	([0.05,0.2], [0.6,0.7], [0.75,0.9])
Very Terrible-YVT	([0.15,0.3], [0.5,0.6], [0.65,0.8])
Terrible-YT	([0.25,0.4], [0.4,0.5], [0.55,0.7])
Medium-YM	([0.4,0.6], [0.1,0.2], [0.4,0.6])
Well-YW	([0.45,0.6], [0.3,0.4], [0.25,0.5])
Very Well-YVW	([0.65,0.8], [0.5,0.6], [0.15,0.3])
Exceedingly Well-YEW	([0.75,0.9], [0.6,0.7], [0.05,0.2])

Table 2

Evaluation information by DD₁

	ZZ₁	ZZ₂	ZZ₃	ZZ₄
YY₁	YM	YT	YVW	YW
YY₂	YVT	YM	YVW	YT
YY₃	YT	YW	YM	YVW
YY₄	YVW	YW	YVT	YM
YY₅	YM	YW	YVT	YVW

Table 3

Evaluation information by DD₂

	ZZ₁	ZZ₂	ZZ₃	ZZ₄
YY₁	YW	YVW	YVT	YM
YY₂	YVT	YVW	YM	YVT
YY₃	YVW	YVT	YM	YT
YY₄	YW	YM	YVT	YVW
YY₅	YM	YT	YVW	YW

Table 4

Evaluation information by DD₃

	ZZ₁	ZZ₂	ZZ₃	ZZ₄
YY₁	YVW	YW	YM	YT
YY₂	YVT	YT	YW	YVW
YY₃	YT	YM	YM	YW
YY₄	YT	YM	YW	YVW
YY₅	YM	YW	YVT	YVT

Table 5

The overall INN-matrix

	ZZ ₁	ZZ ₂
YY ₁	([0.61, 0.64], [0.43, 0.46], [0.47, 0.56])	([0.54, 0.62], [0.44, 0.51], [0.43, 0.54])
YY ₂	([0.82, 0.86], [0.24, 0.43], [0.65, 0.84])	([0.62, 0.68], [0.41, 0.45], [0.45, 0.64])
YY ₃	([0.64, 0.73], [0.28, 0.47], [0.44, 0.58])	([0.32, 0.45], [0.24, 0.28], [0.52, 0.65])
YY ₄	([0.58, 0.65], [0.26, 0.28], [0.54, 0.65])	([0.62, 0.65], [0.42, 0.46], [0.44, 0.53])
YY ₅	([0.64, 0.81], [0.43, 0.45], [0.47, 0.56])	([0.82, 0.88], [0.56, 0.64], [0.57, 0.62])
	ZZ ₃	ZZ ₄
YY ₁	([0.67, 0.84], [0.45, 0.53], [0.42, 0.52])	([0.64, 0.86], [0.43, 0.46], [0.63, 0.65])
YY ₂	([0.58, 0.64], [0.56, 0.64], [0.46, 0.54])	([0.68, 0.84], [0.62, 0.64], [0.54, 0.68])
YY ₃	([0.53, 0.74], [0.43, 0.46], [0.55, 0.64])	([0.82, 0.85], [0.26, 0.42], [0.63, 0.65])
YY ₄	([0.65, 0.82], [0.44, 0.58], [0.66, 0.69])	([0.65, 0.83], [0.21, 0.25], [0.68, 0.82])
YY ₅	([0.65, 0.67], [0.62, 0.78], [0.26, 0.42])	([0.64, 0.82], [0.45, 0.53], [0.45, 0.51])

Step 2. All the attributes are beneficial, there is no need to normalize overall INN-matrix. The normalized overall INN-matrix (See Table 6) is same to overall INN-matrix.

