CN117851898B - Multi-granularity variable-scale fuzzy neighborhood measure and corresponding Choquet-like integral and fault diagnosis method thereof - Google Patents

Abstract

The invention discloses a multi-granularity variable-scale fuzzy neighborhood measure and a corresponding Choquet-like integral and a fault diagnosis method thereof, and a fault diagnosis method based on "attribute reduction + intelligent classifier": input: a complete fault diagnosis decision information table; step 1, using a new attribute reduction method of a decision table based on a Choquet-like integral of a multi-granularity variable-scale fuzzy neighborhood measure, deleting redundant fault features, and realizing dimension reduction of the fault decision information table; the multi-granularity variable-scale fuzzy neighborhood measure and the corresponding Choquet-like integral and a fault diagnosis method thereof, after exporting the required data, for each collected data file, taking every 500 data points as an example, using an existing feature extraction method, all feature parameters are calculated as candidate features. The proposed reduction method of the Choquet-like integral based on the multi-granularity variable-scale fuzzy neighborhood measure is used to realize the fault diagnosis of rolling bearings.

Description

Multi-granularity variable-scale fuzzy neighborhood measure and corresponding Choquet-like integral and fault diagnosis method thereof

Technical Field

The invention relates to the technical field of multi-granularity variable-scale fuzzy, in particular to a multi-granularity variable-scale fuzzy neighborhood measure and a corresponding Choquet-like integral and a fault diagnosis method thereof.

Background

In the existing study, for multiple blurred β -coverage approximation spaces, different attributes in the dataset result in blurred β -coverage of the same threshold β. However, in a real-world problem, different attributes may produce different thresholds β. That is, different fuzzy beta-overlays with different thresholds beta need to be induced in the dataset with different attributes, i.e., the present invention will create a new multi-granularity variable-scale fuzzy theta-overlay approximation space. Moreover, the attribute reduction method (i.e. the feature selection method) based on the existing fuzzy rough set approximation space has certain defects, for example, wang et al [1] finds that some existing attribute reduction methods [2-4] cannot find the attribute reduced, namely cannot delete the redundant attribute in the data; the attribute reduction method proposed by Dai et al [5] has a strong constraint on conditional entropy, as log ₁₀ 0 occurs. Therefore, the invention provides a novel attribute reduction method under the multi-granularity variable-scale fuzzy theta-coverage approximate space, and the method is successfully used for fault diagnosis of the rolling bearing.

Disclosure of Invention

The invention aims to provide a multi-granularity variable-scale fuzzy neighborhood measure and a corresponding Choquet-like integral and a fault diagnosis method thereof, so as to solve the problems in the background technology.

In order to achieve the above purpose, the present invention provides the following technical solutions: a multi-granularity variable-scale fuzzy neighborhood measure and a corresponding Choquet-like integral and a fault diagnosis method thereof are based on a fault diagnosis method of attribute reduction and intelligent classifier:

Input: a complete fault diagnosis decision information table;

Step1, deleting redundant fault characteristics by using a Choquet-like integral decision table attribute reduction method based on multi-granularity variable-scale fuzzy neighborhood measure, and realizing dimension reduction on a fault decision information table;

Step 2, selecting an intelligent classifier model, and establishing an intelligent classifier diagnosis model; constructing a new fault data set according to the reduction determined in the step 1; then, training a diagnostic model by using the model;

step 3, performing fault classification on the test sample symptom set by using a trained intelligent classifier to obtain a diagnosis result;

And (3) outputting: fault diagnosis results and decisions;

The new method for reducing the attributes of the decision table by adopting the multi-granularity variable-scale fuzzy neighborhood measure and the corresponding Choquet-like integral in the step 1 comprises the following steps:

s1, providing a multi-granularity variable-scale fuzzy Θ -coverage approximate space:

Definition 1. Let U be a field, Θ= { β1, …, βi, …, βn }, where βi ε (0, 1;) if Is a fuzzy beta i-coverage of U, thenKnown as multi-granularity variable-scale blurring Θ -coverage on one U; also called (U, Ω) is a multi-granularity variable-scale blur Θ -covering approximation space;

