Study on the Interactive Decision-Making in Warship Cannon Choosing

Transcription

1 78 Study on the Interactive Decision-Maing in Warship Cannon Choosing Dong Peng,2, Luo Zhaohui, Yang Chao 2 Departent of Manageent Science, Naval University of Engineeringy, Wuhan, P.R.China, School of Manageent, Huazhong University of Science and Technology, Wuhan, P.R.China, 4374 (E-ail: rocdong@63.co, navyer@63.co, chaoyang@63.co) Abstract In this paper a odel of arship cannon choosing is established on the basis of interactive decision-aing technology. To solve the proble of arship cannon choosing, an interactive odel of decision-aing is given after analyzing the basic principle of interactive decision-aing, hose feasibility is also proved. This odel aes the decision-aer ore satisfied ith the outcoe by continuously digging out the relative inforation of decision proble. The odel obeys the objective rule of arship cannon choosing. The authors give an exaple to illustrate the validity and the practicability of the established odel. Key ords Warship cannon; Choosing; Interactive decision-aing; Applicability Introduction Cannon can t be substituted by other eapons in arship. As the developent of technology, each country adopts advanced technology to ae the cannon iproved in soe aspects, such as the eight is lighter, the structure is sipler; the reaction is quicer and is roboticized. Cannon presents the characteristic of diversification in order to adapt the different deand of the flat roof of arship []. Warship cannon choosing is an iportant or in the process of arship developing, hich affects the capaign efficiency directly. Aiing at the proble of arship cannon choosing, the paper [2] puts forard the ay of decision-aing through non-fabric fuzzy unit analysis syste theory,hich reduces the subjectivity of arship cannon choosing but sacrifices part of subjective inforation. This paper introduces the theory of interactive decision-aing, establishing the odel of interactive decision-aing in arship cannon choosing, hich not only can solve the proble in the paper [2], but also iprove the degree of satisfaction of decision-aers, the case validates the validity and practicability of the odel. 2 Analysis the Theory of Interactive Decision-aing Interactive Method is one of the iportant ays in the ultiattribute decision aing, hich is a ode gradually approaches the ind, deanding the conversation ith the decision-aer in the process. The basic point of this ode is: () The decision aing is vieed as an uninterrupted process. (2) This ode ephasizes the accuulating of change quantity, and achieve the decision ai through uninterrupted correct. (3) This ode pays attention to the conflict of the finite of the decision-aer s ability and the infinity of the developent of objective things, assuring the correctness of decision-aing. Through the ay of interactive decision-aing, the aer can get the inforation and prefer inforation gradually, hich can help to ae ore satisfying decision. The decision-aer should no the result brought by his specifically prefer, so proper odel and arithetic are needed to present the best anser and its ran, each index and the difference beteen the are also required to presented to the decision-aer in the visual for in order to help to adjust the specifically inforation. The satisfying anser could be gotten through such interactive process. The present DSS, NN, eulational decision and artificial intelligence predigest the decision process in a certain extent and replace part analysis, account and broody process, but they can t replace every aspect decided by cerebru especially in the decision process on ars. Interactive decision-aing can ae the decision-aer analyze and understand the proble sufficiently and guarantee to do satisfying decision furthest, hich is unexapled by other ethods. Interactive decision-aing is applied in various fields [3-6].