Table 6

The normalized overall INN-matrix

	ZZ ₁	ZZ ₂
YY ₁	([0.61, 0.64], [0.43, 0.46], [0.47, 0.56])	([0.54, 0.62], [0.44, 0.51], [0.43, 0.54])
YY ₂	([0.82, 0.86], [0.24, 0.43], [0.65, 0.84])	([0.62, 0.68], [0.41, 0.45], [0.45, 0.64])
YY ₃	([0.64, 0.73], [0.28, 0.47], [0.44, 0.58])	([0.32, 0.45], [0.24, 0.28], [0.52, 0.65])
YY ₄	([0.58, 0.65], [0.26, 0.28], [0.54, 0.65])	([0.62, 0.65], [0.42, 0.46], [0.44, 0.53])
YY ₅	([0.64, 0.81], [0.43, 0.45], [0.47, 0.56])	([0.82, 0.88], [0.56, 0.64], [0.57, 0.62])
	ZZ ₃	ZZ ₄
YY ₁	([0.67, 0.84], [0.45, 0.53], [0.42, 0.52])	([0.64, 0.86], [0.43, 0.46], [0.63, 0.65])
YY ₂	([0.58, 0.64], [0.56, 0.64], [0.46, 0.54])	([0.68, 0.84], [0.62, 0.64], [0.54, 0.68])
YY ₃	([0.53, 0.74], [0.43, 0.46], [0.55, 0.64])	([0.82, 0.85], [0.26, 0.42], [0.63, 0.65])
YY ₄	([0.65, 0.82], [0.44, 0.58], [0.66, 0.69])	([0.65, 0.83], [0.21, 0.25], [0.68, 0.82])
YY ₅	([0.65, 0.67], [0.62, 0.78], [0.26, 0.42])	([0.64, 0.82], [0.45, 0.53], [0.45, 0.51])

Step 3. Obtain the weights through CRITIC (Table 7).

Table 7

The obtained weight

	ZZ ₁	ZZ ₂	ZZ ₃	ZZ ₄
Weight	0.1313	0.3112	0.3104	0.2371

Step 4. Calculate the INNAS (Table 8).

Table 8

The INNAS

	INNAS
ZZ ₁	([0.4134, 0.4312], [0.3224, 0.3514], [0.3432, 0.3449])
ZZ ₁	([0.3561, 0.4384], [0.3084, 0.3149], [0.3193, 0.3424])
ZZ ₃	([0.3442, 0.4942], [0.3231, 0.3612], [0.3637, 0.3894])
ZZ ₄	([0.3925, 0.4614], [0.1634, 0.3149], [0.3012, 0.3149])

Step 5. Calculate the INNPDA and INNNDA (See Tables 9-10).

Table 9

The INNPDA

	ZZ ₁	ZZ ₂	ZZ ₃	ZZ ₄
YY ₁	0.0000	0.0000	0.0000	0.3165
YY ₂	0.4036	0.0000	0.3046	0.0000
YY ₃	0.0000	0.0000	0.0000	0.0000
YY ₄	0.0000	0.0000	0.0000	0.0439
YY ₅	0.4106	0.5752	0.3854	0.0000

Table 10

The INNNDA

	ZZ ₁	ZZ ₂	ZZ ₃	ZZ ₄
YY ₁	0.0000	0.4829	0.0000	0.0283
YY ₂	0.0597	0.0275	0.1583	0.0592
YY ₃	0.3879	0.0474	0.00769	0.0000
YY ₄	0.0000	0.0000	0.0000	0.1689
YY ₅	0.1458	0.0476	0.0868	0.0000

Step 6. Calculate the INNSP and INNSN (See Table 11).

Table 11

The INNSP and INNSN

	INNSP	INNSN
YY ₁	0.1733	0.2249
YY ₂	0.2374	0.1618
YY ₃	0.1033	0.1698
YY ₄	0.1079	0.1349
YY ₅	0.4348	0.1660

Step 7. Calculate the NINNSP and NINNSN is listed in Table 12.

Table 12

The NINNSP and NINNSN

	NINNSP	NINNSN
YY ₁	0.3145	0.0000
YY ₂	0.5079	0.6222
YY ₃	0.0000	0.5565
YY ₄	0.1173	0.8437
YY ₅	1.0000	0.5875

Step 8. Calculate the INNAV (See Table 13).

Table 13

The INNAV

	INNAV	Order
YY ₁	0.2089	5
YY ₂	0.5651	2
YY ₃	0.3299	4
YY ₄	0.4805	3
YY ₅	0.8454	1

Step 9. Relying on the INNAV, the order is: YY₅ > YY₂ > YY₄ > YY₃ > YY₁ and YY₅ is the best participating team of unmanned vehicles.

