CN103780461A - Measurement method of Web QoS through overall consideration of subjective weight and objective weight - Google Patents
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Abstract
Provided is a measurement method of Web QoS through overall consideration of the subjective weight and the objective weight. According to the measurement method, QoS factors of Web services are divided to be subjective factors and the objective factors, wherein the subjective QoS shows the degree of the Web services to meet user preference, and the objective QoS shows the overall performance of the Web services. According to the subjective QoS, on the basis of dividing the levels of the user preference, the subjective weight is adopted to quantize the fuzziness of the user preference so that the subjective requirement of users can be mastered accurately. According to the objective QoS, on the basis of analyzing the data features of QoS properties of the Web services, the objective weight is adopted to correct the one-sidedness of the user preference so that a QoS measurement result can accurately reflect the overall performance of the Web services. Through the overall consideration of the subjective QoS and the objective QoS of the Web services, the accurate QoS measurement result is obtained. The method takes the user subjective preference and the objective features of the QoS data into overall consideration, so that not only is user preference met, but also the overall performance of the Web services is mastered accurately, the accurate QoS measurement is carried out, and the method provides important reference factors for reasonably selecting the Web services and makes a contribution to popularizing the application of the Web services.
Description
Technical field
The present invention relates to a kind of method of measurement of the Web quality QoS (Quality of Service) that considers subjective and objective weight, belong to the technical field of computer application.
Background technology
Because have the Web business of magnanimity in present network, all in the time selecting Web business, user need to be in the face of more and more functions are identical but the candidate Web business that performance is different.How therefrom selecting most suitable Web business to meet user's service quality QoS demand, is the key successfully building towards Web service application.The imbody of QoS demand is its one group of QoS attribute, and each QoS attribute is wherein for characterizing Web business quality information in a certain respect.
Common Web QoS of survice attribute comprises: availability, response time, bandwidth and throughput etc.Owing to having a large amount of candidate Web business, user can not try out one by one to each Web business, to select optimal service.QoS measurement (overall performance Web business being shown by its each QoS attribute quantizes to calculate) is carried out in the performance of this Web business that just need to consider candidate on QoS attribute separately, and selects corresponding Web business according to measurement result.Therefore, QoS method of measurement is the important technology guarantee successfully building towards Web service application accurately.
External situation is: the people such as Xiaoqing Liu have proposed according to user, the satisfaction of each QoS attribute to be carried out the method for QoS measurement: first calculate the satisfaction of user to each QoS attribute based on fuzzy theory, then design " (Compromise) compromises ", " conjunction (Conjunction) " and " (Disjunction) extracts " three kinds of operators, the logical expression that re-uses relative each QoS attribute satisfaction of these three kinds of operators represents different user preferences, finally adopt the result of calculation of logical expression Web business to be carried out to the measurement of its QoS.The method advantage is to express formally various user preference, and still, its logical expression is very complicated, and needs user oneself to design the logical expression of preference separately, causes and is difficult to be used in practical application.The more important thing is, because the contribution of some attribute for QoS can be ignored or amplify to " conjunction (Conjunction) " and " (Disjunction) extracts " two kinds of operators, cause its measuring amount result to be inaccurate.
First the people such as Zhengping Wu arrive different fuzzy sets by each QoS best property of attribute mapping of candidate Web business, such as: will be mapped to " length " response time, " in ", fuzzy sets such as " short ", reliability is mapped to " height ", " in ", fuzzy sets such as " low ", then specify the logical expression that multiple QoS measure (such as: if price " low ", the corresponding time " short ", and reliability " height ", its QoS " height "), and by each attribute in the above-mentioned logical expression of degree of membership substitution for different fuzzy sets, the QoS that finally calculates Web business belongs to respectively " height ", " in ", the degree of membership of " low ", be weighted again summation, obtain final QoS measurement result.Due in QoS measuring process, the method for QoS belong to " in " degree of membership only do simple addition, cause just very general service of QoS attribute in some situation performance, obtain on the contrary higher measurement result, make its measurement result inaccurate, untrue reflection objective reality.
The QoS that Liangzhao Zeng etc. propose measures utility function, is one of this technical field achievement in research with strongest influence power.The form of utility function is ∑ (v
ij× w
j), in formula, v
ijbe the normalization value of j QoS attribute of i Web business, w
jit is the weight of j QoS attribute.The key of utility function is rationally to determine the weight of each QoS attribute.But Authors of Science Articles does not provide the distribution method of QoS attribute weight.