2 79 Su up, interactive decision-aing has such three advantages: () Decision-aer can coprehend the decision in-depth and get ore ipersonal inforation. (2) The decision-aers can definitude glad inforation gradually. (3) Interactive decision-aing can ae us ore satisfy the result on the proble. 3 Interactive Decision-aing in Warship Cannon Choosing 3. Interactive decision-aing analysis in arship cannon choosing Warship cannon choosing involves director departent in ary, use departent, anufacture and potential anufacture (suppose that one aing unit just produce one type of cannon, so use each anufacture for short). Director departent is the organizer and decision-aer, use departent and aing unit are participants. Different to coonly decision, the cannon is the decision object as each aing unit is a decision object in fact. Besides the coon characteristic of artillery, eight, volue, the coplex degree of fabric, the nature of fixing should be also considered in cannon choosing. There are various types of cannons, so different cannons have soething particular. For exaple, the cannon AK-63M in Russia and the Phalan, the AK-63M is lo consued, about 2W, hich is only /3 of GAU-8/A in Holland; Phalan is tightened ith fabric, all equipents of hich are installed in one base except the console and telecontrol base. The difference beteen cannons constitutes any conflicts in choosing, hich aes the director departent hard to ipersonally evaluate cannon unilateral, so conventional decision eans can t satisfy the deand. Interactive decision-aing can solve this proble preferably. Firstly, the director departent in ary consults ith the using departent to ensure the rule of decision and easure inforation correspondingly, hich is given to anufacture; then each anufacture put forard their individual deand under these rules, hich are given to the ary; then director departent correct the forer inforation on the base of their individual deand; such repeat until every side satisfy. This interactive decision-aing can be express as Figure : Ary Manufacture 2 Warship Cannon Choosing Manufacture Using Departent Figure Picture of Warship Cannon Choosing Interactive Decision-aing 3.2 Interactive decision-aing on cannon choosing According upards analysis, ae interactive decision-aing odel on cannon choosing: Suppose there are n types cannon, naely n anufacture participate in evaluation, each cannon has indexes. x denotes the nuber j index in the nuber i cannon, is the eight of this index. The director departent gives judged inforation, ascertain eight range and original eight vector. () Invite l expert to give judge inforation, then l eight vectors can be gotten, just as Table :

3 72 Table Original Weight Vector Given by Experts Experts Index Weight One Index Weight To K Index Weight K K 22 2 K K K K K L l K l 2 l (2) Get the restriction upper liit and restriction loer liit of the eight vectors. Table 2 Weight Restriction Restriction Vector Index One Weight Index To Weight K Index Weight Lb (loer liit) in{ i } in{ } i 2 K in{ } i Ub (upper liit) ax{ i } ax{ } i 2 K ax{ } i () (3) Synthesize eight vectors to get original reference eight vector used in decision process. There are any eans to synthesize eight vector just as arithetic average. This paper constructs a set () () () () of vector = (,, L,, 2 ) T, hich presses closest to other vectors, naely the su of cosine of syste eight vector and other vectors is biggest. Z * l l () E (, ) θ () E = = () = ax cos = ax st. () >, i =, 2,..., i () = i (2) i= θ denote the nip angle beteen () and the eight vector E 2 T = (,, L ) of expert, the cosine of hich is: () E (, ) () () 2 2 = = (3) cos θ ( ) () E i i i i i= i= i= () (4) After ascertaining the original eight vector, director departent feed this inforation bac to anufacture. Each anufacture ascertains on eight according their preference. Adopt linearity adding eight to denote synthesis evaluation result of each type cannon, is the synthesis evaluation result of unit i and is unnon. i= x

4 72 For unit i, i =, L, n, establish odel to calculate Z = ax x (4) i j = j = j = = s. t. Lb( j) Ub( j) j =, L, x T i=, L, i (5) () In the restriction conditiont = x, hich ae the synthesis evaluation result of other i j = cannons are not loer than the synthesis evaluation result given by the ary based of syste reference eight. (5) Each anufacture feed their eight bac to the director departent ho synthesize these eights to get ne reference eights, hich are feed bac to anufacture again.repeat until each one satisfy. Prove the odel: Definition ( ) + and ( ) are to eight vectors of, the distance beteen hich is: ( ) + j j 2 (6) j = d ( +, ) = ( ) Theore Give a sallest nuber bigger than, the odel above ust converge, naely there ust have a best result ( ) + that satisfy the condition: (, ) d+ < ξ. Firstly, () is a result and Φ ust have bound, so ai function ust have best result. After give (), the best result of unit i is: () () () () = (,,, ) T, i =,, i i i2 i L L (7) Get synthesis eight vector (2) according the eans of vector synthesis. (2) is of course the bit in the Φ. So if (, ) d+ ξ, (2) can replace (), then Φ 2 Φ. 2 See the best result of unit i in Φ : (2) = (,,, ) T, i =,, n i i i2 i L L (8) (3) is the synthesis eight vector and Φ 3 Φ 2 Φ can be non fro discursion. So if d ( +, ) ξ, be non: ( ) can replace ( ) and see the best result of unit i in Φ. The folloing can