S2, providing a multi-granularity variable-scale fuzzy Θ -neighborhood:

Definition 2. Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, where And Θ= { β1, …, βi, …, βn }; for any x E U, defining the multi-granularity variable-scale fuzzy Θ -neighborhood of x as:

wherein, Is x atThe fuzzy beta i-minimum description below, IT is a fuzzy logic operator t-modulo induced R-implication operator;

S3, providing up-and-down multi-granularity variable-scale fuzzy neighborhood measure:

Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, where And Θ= { β1, …, βi, …, βn }; for any oneAnd respectively defining the upper and lower multi-granularity variable-scale fuzzy neighborhood measures of X as follows:

S4, choquet-like integration based on up-down multi-granularity variable-scale fuzzy neighborhood measure is proposed:

Definition 4. Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, T be T-modulo, A ε F (U), where U= { x1, …, xn }; then we call Θ= { β1, …, βi, …, βn }, for any And respectively defining the upper and lower multi-granularity variable-scale fuzzy neighborhood measures of X as follows:

Wherein { X (1), X (2), …, X (n) } is an arrangement of { X1, X2, …, xn } such that A (X (1)). Ltoreq.A (X (2)). Ltoreq. …. Ltoreq.A (X (n)), X (i) = { X (i), X (i+1) …, X (n) },

S5, based on S1-S4, a decision table attribute reduction method based on Choquet-like integral of multi-granularity variable-scale fuzzy neighborhood measure is provided:

Input: inputting a decision information table t= (U, a }, where U = { x1, x2, …, xn }, a = { a1, a2, …, am }, bij = aj (xi), i e {1,2, …, n }, j e {1,2, …, m };

Table 1 decision information table t= (U, a U { d })

And (3) outputting: the attributes of the attribute set a are reduced.

Preferably, the S5 implementation process specifically includes:

step 1: inducing multi-granularity variable-scale blurring Θ -covering approximate space: definition of fuzzy sets for any aj ε A Wherein the method comprises the steps ofVariance for attribute aj; thenIs a fuzzy beta j-overlay (beta j epsilon (0, gamma j)),Thus, (U, Ω) is a multi-granularity variable-scale blur Θ -covered approximation space, whereAnd Θ= { β1, …, βi, …, βn }, also known as (U, Ω, d), is a multi-granularity variable-scale fuzzy Θ -coverage group decision information system;

step 2: computing multi-granularity variable-scale fuzzy Θ -neighborhood of all xk E U

Step 3: calculation ofWherein xk ε U, U/d= { D1, …, dt, …, ds } is the division of the domain U with respect to the decision attribute D;

step 4: the minimum Choquet-like reduction Redt of (U, Ω, d) is calculated as follows:

(a)P←{}；

(b)for any D∈U/d

(c)do

(d)Q←P；

(e)

(f)

(e) Q←P∪{C}

(f) P←Q

(h)return P％Suppose

(i)Redt＝{a₍₁₎,…,a_(h)}。。

A fault diagnosis method of multi-granularity variable-scale fuzzy neighborhood measure and corresponding Choquet-like integral comprises the following steps: the bearings used for testing supported the rotating shaft of the motor, and in order to obtain bearing failure data, cracks were machined in the rolling bearings using an electrical discharge machining technique, producing a series of 0.007 inch, 0.014 inch, 0.021 inch, 0.028 inch and 0.4 inch notched fault bearings, wherein not only different size cracks were produced for the outer race faults, but also bearing outer race faults were produced at different positions relative to the load bearing force points, at 3 o ' clock, 6 o ' clock and 12 o ' clock, respectively; in order to measure vibration data of a fault bearing, an acceleration sensor is arranged on a driving end of a motor, a fan end and a base of an experiment platform respectively, and only one single fault type is arranged on the experiment platform in the data acquisition process, so that the fault types in the bearing data set used for testing are all single fault types; in the process of bearing vibration data acquisition, the test platform loads different horsepowers, and the data sampling frequency is 12KHz;

after the required data are exported, taking every 500 data points as an example for each collected data file, and calculating all characteristic parameters by using the existing characteristic extraction method to serve as alternative characteristics; and then, the fault diagnosis of the rolling bearing is realized by using the proposed Choquet-like integral reduction method based on the multi-granularity variable-scale fuzzy neighborhood measure.