Domestic situation is: the Zhu Rui of the National University of Defense Technology has proposed to carry out according to the recommendation of similar users the method for QoS measurement.The method is used for reference the thought of collaborative filtering, first finds similar users, then utilizes QoS that similar users has been made to evaluate to estimate the QoS of Web business.The method is not considered the objective data feature of each QoS attribute of service, only relies on user to measure QoS to the subjective assessment of Web business, does not especially consider the credibility of user to Web business feedback, cannot guarantee the accuracy of its measurement result.
In addition, mostly there is following shortcoming in current existing QoS method of measurement:
(1) the objective characteristics of the QoS attribute data of user's subjective preferences and Web business is not considered, Main Basis user's subjective preferences is measured QoS, causes the one-sidedness of measurement result.
(2) can not the each QoS attribute of pragmatize not same-action in QoS measures, can not be from the angle of practical significance, explain importance or the irreplaceability of each QoS attribute, therefore can not guarantee the reasonability of measurement result.
At present, the development of the various application of Web business is very fast, and the quantity of Web business is more and more, and its QoS numerical value of Measurement accuracy has become the key of selecting Web business.But, in the accuracy that current existing the whole bag of tricks is all measured at QoS, there are various multi-form deficiencies.For this reason, those skilled in the art have carried out a large amount of explorations and research to this.
Summary of the invention
In view of this, the object of this invention is to provide a kind of method of measurement of the Web quality QoS that considers subjective and objective weight, the method is considered the objective characteristics of user's subjective preferences and QoS data, in meeting user preference, can accurately hold the overall performance of Web business, and then carry out QoS accurately and measure, for reasonably selecting Web business that crucial reference factor is provided, for applying of Web business contributes.
In order to achieve the above object, the invention provides a kind of service quality QoS method of measurement of the Web business that considers subjective and objective weight, it is characterized in that: the QoS factor of Web business is divided into two kinds of subjectiveness and objectiveness: subjective QoS represents that Web business meets the degree of user preference, and objective QoS represents the height of Web business overall performance; Wherein, subjective QoS is dividing on the basis of user preference level, adopts subjective weight to quantize the ambiguity of user preference, for the subjective demand of accurately holding user; Objective QoS is analyzing on the data characteristics basis of Web QoS of survice attribute, and the one-sidedness that adopts objective weight to correct user preference, so that the overall performance that QoS measurement result can accurate response Web business; By considering subjective QoS and the objective QoS of Web business, obtain QoS measurement result accurately again; The method comprises following operating procedure:
Step 1, data normalization processing: because of QoS attribute have for forward attribute: value is the bigger the better, and what have is negative sense attribute: value is the smaller the better; And measurement unit's difference of each attribute, the inconvenience that causes QoS to measure, therefore will be normalized each QoS attribute: the value by each Web business on each QoS attribute is converted into [0,1] interval numerical value before QoS measures;
Step 2, calculating SQ
ithe subjective QoS representing: first calculate the subjective weight of the each QoS attribute of each Web business, to can adapt to the difference preference of all types of user, accurately represent the significance level of each QoS attribute in user preference; Calculate SQ in conjunction with the value of the each QoS attribute after normalized again
i; Natural number subscript i is the sequence number of Web business;
Step 3, calculating OQ
ithe objective QoS representing: first calculate the objective weight of the each QoS attribute of each Web business, for the QoS attribute data feature of analyzing candidate Web business, correct the one-sidedness of user preference; Calculate OQ in conjunction with the value of the each QoS attribute after normalized again
i;
Step 4, calculating Q
ithe QoS:Q representing
i=α × SQ
i+ (1-α) × OQ
i, in formula, preference intensity factor-alpha is the degree of dependence to user preference in QoS measuring process, is embodied in subjective QoS and objective QoS in QoS measurement result, i.e. SQ
iand OQ
iboth ratios, and 0≤α≤1, its numerical value is arranged by user.
