Available online at www.sciencedirect.com Available online at www.sciencedirect.com
Procedia Engineering
ProcediaProcedia Engineering 00 (2011) Engineering 29 000–000 (2012) 1590 – 1595 www.elsevier.com/locate/procedia
2012 International Workshop on Information and Electronics Engineering (IWIEE)
An Improved Evaluation Method based on Cloud Models for Situation Consistency within the Battlefield of Joint Operations FAN Lin-juna*, LING Yun-xianga, LIAO Liang-caia, LI Ben-xiana Science and Technology on Information Systems Engineering,National Univ. of Defense Technology, Changsha 410073,China
Abstract To improve rationality and veracity of situation consistency assessment in battlefield and deal with the conversion from qualitative remark to quantitative evaluation effectively in evaluation, the improved assessment Method of Cloud Gravity Centre (MCGC) in Cloud Theory and Structure Entropy Weight (SEW) calculating index’s weight are introduced. By a simple example, the situation consistency of Air Intelligence Picture is evaluated. Each index’s entropy formula is revised based on variance in probability theory to increase reliability of MCGC. The indices’ weights are considered in each-level indices’ calculation for its expected value and entropy to insure this method’s rationality. The method of SEW makes sure the weight’s calculation simple. The research indicates that the modified MCGC is scientific and feasible in situation consistency assessment in battlefield.
© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University of Science and Technology Open access under CC BY-NC-ND license. Keywords: battlefield situation; situation consistency assessment; MCGC;cloud model;SEW
1. Introduction People’s cognition illegibility and thought’s subjectivity result in uncertainty and randomicity of correlative assessment works[1]. To improve evaluation quality, it is essential to deal with fuzzy issues and random ones effectively. The method based on proportion theory is a classical one to solve random issues, but not adapting to fuzzy ones. On the contrary, fuzzy theory is not fit for random problems. An excellent route is provided by cloud theory based on proportion theory and fuzzy theory to resolve the
* Corresponding author. Tel.: +86-731-84576270. E-mail address:
[email protected].
1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.01.178
2
FANFAN Lin-jun et al.Procedia / ProcediaEngineering Engineering0029(2011) (2012)000–000 1590 – 1595 Lin-jun/
conversion issue between qualitative and quantitative[2]. The method of cloud gravity centre (MCGC) is an implement of cloud theory in evaluation mission, achieving on the reasonable conversion from qualitative linguistic description to quantitative numerical expressions based on representability of the Expected value (Ex for short as below) and entropy (En for short as below) [3]. However, there are some flaws in traditional MCGC. Firstly, the En’s formula of the lowest indices is simple. Secondly, each-level indexes’ weights is not considered in calculation formulas of Ex and En. Thirdly, AHP is subjective in the calculation of index’s weight. At present, home and overseas scholars are fasten on situation appearance, situation estimate and its methods in battlefield posture researches, but the researches of Situation consistency assessment are few. With regard to battlefield situation forecast, LEI Ying-jie[4] brings forward a multi-level evaluation index system, however in assessment of situation consistency within the battlefield of joint operations authoritative multi-level situation consistency assessment index system is not established. Currently, situation consistency is judged with qualitative analysis by