CN112465337A - Sewage treatment plant site selection method based on hesitation fuzzy language term set - Google Patents

Sewage treatment plant site selection method based on hesitation fuzzy language term set Download PDF

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CN112465337A
CN112465337A CN202011337122.1A CN202011337122A CN112465337A CN 112465337 A CN112465337 A CN 112465337A CN 202011337122 A CN202011337122 A CN 202011337122A CN 112465337 A CN112465337 A CN 112465337A
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黄海辉
杨敬尊
徐光侠
刘俊
马创
赵娟
李威
唐苏乐
谢明月
金浩宇
沈旭
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Chongqing University of Post and Telecommunications
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Abstract

The invention relates to the field of decision support and decision theory, in particular to a sewage treatment plant site selection method based on a hesitation fuzzy language term set, which comprises the steps of obtaining alternative plant sites of a sewage treatment plant, and evaluating the alternative plant sites by an expert group at least in the aspects of construction investment cost, related planning, related laws and regulations and natural factors; adopting a classic 7-value language term set as a language term set, and constructing a language decision matrix according to the evaluation of an expert group; a language decision matrix is positively quantized, and a positive ideal value and a negative ideal value are determined; determining the distance between each candidate plant address and the positive ideal value and the negative ideal value, calculating to obtain a comprehensive evaluation index of each candidate plant address according to the distance, and recommending the highest comprehensive evaluation index to the user; the invention effectively avoids the loss of evaluation information, so that the evaluation is more in line with the intention of a decision maker, and the precision of the evaluation result is improved.

Description

Sewage treatment plant site selection method based on hesitation fuzzy language term set
Technical Field
The invention relates to the field of decision support and decision theory, in particular to a sewage treatment plant site selection method based on a hesitation fuzzy language term set.
Background
The urban sewage treatment plant is an important infrastructure of a city, is one of important measures for preventing pollution and protecting the environment at home and abroad at present, and plays an important role in controlling water environmental pollution. With the development of urban construction, the development of industrial areas and the acceleration of the construction speed of new residential areas, the layout planning of urban sewage treatment plants becomes a key problem for the construction and management of the urban sewage treatment plants. The site selection of the sewage treatment plant is related to whether the social benefit, the economic benefit and the environmental benefit of the construction of the sewage treatment system can reach the best, is related to the coordinated development of urban economy, resources and environment, is more related to the sustainable development of the city, and has important responsibility.
At present, a lot of methods for site selection planning of sewage treatment plants are available, and a simple weighting method, a multiplication weighting method, an entropy weight method, an analytic hierarchy process, an approximate ideal solution, a gray correlation analysis method and the like are common, but in the above methods, most of evaluation information is given in a quantitative form, and preference information of experts cannot be accurately reflected, so that the final decision result is not accurate enough.
The hesitation fuzzy language term set is used as a brand-new decision tool, and a flexible and convenient way is provided for information expression and decision of people; it provides a flexible form to express people's view, strengthens the extraction of language information. The method can convert complex language information into a language expression, and extracts the language expression into the HFLTS capable of being operated by a text free method and a conversion function, and the introduction of the method enriches and develops the theoretical space of word calculation. The hesitation fuzzy language term set has been widely applied to practical decision-making problems such as university evaluation, machine engine evaluation, production strategy decision, movie recommendation system, medical diagnosis, vendor selection, and the like.
Disclosure of Invention
In order to better solve the problem of site selection of a sewage treatment plant, the invention provides a method for site selection of the sewage treatment plant based on a hesitation fuzzy language term set, which specifically comprises the following steps:
acquiring an alternative plant address of a sewage plant, and evaluating the alternative plant address at least in the aspects of construction investment cost, related planning, related laws and regulations and natural factors by an expert group;
adopting a classic 7-value language term set as a language term set, and constructing a language decision matrix according to the evaluation of an expert group;
a language decision matrix is positively quantized, and a positive ideal value and a negative ideal value are determined;
and determining the distance between each candidate plant address and the positive ideal value and the negative ideal value, calculating to obtain a comprehensive evaluation index of each candidate plant address according to the distance, and recommending the highest comprehensive evaluation index to the user.
Further, the forward language decision matrix comprises:
neg(si)＝sjand i + j is 0;
wherein neg(s)i) For the original language term siAnd (4) a negative operator.