The key technology that the present invention considers the method for measurement of the Web quality QoS of subjective and objective weight is to calculate objective weight.Because the calculating of objective weight needs the QoS data distribution characteristics of multianalysis candidate Web business, could do you accurately judge the discrimination of each QoS attribute for different Web business? and then drawing the objective weight with practical significance, why more important than another attribute certain attribute of reasonable dismissal is.In addition, the innovative technology of the inventive method also comprises following 2 points:
(A) having proposed first QoS measurement is user preference and the coefficient result of candidate Web business, the data characteristics of the QoS attribute of user preference and candidate Web business should be considered.
(B) the objective weight computational methods that the present invention proposes can each QoS attribute of pragmatize not same-action in QoS measures so that measurement result can reflect the overall performance of Web business exactly.
The advantage of the inventive method is: can automatically adapt to various dissimilar user preferences, the ambiguity of user preference is reasonably quantized, so that the QoS measurement result of Web business can accurately reflect user's request.Considered the data characteristics of the QoS attribute of candidate Web business, the one-sidedness of having corrected user preference, so that QoS measurement result has really embodied the overall performance of Web business, thereby obtains measurement result accurately comprehensively.The inventive method applicable performance is strong, and the QoS that can be used in all kinds Web business measures.Therefore, the present invention has higher accuracy and stronger practicality, has good application value.
Accompanying drawing explanation
Fig. 1 is the QoS method of measurement operating procedure flow chart of the present invention's Web business of considering subjective and objective weight.
Embodiment
For making the object, technical solutions and advantages of the present invention clearer, below in conjunction with accompanying drawing, the present invention is described in further detail.
The present invention considers the service quality QoS method of measurement of the Web business of subjective and objective weight, that the QoS factor of Web business is divided into two kinds of subjectiveness and objectiveness: subjective QoS represents that Web business meets the degree of user preference, and objective QoS represents the height of Web business overall performance; Wherein, subjective QoS is dividing on the basis of user preference level, adopts subjective weight to quantize the ambiguity of user preference, for the subjective demand of accurately holding user; Objective QoS is analyzing on the data characteristics basis of Web QoS of survice attribute, and the one-sidedness that adopts objective weight to correct user preference, so that the overall performance that QoS measurement result can accurate response Web business; By considering subjective QoS and the objective QoS of Web business, obtain QoS measurement result accurately again
Referring to Fig. 1, introduce the concrete operation step of the inventive method:
Step 1, data normalization processing: because of QoS attribute have for example, for forward attribute (throughput): value is the bigger the better, and what have is negative sense attribute (for example price): value is the smaller the better; And measurement unit's difference of each attribute, the inconvenience that causes QoS to measure, therefore, before QoS measures, need to be normalized each QoS attribute: the value by each Web business on each QoS attribute is converted into [0,1] interval numerical value.This step comprises following content of operation:
(11) the Web business composition that all candidates is set is gathered WS={ws
1, ws
2..., ws
i..., ws
s, in formula, ws is the Web business in this WS set, and natural number subscript i is the sequence number of Web business, and in its maximum, i.e. this set, Web business adds up to s.
(12) whole QoS attribute compositions of establishing Web business are gathered P={p
1, p
2..., p
j..., p
t, in formula, p is each QoS attribute, and natural number subscript j is the sequence number of Web QoS of survice attribute, and in its maximum, i.e. this set, QoS attribute adds up to t.
(13) to each ws
iat QoS attribute p
jthe normalized of upper execution value:
If p
jfor forward attribute, adopt formula
carry out normalized;
If p
jfor negative sense attribute, adopt formula
carry out normalized; Wherein, d is the value of QoS attribute, and nd is normalized QoS property value, d
i,jfor ws
iat p
jon value, nd
i,jfor d
i,jnumerical value after normalized,
with
be respectively { d
1, j, d
2, j..., d
s,jin minimum value and maximum.
Step 2, calculating SQ
ithe subjective QoS representing: first calculate the subjective weight of the each QoS attribute of each Web business, to can adapt to the difference preference of all types of user, accurately represent the significance level of each QoS attribute in user preference; Calculate SQ in conjunction with the value of the each QoS attribute after normalized again
i; Natural number subscript i is the sequence number of Web business.
User preference is user in the time selecting Web business, is concerned about the performance of Web business on which QoS attribute.The user preference of different user is very not identical, and such as some user is concerned about the performance of Web business on bandwidth and throughput, and some user is concerned about the performance of Web business in response time and reliability.Each QoS attribute in Web collection of services P has objective weight, and the QoS attribute of still, only have QoS attribute that user is concerned about, gathering in two subset A and the B of P just has subjective weight.