commanders who have abundant training and actual battle experiences[5]. It is more subjective and casual, so its rationality and accuracy is disputed and doubted. Situation consistency is mostly a qualitative issue, traditional AHP and Fuzzy Comprehensive Evaluation (FCE) are not adapt to this kind of one. It is greatly significant in theory and practice for improving battlefield situation consistency that the index system of situation consistency and its assessment method are studied. In this paper, aiming at some deficiencies of MCGC, several modified activities are finished and the assessment of some indices on battlefield situation consistency is fulfilled. Compare with traditional AHP and FCE, the improved MCGC is very suitable for dealing with qualitative and quantitative issues in integrated evaluation. 2. Improved MCGC The mainly improved works based on MCGC[3] and our previous application researches[6,8] are that the formula of lower indices’ En and the ones of upper indices’ Ex and En are revised and the method of SEW to calculate the index’s weights is introduced. Considering the length of paper, the especial steps of MCGC is ignored, referred to the paper [3]. 2.1. Revise 1: confirming index’s weight by SEW The index’s weight in traditional MCGC received by AHP is excessively subjective. However the method of SEW improves the weight’s objectivity and veracity by considering subjective and objective factors and combining qualitative analysis and quantitative one. There are basic steps for SEW as follows: Step 1 create especial order based on expert’s remarks; Step 2 analyze blind degree and obtain the cognition degree as a whole; Step 3 deal with the overall congition degree unitarily; The detailed calculation steps is referred to the paper[7]. 2.2. Revise 2: representing qualitative indices with cloud model By the judgements of all experts we can get t-groups of evaluating sets for each linguistic term index and then represent qualitative evaluating terms with cloud model. For example, we use a one-dimensional cloud model to measure t-evaluating terms, the improved mathematical formulas are:
1591
1592
FANLin-jun/ Lin-junProcedia et al. / Procedia Engineering 29 000–000 (2012) 1590 – 1595 FAN Engineering 00 (2011) l
l
l
l
l
Ex1 En1 + Ex 2 En 2 + L + Ex t Ent
l
Ex =
l
l
En1 + En 2 + L + En t
1
l
= En
t
3
l
(1)
l
t
∑ ( Ex
l i
l
− Ex )
(2)
2
i =1
2.3. Revise 3: computing Ex and En of upper indices After calculating the Ex and En of lower indices, the upper indices’ Ex and En could be figured considering the weight[8] calculated by SEW in the hierarchy of evaluation index system. The modified mathematical formulas are: k
∑w
S
= Ex
i
∗ Ex i
(3)
U
i =1 k
En = S
∑ w ∗ ( Ex i
U i
− Ex ) S
(4)
2
i =1
S
S
U
U
Ex and En are respectively Ex and En of upper index Y， Exi and Eni are respectively ones of lower index i. wi is the relative weight of lower index i to upper index Y.
3. Illustration In this paper, the assessment index system of situation consistency is not an important point, so several macroscopcial qualitative indices are presented to verify scientificity and feasibility of this method. There exists five central factors influencing situation consistency within the battlefield: integrality of situation picture, veracity of data, continuity of aim, aim’s delay and the degree of shared consistent information[9]. Via these factors, five indexes are abstracted. There are proportion of aims in situation picture, exact degree of aims, continuous degree of aims, delay of aims to content the requirement of war and relative consistency of aims’ situation (see Fig.1.a). We take revised MCGC to carry out the quantitative evaluation (its calculation steps sees in Fig.1.b).