5 Φ Φ L Φ Φ (9) After each repetition, the scope of result is reduced and because it has bound, hen giving the sallest nuber ξ >, there ust be the best result ( ) + to satisfy (, ) ξ, d+ < N, hich the odel ust conver. 4 Case Analysis Adopt the applicability of cannons as exaple. Giveξ = E 3. There are three types of cannons, the attribute of hich are shon in Table 3: Table 3 Attribute Indexes Attributes Cannons Personnel Fabric Installing Warship Weight Base Radius* Exploitation Weave Adaptability Technique Ⅰ.92t VA 4 2 Ⅱ.83t VA 3 4 Ⅲ 2.5t VA 2 3 *Annotate: Volue is scaled by radius of base and exploitation use average exploitation. Since the structure adaptability and install arship technique are synthesis indexes, the ethod is: () Define tone arithetic operators: Table 4 Mood Arithetic Operators Bad Relative Bad Coon Good Excellent Mar (2) Invite experts to grade the three anufactures. The integration degree, the ay of supply bob and the characteristic of base are the ain standards to evaluate the frae adaptability; technique of anufactures, the level of orers and the proportion of specialized orers are used to ascertain install arship technique aturate degree. All three cannons are autoatic and there are no people, so e don t consider the effect of people to cannon adaptability. Weight, volue and exploitation are cathode indexes, so x = in x x are used as standard; frae adaptability and install arship technique are anode indexes, so x = x ax x are used as standard. (3) Invite four experts to copare indexes in pair, estiate atrix can be obtained. A / / = /2 /3 /2 2 A = /3 /4 /2 2 /4 /5 2 2 /2 /5 2 3 /3 /4 /2 /2 /4 /5 /2 /3 () (2)

6 723 A 2 /2 /4 2 2 /2 /4 2 /2 /4 /3 2 /2 /4 /2 2 = A = / /2 5 /2 /2 /3 /5 /2 /2 /4 /5 (3) (4) (4) Calculate the odel through Matlab requiring four circulations, then ultiate synthesis eight can be gotten. Synthesized eight vector and d corresponding are as follos: Table 5 Results Corresponding to Each Circulation Circulation Weight Vectors d One To Three Four After four circulations, the decision circulation finishes according to qualification d 4 < ξ and e get the best eight vector, hich is used to do the synthesis evaluation of each unit, naely ai function result that is used to ran the cannons, just as Table 6: Table 6 Synthesis Result and the Ran of Cannons Cannon I Cannon II Cannon III Synthesis Result Ran 2 3 According the result, the cannon II is better than cannon I and cannon III in the installing arship adaptability, but cannon I and cannon III are as uch as in the synthesis evaluation result, shoing the difference is not obvious. 5 Conclusions This paper analyzes the rule of cannon choosing based on the characteristics of cannon and arship developing. According the theory of interactive decision-aing, the interactive decision-aing odel on cannon choosing is established, hich sufficiently considers the deand of each decision aer and unifies the deand into one odel, try to satisfying every unit. The case validates the practicability of the odel. References [] Ship Inforation Center of China. Ary Equipent Manual of Navy [M]. Being: Press of National Defense Industry, 2 (In Chinese) [2] Yang Jianjun, Hu Tao, Li Fang. Quantity Evaluation Methods Research of Warship Cannon Using Adaptability in Warship Cannon Selection [J]. Ship Science and Technology, 28 (In Chinese) [3] Zhang Lixing. An Iproved Method of Interactive Multi-objective Decision-aing Based on Objective Satisfaction Degree [J]. Systes Engineering, 24 (In Chinese) [4] Xie Meifang, Li Mengjun. An Application of Interactive Optiizing Weights to Product Developent Decision [J]. Systes Engineering, 25 (In Chinese)

7 724 [5] Liu Peng, Zhang Yuanlin, Yan Xiangtao. The Method of Interactive Group Decision-aing for AHP Based on Experts Dynaic Weights [J]. Matheatics in Practice and Theory, 27 (In Chinese) [6] Wang Min, Wang Lizheng, et al. Applicatin of an Interactive Optial Method to Ship For Design [J]. Journal of Wuhan University of Technology, 22 (In Chinese)