In this step 2, the operation of calculating subjective weight comprises following content:
(21) the QoS attribute of first user being concerned about is divided into two classes: using user be concerned about most, QoS attribute that must be first satisfied is as main preference attribute, and the set of this part QoS attribute composition is set
wherein, natural number u and m are respectively sequence number and the sums thereof of main preference attribute, and all subscript a
u(u=1,2 ..., m) the subset A of composition P.
(22) be less important preference attribute by QoS subjective attribute lower user's degree of attentiveness, that can make suitable compromise, and the set of this part QoS attribute composition is set
wherein, natural number v and n are respectively sequence number and the sums thereof of less important preference attribute, and all subscript b
v(v=1,2 ..., n) the subset B of composition P.Obviously, A and B are the subsets of P.
(23) the subjective weight of all QoS attributes in subset A is set identical, is all
the subjective weight of all QoS attributes is set in subset B more identical, is all
wherein, input variable β (0≤β≤1) is the respective value that user arranges according to user preference separately, for user preference, the significance level of the main preference attribute of cause is higher than less important preference attribute, therefore the subjective weight of less important preference attribute is β (0≤β≤1) times of the subjective weight of main preference attribute.
(24) each Web business ws in set of computations WS according to the following equation
isubjective QoS:
Step 3, calculating OQ
ithe objective QoS representing: first calculate the objective weight of the each QoS attribute of each Web business, for the QoS attribute data feature of analyzing candidate Web business, correct the one-sidedness of user preference; Calculate OQ in conjunction with the value of the each QoS attribute after normalized again
i.
The one-sidedness of user preference shows both ways: the one, and because user does not know the distribution characteristics of candidate Web QoS of survice attribute data, therefore user preference can not each QoS attribute effect in services selection of objective embodiment.The 2nd, because Web business has multiple QoS attributes, and user preference may be only concerned about part QoS subjective attribute wherein, thereby ignores the effect of other QoS attributes in QoS measures.
In this step 3, to the each QoS attribute p in QoS community set P
jthe calculating operation of objective weight comprise following content:
(31) all Web business in observation WS are at this QoS attribute p
jon value condition:
If each Web business is at p
jon value when all different, (now each Web business is at p at most s different value
jon value all different);
And if all Web business are at p
jon value when all identical, minimum only have 1 value (now all Web business be at p
jon value identical);
Suppose that all Web business in WS are at QoS attribute p
j(1≤k≤s) individual different numerical value, by these numerical value composition set T={d for upper total k
1, d
2...., d
h...., d
k, in formula, d is the value of QoS attribute, natural number h and k are respectively sequence number and total numbers of value in set T;
Be arranged on again p
jupper value is d
hweb number of services be l
h, p
jreference degree be:
(32) according to above-mentioned steps (31), solve the reference degree that obtains all QoS attributes in QoS community set P, then by the reference degree composition set R={r of all QoS attributes
1, r
2..., r
j..., r
t, in formula, r
jfor j QoS attribute p in P
jreference degree, natural number subscript j and t are sequence number and total number, the p of Web QoS of survice attribute
jobjective weight be
(33) according to above-mentioned steps (32), solve the objective weight that obtains gathering all QoS attributes in P, then by the objective weight composition set OW={ow of all QoS attributes
1, ow
2..., ow
j..., ow
t, wherein, ow is objective weight, ow
jfor p
jobjective weight; Calculate according to the following equation the more each Web business ws in WS
iobjective QoS:
Step 4, calculating Q
ithe QoS:Q representing
i=α × SQ
i+ (1-α) × OQ
i, in formula, preference intensity factor-alpha is the degree of dependence to user preference in QoS measuring process, is embodied in subjective QoS and objective QoS in QoS measurement result, i.e. SQ
iand OQ
iboth ratios, and 0≤α≤1, its numerical value is arranged by user.
The present invention has carried out repeatedly embodiment test, and the result of l-G simulation test is successfully, has realized goal of the invention.