Fig.1. (a) the indices of situation consistency in battlefield; (b) the steps of improved MCGC
3.1. Fixing on indices of situation consistency In this paper, the assessment indexes of situation consistency in battlefield mainly consists of five ones as follows:
FANFAN Lin-jun et al.Procedia / ProcediaEngineering Engineering0029(2011) (2012) 1590 – 1595 Lin-jun/ 000–000
4
1. Proportion of aims (PA for short) 4. Continuous degree of aims (CDA)
2. Exact degree of aims (EDA) 3. Delay of aims (DA) 5.Relative consistency of aims (RCA)
3.2. Getting indices’ state terms via experts’ evaluation To Introduce assessment sets of CGC and get rid of some non-influencing comment terms, we get the evaluation sets S = {s1 , s2 , L , s10 } = {worst, very bad (vb for short), worse, bad, general, little good (lg for short), good, better, very good(vg for short), best}. The method of traditional Delphi expert’s forecast is used and ten experts are invited to participate the assesment. Finally we get some linguistic remaks on each index’s state as shown in Table 1. Table 1 : the state value of each index Expert ID 1
PA general
EDA bad
CDA best
DA worse
RCA best good
2
lg
vg
general
general
3
general
general
vg
general
vg
4
good
lg
vg
good
general
5
better
good
general
bad
vg
6
bad
general
better
good
vg
7
good
general
bad
vg
worse
8
best
vg
general
lg
good
9
general
good
vg
bad
vg
10
lg
vg
best
good
vg
Ideal State
best
best
best
best
best
3.3. Calculating indices’ weights by SEW We ensure that all indexes’ weights are calculated by some experts’ synthetic remarks via the method of SEW. The weight vector is: W = ( w , w ,..., w ) =(0.106,0.185,0.114,0.257, 0.338). 1
11
12
15
3.4. Conversion between qualitative and quantitative According to the qualitative assessment sets of cloud model in CGC, we set ten comment terms in continuous numerical interval [0,1]. Each linguistic term’s corresponding constant interval is showed in Table 2 that LT symbols for Linguistic Term and CI is Constant Interval. Table 2 : linguistic term’s CI and formula with cloud model LT worst vb worse bad general lg good better
CI (0.00,0.15) (0.05,0.25) (0.15,0.35) (0.25,0.45) (0.35,0.55) (0.45,0.65) (0.55,0.75) (0.65,0.85)
Ex 0.00 0.15 0.25 0.35 0.45 0.55 0.65 0.75
En 0.0125 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333 0.0333
1593
1594
FANLin-jun/ Lin-junProcedia et al. / Procedia Engineering 29 000–000 (2012) 1590 – 1595 FAN Engineering 00 (2011) vg best
(0.75,0.95) (0.85,1.00)
0.85 1.00
0.0333 0.0125
According to the characteristic of cloud model’s normal distribution and referring to Ex data in Table 2, the weighted approach degree of various comment terms’ cloud model is obtained (here Ex is the weighted approach degree) and a qualitative evaluating cloud generator is constructed as shown in Fig.2.
Fig.2 : the Qualitative Evaluating Cloud Generator
As to the qualitative evaluating Cloud Generator (see Fig.2) and Ex value of each linguistic term’s evaluation as shown in Table 2 and combining each index’s state term the experts give as shown in Table 1, we use the comprehensive centre of cloud gravity G1 to measure the situation consistency in joint operations and then get the decision matrix: G = ( G , G , G , G , G ) , G ( j = 1, 2, 3, 4, 5) is the column vector of G1 , representing each lowerlevel index. 1
11
12
13
14
15
1j
⎧0.45 ⎪ ⎪0.55 ⎪0.45 ⎪ ⎪0.65 ⎪⎪0.75 G1 = ⎨ ⎪0.35 ⎪0.65 ⎪ ⎪1.00 ⎪0.45 ⎪ ⎩⎪0.55
0.35 0.85 0.45 0.55 0.65 0.45 0.45 0.85 0.65 0.85
1.00 0.45 0.85 0.85 0.45 0.75 0.35 0.45 0.85 1.00
0.25 0.45 0.45 0.65 0.35 0.65 0.85 0.55 0.35 0.65
1.00 ⎫ 0.65⎪⎪ 0.85⎪ ⎪ 0.45⎪ 0.85⎪⎪ ⎬ 0.85⎪ 0.25⎪ ⎪ 0.65⎪ 0.85⎪ ⎪ 0.85⎭⎪
Also referring to Table 2, decision matrix G1 and formulas (1), (2), we can get Ex and En of each index as shown in Table 3 that IP symbols for index parameter. Table 3 : Ex and En of each index
IP Ex En
PA 0.56 0.0282
EDA 0.61 0.0324