Further, a score function based on a distance correction function is constructed, the score of each attribute of the candidate factory address is calculated according to the function, the attribute value with the highest score in the attributes is used as a positive ideal value of the factory address, the attribute value with the lowest score in the attributes is used as a negative ideal value of the factory address, and the score function is expressed as:
Figure BDA0002797582400000021
wherein, G (H)s) A scoring function for each set of hesitant fuzzy language terms;
Figure BDA0002797582400000022
is g (delta)l) Average value of (d); # HsGathering the number of linguistic terms for each group of hesitant ambiguous linguistic terms; var (t) is a variance calculated by substituting the language term subscript of HFLTS into the distance correction function; g (. delta.) ofl) The value after the distance correction function g (x) is substituted for the language index; hsTo represent a set of hesitant ambiguous linguistic terms, δlAre subscripts to the language term.
Further, the distance correction function is expressed as:
Figure BDA0002797582400000024
wherein, thetaαIs the value of the distance correction function; α is a subscript of the linguistic term; τ is the subscript maximum of the selected linguistic term.
Further, determining the distance between each of the candidate plant sites and the positive ideal value and the negative ideal value comprises:
Figure BDA0002797582400000023
Figure BDA0002797582400000031
Figure BDA0002797582400000032
wherein the content of the first and second substances,
Figure BDA0002797582400000033
is attribute HiAnd positive ideal value H+The distance between them; m is the number of evaluation attributes, each attribute has a positive ideal solution and a negative ideal solution, and the distance from each evaluation value to the positive ideal solution and the negative ideal solution needs to be calculated; omegaiIs the weight of the ith attribute;
Figure BDA0002797582400000034
is attribute HiAnd a negative ideal value H-The distance between them; l is the number of linguistic terms;
Figure BDA0002797582400000035
for the first hesitant fuzzy language term set
Figure BDA0002797582400000036
The index of the l-th language term of (c),
Figure BDA0002797582400000037
is the second hesitant fuzzy language term set
Figure BDA0002797582400000038
Subscripts of the l-th language item of (a); τ is the subscript maximum of the selected linguistic term.
Further, the comprehensive evaluation index of the alternative plant site is expressed as:
Figure BDA0002797582400000039
wherein the content of the first and second substances,
Figure BDA00027975824000000310
is a comprehensive evaluation index;
Figure BDA00027975824000000311
is attribute HiAnd positive ideal value H+The distance between them;
Figure BDA00027975824000000312
is attribute HiAnd a negative ideal value H-The distance between them.
The invention considers the influence of the distance between the hesitation fuzzy language term sets on the score value from the psychological angle of a decision maker by means of the distance correction function, provides a new score function based on the distance correction function, the new score function can reflect the psychological behaviors of people during decision making, and provides a multi-attribute decision method taking the attribute value as the score value based on the novel score function and the hesitation fuzzy language term sets, thereby improving the decision accuracy and leading the decision result to be more in line with the actual situation.
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FIG. 1 is a flow chart of a sewage treatment plant site selection method based on a hesitation fuzzy language term set according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a sewage treatment plant site selection method based on a hesitation fuzzy language term set, and as shown in figure 1, the method specifically comprises the following steps:
acquiring an alternative plant address of a sewage plant, and evaluating the alternative plant address at least in the aspects of construction investment cost, related planning, related laws and regulations and natural factors by an expert group;
adopting a classic 7-value language term set as a language term set, and constructing a language decision matrix according to the evaluation of an expert group;
a language decision matrix is positively quantized, and a positive ideal value and a negative ideal value are determined;
and determining the distance between each candidate plant address and the positive ideal value and the negative ideal value, calculating to obtain a comprehensive evaluation index of each candidate plant address according to the distance, and recommending the highest comprehensive evaluation index to the user.
Example 1
In this embodiment, it is assumed that there are 4 sites of the existing alternative sewage treatment plant, which are H respectivelyi(i ═ 1,2,3, 4). An evaluation group E consisting of 3 expertsi(i ═ 1,2,3,) have different backgrounds and knowledge, and the recommended attribute for the location of the wastewater treatment plant is C1: construction investment cost, C2: correlation planning, C3: relevant laws and regulations, C4: natural factors, wherein the weight value of each attribute is ω1＝0.4，ω2＝ω3＝ω40.2. The embodiment specifically comprises the following steps of:
(1) and acquiring a language evaluation matrix of the expert.