Claims (6)
1. one kind considers the service quality QoS method of measurement of the Web business of subjective and objective weight, it is characterized in that: the QoS factor of Web business is divided into two kinds of subjectiveness and objectiveness: subjective QoS represents that Web business meets the degree of user preference, and objective QoS represents the height of Web business overall performance; Wherein, subjective QoS is dividing on the basis of user preference level, adopts subjective weight to quantize the ambiguity of user preference, for the subjective demand of accurately holding user; Objective QoS is analyzing on the data characteristics basis of Web QoS of survice attribute, and the one-sidedness that adopts objective weight to correct user preference, so that the overall performance that QoS measurement result can accurate response Web business; By considering subjective QoS and the objective QoS of Web business, obtain QoS measurement result accurately again; The method comprises following operating procedure:
Step 1, data normalization processing: because of QoS attribute have for forward attribute: value is the bigger the better, and what have is negative sense attribute: value is the smaller the better; And measurement unit's difference of each attribute, the inconvenience that causes QoS to measure, therefore will be normalized each QoS attribute: the value by each Web business on each QoS attribute is converted into [0,1] interval numerical value before QoS measures;
Step 2, calculating SQ
ithe subjective QoS representing: first calculate the subjective weight of the each QoS attribute of each Web business, to can adapt to the difference preference of all types of user, accurately represent the significance level of each QoS attribute in user preference; Calculate SQ in conjunction with the value of the each QoS attribute after normalized again
i; Natural number subscript i is the sequence number of Web business;
Step 3, calculating OQ
ithe objective QoS representing: first calculate the objective weight of the each QoS attribute of each Web business, for the QoS attribute data feature of analyzing candidate Web business, correct the one-sidedness of user preference; Calculate OQ in conjunction with the value of the each QoS attribute after normalized again
i;
Step 4, calculating Q
ithe QoS:Q representing
i=α × SQ
i+ (1-α) × OQ
i, in formula, preference intensity factor-alpha is the degree of dependence to user preference in QoS measuring process, is embodied in subjective QoS and objective QoS in QoS measurement result, i.e. SQ
iand OQ
iboth ratios, and 0≤α≤1, its numerical value is arranged by user.
2. method according to claim 1, is characterized in that: described step 1 comprises following content of operation:
(11) the Web business composition that all candidates is set is gathered WS={ws
1, ws
2..., ws
i..., ws
s, in formula, ws is the Web business in this WS set, and natural number subscript i is the sequence number of Web business, and in its maximum, i.e. this set, Web business adds up to s;
(12) whole QoS attribute compositions of establishing Web business are gathered P={p
1, p
2..., p
j..., p
t, in formula, p is QoS attribute, and natural number subscript j is the sequence number of Web QoS of survice attribute, and in its maximum, i.e. this set, QoS attribute adds up to t;
(13) to each ws
iat QoS attribute p
jthe normalized of upper execution value:
If p
jfor forward attribute, adopt formula
carry out normalized;
If p
jfor negative sense attribute, adopt formula
carry out normalized; Wherein, d is the value of QoS attribute, and nd is normalized QoS property value, d
i,jfor ws
iat p
jon value, nd
i,jfor d
i,jnumerical value after normalized,
with
be respectively { d
1, j, d
2, j..., d
s,jin minimum value and maximum.
3. method according to claim 1 and 2, is characterized in that: in described step 2, the calculating operation of subjective weight comprises following content:
(21) the QoS attribute of first user being concerned about is divided into two classes: using user be concerned about most, QoS attribute that must be first satisfied is as main preference attribute, and the set of this part QoS attribute composition is set
wherein, natural number u and m are respectively sequence number and the sums thereof of main preference attribute, and all subscript a
u(u=1,2 ..., m) the subset A of composition P;
(22) be less important preference attribute by QoS subjective attribute lower user's degree of attentiveness, that can make suitable compromise, and the set of this part QoS attribute composition is set
wherein, natural number v and n are respectively sequence number and the sums thereof of less important preference attribute, and all subscript b
v(v=1,2 ..., n) the subset B of composition P;
(23) the subjective weight of all QoS attributes in subset A is set identical, is all
the subjective weight of all QoS attributes is set in subset B more identical, is all
wherein, input variable β (0≤β≤1) is the numerical value that user arranges according to user preference separately, for user preference, the significance level of the main preference attribute of cause is higher than less important preference attribute, therefore the subjective weight of less important preference attribute is β (0≤β≤1) times of the subjective weight of main preference attribute;
(24) each Web business ws in set of computations WS according to the following equation
isubjective QoS:
4. method according to claim 3, is characterized in that: the each QoS attribute in described QoS community set P has objective weight, and only have QoS attribute that user is concerned about, QoS attribute in the subset A and the B that gather P just has subjective weight.