Compared with the prior art, the invention has the beneficial effects that:

1. The multi-granularity variable-scale fuzzy neighborhood measure and the corresponding Choquet-like integral and fault diagnosis method thereof are used for testing that a used bearing supports a rotating shaft of a motor, and in order to obtain bearing fault data, a crack is processed on a rolling bearing by using an electric spark processing technology, so that a series of fault bearings with the notch diameters of 0.007 inch, 0.014 inch, 0.021 inch, 0.028 inch and 0.4 inch are generated. Wherein not only are cracks of different sizes generated for the outer ring faults, but also bearing outer ring faults are manufactured at different positions relative to the load bearing point, and the bearing outer ring faults are respectively positioned at 3 o ' clock, 6 o ' clock and 12 o ' clock of the bearing point; in order to measure vibration data of a fault bearing, an acceleration sensor is arranged on a driving end of a motor, a fan end and a base of an experiment platform respectively, and only one single fault type is arranged on the experiment platform in the data acquisition process, so that the fault types in the bearing data set used for testing are all single fault types; in the process of bearing vibration data acquisition, the test platform loads different horsepowers, and the data sampling frequency is 12KHz;

after the required data are exported, taking every 500 data points as an example for each collected data file, and calculating all characteristic parameters by using the existing characteristic extraction method to serve as alternative characteristics; and then, the fault diagnosis of the rolling bearing is realized by using the proposed Choquet-like integral reduction method based on the multi-granularity variable-scale fuzzy neighborhood measure.

Drawings

FIG. 1 is a schematic flow chart of the present invention.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Referring to fig. 1, the present invention provides a technical solution: a multi-granularity variable-scale fuzzy neighborhood measure and a corresponding Choquet-like integral and a fault diagnosis method thereof are based on a fault diagnosis method of attribute reduction and intelligent classifier:

Input: a complete fault diagnosis decision information table;

Step1, deleting redundant fault characteristics by using a Choquet-like integral decision table attribute reduction method based on multi-granularity variable-scale fuzzy neighborhood measure, and realizing dimension reduction on a fault decision information table;

Step 2, selecting an intelligent classifier model, and establishing an intelligent classifier diagnosis model; constructing a new fault data set according to the reduction determined in the step 1; then, training a diagnostic model by using the model;

step 3, performing fault classification on the test sample symptom set by using a trained intelligent classifier to obtain a diagnosis result;

And (3) outputting: fault diagnosis results and decisions;

The new method for reducing the attributes of the decision table by adopting the multi-granularity variable-scale fuzzy neighborhood measure and the corresponding Choquet-like integral in the step 1 comprises the following steps:

s1, providing a multi-granularity variable-scale fuzzy Θ -coverage approximate space:

Definition 1. Let U be a field, Θ= { β1, …, βi, …, βn }, where βi ε (0, 1;) if Is a fuzzy beta i-coverage of U, thenKnown as multi-granularity variable-scale blurring Θ -coverage on one U; also called (U, Ω) is a multi-granularity variable-scale blur Θ -covering approximation space;

S2, providing a multi-granularity variable-scale fuzzy Θ -neighborhood:

Definition 2. Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, where And Θ= { β1, …, βi, …, βn }; for any x E U, defining the multi-granularity variable-scale fuzzy Θ -neighborhood of x as:

wherein, Is x atThe fuzzy beta i-minimum description below, IT is a fuzzy logic operator t-modulo induced R-implication operator;

S3, providing up-and-down multi-granularity variable-scale fuzzy neighborhood measure:

Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, where And Θ= { β1, …, βi, …, βn }; for any oneAnd respectively defining the upper and lower multi-granularity variable-scale fuzzy neighborhood measures of X as follows:

S4, choquet-like integration based on up-down multi-granularity variable-scale fuzzy neighborhood measure is proposed:

Definition 4. Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, T be T-modulo, A ε F (U), where U= { x1, …, xn }; then we call Θ= { β1, …, βi, …, βn }, for any And respectively defining the upper and lower multi-granularity variable-scale fuzzy neighborhood measures of X as follows:

Wherein { X (1), X (2), …, X (n) } is an arrangement of { X1, X2, …, xn } such that A (X (1)). Ltoreq.A (X (2)). Ltoreq. …. Ltoreq.A (X (n)), X (i) = { X (i), X (i+1) …, X (n) },

S5, based on S1-S4, a decision table attribute reduction method based on Choquet-like integral of multi-granularity variable-scale fuzzy neighborhood measure is provided:

Input: inputting a decision information table t= (U, a }, where U = { x1, x2, …, xn }, a = { a1, a2, …, am }, bij = aj (xi), i e {1,2, …, n }, j e {1,2, …, m };

Table 1 decision information table t= (U, a U { d })

And (3) outputting: the attributes of the attribute set a are reduced.

Preferably, the S5 implementation process specifically includes:

step 1: inducing multi-granularity variable-scale blurring Θ -covering approximate space: definition of fuzzy sets for any aj ε A Wherein the method comprises the steps ofVariance for attribute aj; thenIs a fuzzy beta j-overlay (beta j epsilon (0, gamma j)),Thus, (U, Ω) is a multi-granularity variable-scale blur Θ -covered approximation space, whereAnd Θ= { β1, …, βi, …, βn }, also known as (U, Ω, d), is a multi-granularity variable-scale fuzzy Θ -coverage group decision information system;

step 2: computing multi-granularity variable-scale fuzzy Θ -neighborhood of all xk E U

Step 3: calculation ofWherein xk ε U, U/d= { D1, …, dt, …, ds } is the division of the domain U with respect to the decision attribute D;

step 4: the minimum Choquet-like reduction Redt of (U, Ω, d) is calculated as follows:

(a)P←{}；

(b)for any D∈U/d

(c)do

(d)Q←P；

(e)

(f)

(e) Q←P∪{C}

(f) P←Q

(h)return P％Suppose

(i)Redt＝{a₍₁₎,…,a_(h)}。。

A fault diagnosis method of multi-granularity variable-scale fuzzy neighborhood measure and corresponding Choquet-like integral comprises the following steps: the bearings used for testing supported the rotating shaft of the motor, and in order to obtain bearing failure data, cracks were machined in the rolling bearings using an electrical discharge machining technique, producing a series of 0.007 inch, 0.014 inch, 0.021 inch, 0.028 inch and 0.4 inch notched fault bearings, wherein not only different size cracks were produced for the outer race faults, but also bearing outer race faults were produced at different positions relative to the load bearing force points, at 3 o ' clock, 6 o ' clock and 12 o ' clock, respectively; in order to measure vibration data of a fault bearing, an acceleration sensor is arranged on a driving end of a motor, a fan end and a base of an experiment platform respectively, and only one single fault type is arranged on the experiment platform in the data acquisition process, so that the fault types in the bearing data set used for testing are all single fault types; in the process of bearing vibration data acquisition, the test platform loads different horsepowers, and the data sampling frequency is 12KHz;

after the required data are exported, taking every 500 data points as an example for each collected data file, and calculating all characteristic parameters by using the existing characteristic extraction method to serve as alternative characteristics; and then, the fault diagnosis of the rolling bearing is realized by using the proposed Choquet-like integral reduction method based on the multi-granularity variable-scale fuzzy neighborhood measure.