In the embodiment, the sewage plant candidate is evaluated by adopting the classical 7-value language term set, namely S ═ S-3Poor result is s-2Poor result of s-1A little worse, s0General, s1Slightly better, s2Good as3Fine }, taking the evaluation of each plant address attribute by the expert group as a language decision matrix, wherein each row of the matrix is the evaluation of each attribute of one candidate plant address by the expert group, and each column is the evaluation of the same attribute of each candidate plant address by the expert group, as shown in fig. 1, the matrix in the embodiment is represented as:
Figure BDA0002797582400000043
Figure BDA0002797582400000041
indicates the evaluator is in the attribute Cj(j ═ 1,2,3,4) for candidate position Hi(i is 1,2,3, 4).
TABLE 1 hesitation fuzzy language decision matrix
Figure BDA0002797582400000042
Figure BDA0002797582400000051
(2) A language decision matrix is forward.
C1: the construction investment cost is a cost-type attribute, which needs to be converted into a profitability attribute.
The matrix regularization formula is expressed as:
neg(si)＝sj(i+j＝0)；
the embodiment adopts the classic 7-value language term set to evaluate the alternative plant address of the sewage plant, namely S ═ S-3Poor result is s-2Poor result of s-1A little worse, s0General, s1Slightly better, s2Good as3Fine, in this embodiment τ is 3, the normalized language decision matrix due to ambiguity is shown in table 2.
TABLE 2 Forward hesitation fuzzy language decision matrix
Figure BDA0002797582400000052
(3) A positive ideal solution and a negative ideal solution are determined.
The process of determining the positive ideal solution and the negative ideal solution includes:
step 1: defining a distance correction function, and setting S as SαI α ═ τ, …, -1,0,1, … τ } is a set of linguistic terms, with a strictly monotonic increase, i.e.:
function g: sα→θα(α＝-τ,…,-1,0,1,…τ)，0≤θαAnd g is called as a distance correction function, and is less than or equal to 1.
The expression of the distance correction function is:
Figure BDA0002797582400000053
the function satisfies the following properties:
property (1):
Figure BDA0002797582400000054
g(sα)∈[-1,1]；
property (2): function g(s)α) At [ - τ, τ]Strictly monotonically increasing.
Step 2: defining a score function based on a distance correction function, and setting S as { S ═ S-τ,…s0,…,sτIs a set of language terms that,
Figure BDA0002797582400000066
is a hesitation fuzzy language term set based on S, based on distance correction function, then HsScore function G (H) ofs) Can be defined as:
Figure BDA0002797582400000061
wherein:
Figure BDA0002797582400000062
and step 3: calculating the score value of each attribute value by using a score function formula, and calculating the score value G (h) of each attribute11),G(h21),,G(hn1)，G(h12),G(h22),…,G(hn2),G(h1m),G(h2m),G(hnm)。
And 4, step 4: a positive ideal solution and a negative ideal solution are obtained, respectively expressed as:
Figure BDA0002797582400000063
Figure BDA0002797582400000064
through calculation, the score matrix of each evaluation value of the present embodiment is shown in table 3.
TABLE 3 scoring matrix
Figure BDA0002797582400000065
From the above table, it can be seen that:
H+＝{{s2,s3},{s3},{s2,s3},{s2,s3}}；
H-＝{{s-2,s-1,s1},{s-1,s0},{s0,s1},{s-1,s0}。
(4) calculating the distance between each evaluation object and the positive ideal solution and the negative ideal solution
The calculation formula for calculating the distance between each evaluation object and the positive ideal solution and the negative ideal solution is as follows:
Figure BDA0002797582400000071
Figure BDA0002797582400000072
wherein the content of the first and second substances,
Figure BDA0002797582400000073
ωiin order to be a weight vector, the weight vector,
Figure BDA0002797582400000074
and m is 4 and is the number of attributes.
In the present embodiment, the distance between the candidate position and the ideal solution is shown in table 4.
TABLE 4 distance between candidate position and ideal solution
Figure BDA0002797582400000075
(6) Calculating the comprehensive evaluation index of each evaluation object
The formula for calculating the comprehensive evaluation index of each evaluation object is as follows:
Figure BDA0002797582400000076
wherein the content of the first and second substances,
Figure BDA0002797582400000077
according to the calculated comprehensive evaluation index
Figure BDA0002797582400000078
The larger the evaluation index is, the larger the corresponding priority is, and the comprehensive evaluation index of all the evaluation objects is
Figure BDA0002797582400000079
And finding out the optimal position for the construction of the sewage treatment plant according to ascending order. The comprehensive evaluation index value of each evaluation object is shown in table 5.