CDA 0.66 0.0576
DA 0.52 0.0301
RCA 0.71 0.0465
3.5. Denoting the situation consistency with a five-dimensional integrated vector We can get the five-dimensional comprehensive vector of G1 by the Ex of Table 3 and the indexes’ weights as follows: G1 = {G11 , G12 , G13 , G14 , G15} = {w11 Ex1 , w12 Ex2 , w13 Ex3 , w14 Ex4 , w15 Ex5 } = {0.0594,0.1129,0.0752,0.1336,0.2400} 3.6. Getting the unitary vector of CGC and the weighted approach degree By MCGC, the comprehensive vector of CGC in ideal state about situation consistency is: 0 0 0 0 0 0 T G1= (G11 , G12 , G13 , G14 , G15= ) W1 × M T =(0.106,0.185,0.114,0.257,0.338) ×(1,1,1,1,1)
5
FANFAN Lin-jun et al.Procedia / ProcediaEngineering Engineering0029(2011) (2012) 1590 – 1595 Lin-jun/ 000–000
6
=(0.106,0.185,0.114,0.257,0.338) After G1 is normalized, we get G1 = {0.4396,0.3897,0.3404,0.4802,0.2899}. And then the value of λ calculated by MCGC is 0. 67. And also we can get the Ex (the value is 0.62) and En (the value is 0.0059) of the whole situation consistency via the formulas (3) and (4). T
3.7. Results and discussion We know that the ideal weighted approach degree λ is 1 and the actual one in some state λ is 0.67. After the degree λ is typed in the evaluating cloud generator (see Fig.2), We can detect that the cloud drops are fitly fallen down in the domain of “good” cloud object. Thereforce, the final remark is that the situation consistency of the whole battlefield is represented by the linguistic term “good”. 0
4. Conclusion and future work In this paper, we present an improved MCGC to solve the assessment issue of situation consistency within the battlefield of joint operations. Especially, MCGC is modified based on the ideas of variance formula in Probability Theory and weight’s calculation by SEW. In the end of the paper, we provide an example to calculate the synthetic assessment value of situation consistency in the whole battlefield and validate scientificity and reasonability of the improved MCGC. The research improve the accuracy of situation consistency assessment for commanders. Next, a perfectly multi-level assessment index system will be established for the evaluation of situation consistency and some assessment work will be carried on via the improved method. Acknowledgements This work is supported by National Natural Science Foundation of China under Grant NO.60875048 and National Key Technology R&D Program of China under Grant NO.2009BAG12A05. References [1] [2]
DEYI Li, YI Du. Artificial Intelligence with Uncertainty, Journal of Software, 2004,15(11):1583-1594.
Li Deyi, Meng Haijun, Shi Xueme. Membership clouds and membership cloud generations, Journal of Computer Research and Development,1995,32(6):15-20. [3] Chen Chen, Wang Qiang, Wang Xiaoen. Air-attack Targets Threat Evaluation on MCGC, Computer Measurement & Control, 2009,17(2):354-356. [4] LEI Ying-jie, WANG Bao-shu, WANG Yi. Techniques for Battlefield Situation Assessment Based on Intuitionistic Fuzzy Decision, ACTA ELECTRONICA SINICA, 2006,34(12):2175-2179. [5] David S.Alberts, Richard E.Hayes, UNDERSTANDING COMMAND AND CONTROL. Washington, DC: CCRP Publication Series, 2006, chapter 5. [6] LIAO Liang-cai, FAN Lin-jun, WANG Peng. Method of Organization Performance Evaluation Based on Cloud Theory, Systems Engineering , 2010,28(1):99-104. [7] CHENG Qi-yue. Structure entropy weight method to confirm the weight of evaluating index, Systems EngineeringTheory & Practice, 2010,30(7):1225-1228. [8] LIAO Liang-cai, David Carmicheal. Evaluation Method Based on Cloud Theory and Utility Theory and Its Application in Owner Evaluation, Systems Engineering, 2010,28(8):39-45. [9] LI Jun-ling, Zhao Zong-gui. The analysis of the concept and impact factor of situation consistency within the battlefield of joint operations. in Proceedings of the 28th Research Institute of CETC, 2007:359-365.
1595