To sum up: as shown in FIG. 1, in order to analyze the application of the decomposition algorithm in the rotating machinery vibration signals when the multi-granularity variable-scale fuzzy neighborhood measure and the corresponding Choquet-like integral and fault diagnosis method thereof are used, experiments [123,124] are carried out by using the bearing data of Kaiser Chu Da science (CASE WESTERN RESERVE University). The Kasi Chu Da bearing fault experiment platform consists of a motor with 2 horsepower, wherein the motor is placed on the left side of the platform, a torque sensor and an encoder are arranged in the middle of the platform, and a dynamometer is placed on the right side of the platform. The bearings used for the test support the rotating shaft of the motor and in order to obtain bearing failure data, cracks were machined into the rolling bearing using an electrical discharge machining technique, producing a series of scored failure bearings having 0.007 inches, 0.014 inches, 0.021 inches, 0.028 inches and 0.4 inches in diameter. Wherein not only are different sizes of cracks generated for the outer ring faults, but also bearing outer ring faults are manufactured at different positions relative to the load bearing point, at 3 o ' clock, 6 o ' clock and 12 o ' clock of the bearing point respectively. In order to measure vibration data of a fault bearing, the test platform is respectively provided with acceleration sensors at the driving end of the motor, the fan end and the base, and only one single fault type is arranged on the test platform in the data acquisition process, so that the fault types in the bearing data set used for testing are all single fault types. In the process of bearing vibration data acquisition, the test platform loads different horsepowers, and the data sampling frequency is 12KHz.

After the required data are derived, taking every 500 data points as an example for each acquired data file, all characteristic parameters are calculated by using the existing characteristic extraction method and are used as alternative characteristics (three types of data are mainly processed, the data information is shown in table 1, and the data information after characteristic extraction is shown in table 2). And then, the fault diagnosis of the rolling bearing is realized by using the proposed Choquet-like integral reduction method (the reduced data information is shown in the table 3) based on the multi-granularity variable-scale fuzzy neighborhood measure.

Table 1 three types of rolling bearing data

Table 2 data information after extraction of alternative features

TABLE 3 reduced data information

Finally, on one hand, the data in the table 2 are directly processed by an intelligent fault diagnosis method (support vector machine, self-adaptive enhancement and K neighbor algorithm); on the other hand, the data is optimized by the proposed Choquet-like integral reduction method based on the multi-granularity variable-scale fuzzy neighborhood measure, and then fault data (data after attribute reduction is carried out on the data in the table 2) is processed by an intelligent fault diagnosis method, so that the functions of improving the accuracy and optimizing the model are realized. The results are shown in tables 4,5 and 6.

TABLE 4 comparison of fault diagnosis for dataset1 (Dataset 1)

TABLE 5 comparison of fault diagnosis for dataset2 (Dataset 2)

TABLE 6 comparison of fault diagnosis for dataset3 (Dataset 3)

Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (3)

1. A multi-granularity variable-scale fuzzy neighborhood measure and corresponding Choquet-like integral fault diagnosis method is characterized in that:

The fault diagnosis method based on the attribute reduction and the intelligent classifier comprises the following steps:

Input: a complete fault diagnosis decision information table;

Step1, deleting redundant fault characteristics by using a Choquet-like integral decision table attribute reduction method based on multi-granularity variable-scale fuzzy neighborhood measure, and realizing dimension reduction on a fault decision information table;

Step 2, selecting an intelligent classifier model, and establishing an intelligent classifier diagnosis model; constructing a new fault data set according to the reduction determined in the step 1; then, training a diagnostic model by using the model;

step 3, performing fault classification on the test sample symptom set by using a trained intelligent classifier to obtain a diagnosis result;

And (3) outputting: fault diagnosis results and decisions;

The new method for reducing the attributes of the decision table by adopting the multi-granularity variable-scale fuzzy neighborhood measure and the corresponding Choquet-like integral in the step 1 comprises the following steps:

s1, providing a multi-granularity variable-scale fuzzy Θ -coverage approximate space:

Definition 1. Let U be a field, Θ= { β1, …, βi, …, βn }, where βi ε (0, 1;) if Is a fuzzy beta i-coverage of U, thenKnown as multi-granularity variable-scale blurring Θ -coverage on one U; also called (U, Ω) is a multi-granularity variable-scale blur Θ -covering approximation space;

S2, providing a multi-granularity variable-scale fuzzy Θ -neighborhood:

Definition 2. Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, where And Θ= { β1, …, βi, …, βn }; for any x E U, defining the multi-granularity variable-scale fuzzy Θ -neighborhood of x as:

wherein, Is x atThe fuzzy beta i-minimum description below, IT is a fuzzy logic operator t-modulo induced R-implication operator;

S3, providing up-and-down multi-granularity variable-scale fuzzy neighborhood measure:

Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, where And Θ= { β1, …, βi, …, βn }; for any oneAnd respectively defining the upper and lower multi-granularity variable-scale fuzzy neighborhood measures of X as follows:

S4, choquet-like integration based on up-down multi-granularity variable-scale fuzzy neighborhood measure is proposed:

Definition 4. Let (U, Ω) be a multi-granularity variable-scale blur Θ -covered approximation space, T be T-modulo, A ε F (U), where U= { x1, …, xn }; then we call Θ= { β1, …, βi, …, βn }, for any And respectively defining the upper and lower multi-granularity variable-scale fuzzy neighborhood measures of X as follows:

Wherein { X (1), X (2), …, X (n) } is an arrangement of { X1, X2, …, xn } such that A (X (1)). Ltoreq.A (X (2)). Ltoreq. …. Ltoreq.A (X (n)), X (i) = { X (i), X (i+1) …, X (n) },

S5, based on S1-S4, a decision table attribute reduction method based on Choquet-like integral of multi-granularity variable-scale fuzzy neighborhood measure is provided:

input: the decision information table t= (U, a U { d }) is input, where u= { x1, x2, …, xn }, a =

{a1,a2,…,am},bij＝aj(xi),i∈{1,2,…,n},j∈{1，2，…，m}；

And (3) outputting: the attributes of the attribute set a are reduced.

2. The multi-granularity variable-scale fuzzy neighborhood measure and corresponding Choquet-like integral fault diagnosis method according to claim 1, wherein the method is characterized in that: the S5 implementation process specifically comprises the following steps:

step 1: inducing multi-granularity variable-scale blurring Θ -covering approximate space: definition of fuzzy sets for any aj ε A Wherein the method comprises the steps ofVariance for attribute aj; thenIs a fuzzy beta j-overlay (beta j epsilon (0, gamma j)),Thus, (U, Ω) is a multi-granularity variable-scale blur Θ -covered approximation space, whereAnd Θ= { β1, …, βi, …, βn }, also known as (U, Ω, d), is a multi-granularity variable-scale fuzzy Θ -coverage group decision information system;

step 2: computing multi-granularity variable-scale fuzzy Θ -neighborhood of all xk E U

Step 3: calculation ofWherein xk ε U, U/d= { D1, …, dt, …, ds } is the division of the domain U with respect to the decision attribute D;

step 4: the minimum Choquet-like reduction Redt of (U, Ω, d) is calculated as follows:

(a)P←{}；

(b)for any D∈U/d

(c)do

(d)Q←P；

(e)

(f)

(e)Q←P∪{C}

(f)P←Q

(h)return P％Suppose

(i)Redt＝{a₍₁₎,…,a_(h)}。

3. A method for diagnosing multi-granularity variable-scale fuzzy neighborhood measure and corresponding Choquet-l ike integral fault, comprising any one of claims 1-2, characterized in that: the bearings used for testing supported the rotating shaft of the motor, and in order to obtain bearing failure data, cracks were machined in the rolling bearings using an electrical discharge machining technique, producing a series of 0.007 inch, 0.014 inch, 0.021 inch, 0.028 inch and 0.4 inch notched fault bearings, wherein not only different size cracks were produced for the outer race faults, but also bearing outer race faults were produced at different positions relative to the load bearing force points, at 3 o ' clock, 6 o ' clock and 12 o ' clock, respectively; in order to measure vibration data of a fault bearing, an acceleration sensor is arranged on a driving end of a motor, a fan end and a base of an experiment platform respectively, and only one single fault type is arranged on the experiment platform in the data acquisition process, so that the fault types in the bearing data set used for testing are all single fault types; in the process of bearing vibration data acquisition, the test platform loads different horsepowers, and the data sampling frequency is 12KHz;

after the required data are exported, taking every 500 data points as an example for each collected data file, and calculating all characteristic parameters by using the existing characteristic extraction method to serve as alternative characteristics; and then, the fault diagnosis of the rolling bearing is realized by using the proposed Choquet-like integral reduction method based on the multi-granularity variable-scale fuzzy neighborhood measure.