4.2 Compare analysis

In this part, the INN-EDAS is made comparison with existing methods to show its superiority. Firstly, The INN-EDAS is compared with INNWA and INNWG [43]. Eventually, the obtained results are depicted in Table 14.

Table 14
The obtained results

Methods Order The optimal choice The worst choice

INNWA [43] YY₅ > YY₂ > YY₄ > YY₃ > YY₁ YY ₅ YY ₁

INNWG [43] YY₅ > YY₂ > YY₄ > YY₃ > YY₁ YY ₅ YY ₁

INN-EDAS YY₅ > YY₂ > YY₄ > YY₃ > YY₁ YY ₅ YY ₁

	Methods	Order	The optimal choice	The worst choice
INNWA [43]	YY₅ > YY₂ > YY₄ > YY₃ > YY₁	YY ₅	YY ₁
INNWG [43]	YY₅ > YY₂ > YY₄ > YY₃ > YY₁	YY ₅	YY ₁
INN-EDAS	YY₅ > YY₂ > YY₄ > YY₃ > YY₁	YY ₅	YY ₁

Derived from Table 12, it is very evident that the obtained best participating team of unmanned vehicles is YY₅, while the worst participating team of unmanned vehicles is YY₁. This verifies the INN-EDAS method is reasonable and effective.

5 Conclusion

The evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles is looked as the MAGDM. In this paper, the INN-EDAS decision method is devised for defined MAGDM. The weight values are decided with CRITIC method. Then, a novel INN-EDAS method is built for MAGDM and the calculating steps are listed. Eventually, the evaluation of comprehensive obstacle-avoiding behavior for unmanned vehicles has been well given to show that the superiority. The research in this paper is part of the research and evaluation of the intelligent behavior of unmanned vehicles, which only analyzes and evaluates the obstacle avoidance behavior, and is far from being able to evaluate the comprehensive intelligence level of unmanned vehicles in general, there may be some possible limitations of this research, which can be further explored in future research: (1) It is a worthwhile research topic to apply prospect theory [88 –91] to MAGDM under INNs; (2) It is also worthwhile to apply regret theory [92 –95] to the study of MAGDM under INNs; (3) In subsequent studies, the application and methods needs to be investigated in the bipolar neutrosophic set environment [96] and other uncertain settings [97 –99]; (4) Improve the comprehensiveness of the evaluation. Comprehensive analysis and evaluation of multiple types of driving behaviors, transforming qualitative evaluation into quantitative evaluation, so as to make a comprehensive evaluation of the intelligence level of driverless vehicles and make targeted corrections to the factors affecting the intelligence level to promote the improvement of driverless vehicle technology. (5) Improve the evaluation index system of driverless vehicles. At present, the evaluation indexes of driverless vehicles are not very systematic, and future research needs to consider the complexity of the environment and the influence of environmental factors and their complexity on the intelligence level of driverless vehicles.

Footnotes

Acknowledgment

The work was supported by the key scientific research platforms and projects of ordinary universities in Guangdong Province in 2022 (2022ZDZX1058), Basic and Applied Basic Research Project of Guangzhou Basic Research Plan in 2022 (1715) and 2022 Guangdong Provincial Science and Technology Innovation Strategy Special Fund Project (Climbing Plan) (pdjh2022b0857).

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Research and evaluation on comprehensive obstacle-avoiding behavior for unmanned vehicles based on the interval neutrosophic number multiple attribute group decision making

Abstract

Keywords

1 Introduction

2 Preliminaries

4.1 Numerical example

Table 14 The obtained results Methods Order The optimal choice The worst choice INNWA [43] YY5 > YY2 > YY4 > YY3 > YY1 YY 5 YY 1 INNWG [43] YY5 > YY2 > YY4 > YY3 > YY1 YY 5 YY 1 INN-EDAS YY5 > YY2 > YY4 > YY3 > YY1 YY 5 YY 1

Footnotes

Acknowledgment

References

Table 14
The obtained results

Methods Order The optimal choice The worst choice

INNWA [43] YY₅ > YY₂ > YY₄ > YY₃ > YY₁ YY ₅ YY ₁

INNWG [43] YY₅ > YY₂ > YY₄ > YY₃ > YY₁ YY ₅ YY ₁

INN-EDAS YY₅ > YY₂ > YY₄ > YY₃ > YY₁ YY ₅ YY ₁