5. method according to claim 1 and 2, is characterized in that: in described step 3, for the each QoS attribute p in QoS community set P
jthe calculating operation of objective weight comprise following content:
(31) all Web business in observation WS are at this QoS attribute p
jon value condition:
If each Web business is at p
jon value when all different, have at most s different value;
And if all Web business are at p
jon value when all identical, minimum only have 1 value;
Suppose that all Web business in WS are at QoS attribute p
j(1≤k≤s) individual different numerical value, by these numerical value composition set T={d for upper total k
1, d
2...., d
h...., d
k, in formula, d is the value of QoS attribute, natural number h and k are respectively sequence number and total numbers of value in set T;
Be arranged on again p
jupper value is d
hweb number of services be l
h, p
jreference degree be:
(32) according to above-mentioned steps (31), solve the reference degree that obtains all QoS attributes in QoS community set P, then by the reference degree composition set R={r of all QoS attributes
1, r
2..., r
j..., r
t, in formula, r
jfor j QoS attribute p in P
jreference degree, natural number subscript j and t are sequence number and total number, the p of Web QoS of survice attribute
jobjective weight be
(33) according to above-mentioned steps (32), solve the objective weight that obtains gathering all QoS attributes in P, then by the objective weight composition set OW={ow of all QoS attributes
1, ow
2..., ow
j..., ow
t, wherein, ow is objective weight, ow
jfor p
jobjective weight; Calculate according to the following equation the each Web business ws in WS
iobjective QoS:
6. method according to claim 1 and 2, is characterized in that: the one-sidedness of the user preference in described step 3 shows both ways:
The one, because user does not know the distribution characteristics of candidate Web QoS of survice attribute data, therefore each QoS attribute effect in services selection that user preference can not objective embodiment;
The 2nd, because Web business has multiple QoS attributes, and user preference may be only concerned about part QoS subjective attribute wherein, thereby ignores the effect of other QoS attributes in QoS measures.
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| CN107133268A (en) * | 2017-04-01 | 2017-09-05 | 南京邮电大学 | A kind of collaborative filtering for Web service recommendation |
| CN115964570A (en) * | 2023-03-17 | 2023-04-14 | 湖南师范大学 | Cloud service recommendation method and device based on QoS multi-period change characteristic prediction |
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| CN101364899A (en) * | 2008-10-10 | 2009-02-11 | 北京航空航天大学 | Web QoS evaluating method based on cloud model |
| CN101404589A (en) * | 2008-11-14 | 2009-04-08 | 北京邮电大学 | WEB service single Qos attribute appraisement method based on user requirement |
| CN101399707A (en) * | 2008-11-20 | 2009-04-01 | 北京邮电大学 | Method and device for selecting internet service based on credit |
| CN102880637A (en) * | 2012-08-07 | 2013-01-16 | 东南大学 | Dynamic Web service trust evaluation method based on user honesty |
| CN103077177A (en) * | 2012-08-28 | 2013-05-01 | 华南理工大学 | Fuzzy QoS (Quality of Service) selection method for web service in combination with expert opinion and user preference |
| CN103412918A (en) * | 2013-08-08 | 2013-11-27 | 南京邮电大学 | Quality of service (QoS) and reputation based method for evaluating service trust levels |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107133268A (en) * | 2017-04-01 | 2017-09-05 | 南京邮电大学 | A kind of collaborative filtering for Web service recommendation |
| CN107133268B (en) * | 2017-04-01 | 2020-03-31 | 南京邮电大学 | Collaborative filtering method for Web service recommendation |
| CN115964570A (en) * | 2023-03-17 | 2023-04-14 | 湖南师范大学 | Cloud service recommendation method and device based on QoS multi-period change characteristic prediction |
| CN115964570B (en) * | 2023-03-17 | 2023-06-02 | 湖南师范大学 | Cloud service recommendation method and device based on QoS multi-period change feature prediction |
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| CN103780461B (en) | 2017-04-26 |
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