TABLE 5 comprehensive evaluation index
Figure BDA00027975824000000710
As can be seen from Table 5, in the present embodiment
Figure BDA0002797582400000081
So alternative H is known2The method is the best position for building a sewage treatment plant.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (7)

1. A sewage treatment plant site selection method based on a hesitation fuzzy language term set is characterized by comprising the following steps:
acquiring an alternative plant address of a sewage plant, and evaluating the alternative plant address at least in the aspects of construction investment cost, related planning, related laws and regulations and natural factors by an expert group;
adopting a classic 7-value language term set as a language term set, and constructing a language decision matrix according to the evaluation of an expert group;
a language decision matrix is positively quantized, and a positive ideal value and a negative ideal value are determined;
and determining the distance between each candidate plant address and the positive ideal value and the negative ideal value, calculating to obtain a comprehensive evaluation index of each candidate plant address according to the distance, and recommending the highest comprehensive evaluation index to the user.
2. The method of claim 1, wherein the forward language decision matrix comprises:
neg(si)＝sjand i + j is 0;
wherein neg(s)i) For the original language term siAnd (4) a negative operator.
3. The method as claimed in claim 1, wherein a score function based on a distance correction function is constructed, a score of each attribute of the candidate plant site is calculated according to the function, an attribute value with the highest score in the attributes is used as a positive ideal value of the plant site, an attribute value with the lowest score in the attributes is used as a negative ideal value of the plant site, and the score function is expressed as:
Figure FDA0002797582390000011
wherein, G (H)s) A scoring function for each set of hesitant fuzzy language terms;
Figure FDA0002797582390000012
is g (delta)l) Average value of (d); l is the number of language terms in each group of the hesitant fuzzy language term set; var (t) is a variance calculated by substituting the language term subscript of HFLTS into the distance correction function; g (. delta.) ofl) The value after the distance correction function g (x) is substituted for the language index; hsTo represent a set of hesitant ambiguous linguistic terms, δlAre subscripts to the language term.
4. The method as claimed in claim 3, wherein the calculated variance after the language term subscript of HFLTS is substituted into the distance correction function is expressed as:
Figure FDA0002797582390000021
wherein g (- τ) to g (τ) are distance correction functions with scores of- τ to τ, respectively.
5. The method of claim 3, wherein the distance correction function is expressed as:
Figure FDA0002797582390000022
wherein, thetaαIs the value of the distance correction function; α is a subscript of the linguistic term; τ is the subscript maximum of the selected linguistic term.
6. The method of claim 1, wherein determining the distance between each candidate plant site and the positive and negative ideal values comprises:
Figure FDA0002797582390000023
Figure FDA0002797582390000024
Figure FDA0002797582390000025
wherein the content of the first and second substances,
Figure FDA0002797582390000026
is attribute HiAnd positive ideal value H+The distance between them; m is the number of evaluation attributes, ωiIs the weight of the ith attribute;
Figure FDA0002797582390000027
is attribute HiAnd a negative ideal value H-The distance between them; l is the number of linguistic terms;
Figure FDA0002797582390000028
for the first hesitant fuzzy language term set
Figure FDA0002797582390000029
τ is the maximum value of the subscript of the selected language term.
7. The method as claimed in claim 1, wherein the comprehensive evaluation index of the alternative plant site is expressed as:
Figure FDA00027975823900000210
wherein the content of the first and second substances,
Figure FDA00027975823900000211
to synthesizeAn evaluation index;
Figure FDA00027975823900000212
is attribute HiAnd positive ideal value H+The distance between them;
Figure FDA00027975823900000213
is attribute HiAnd a negative ideal value H-The distance between them; and n is the number of the alternative plant addresses.
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CN113469565A (en) * 2021-07-21 2021-10-01 中国人民解放军国防科技大学 Multifunctional equipment scheme selection method under capacity uncompensable mechanism and related equipment
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CN113361853A (en) * 2021-04-28 2021-09-07 合肥工业大学 Satellite emergency task planning scheme efficiency evaluation method and system of new consensus model
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CN113469565B (en) * 2021-07-21 2023-08-22 中国人民解放军国防科技大学 Multifunctional equipment scheme selection method under capability uncompensated mechanism and related equipment
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