Interval intuitionistic fuzzy multi-attribute decision making method based on improved entropy and score function

A multi-attribute decision-making, intuition-fuzzy technology, applied in data processing applications, instruments, forecasting, etc., can solve problems such as business and personal economic losses, inability to correctly determine the pros and cons of plans, loss of information, etc.

Inactive Publication Date: 2019-01-04
CHENGDU UNIV OF INFORMATION TECH
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Problems solved by technology

[0005] The first category is about the determination of attribute weights: divided into three types, one is about the situation where the attribute weights of the scheme are known, the other is when the attribute weights are partially known, and the last one is about the scheme when the attribute weights are completely unknown. the preferred question
[0006] The second category is for the sorting problem of interval numbers. Pavel takes the median point of the interval number as the sorting basis. Although this method has a small amount of calculation, the median point cannot fully reflect the characteristics of the interval number and will lose a lot of information.
[0008] (1) The existing methods for determining weights, on the one hand, are subjective and cannot correctly reflect the importance of each indicator, which in turn affects the decision-making results
On the other hand, calculating the index attribute weights through the existing linear programming method will lead to a cumbersome calculation process.
[0009] (2) The existing interval intuitionistic fuzzy entropy has defects when the entropy reaches the maximum value, which indirectly affects the determination of the weight of the attribute index and the final decision result;
[0010] (3) There are limitations in the existing scoring function, and to a certain extent, it cannot solve the problem of invalid sorting of some interval numbers, which leads to the inability to correctly determine the pros and cons of the scheme and make wrong judgments
It is necessary to sort them from the concentration of many target solutions. If the weight distribution method and sorting function are inaccurate, it will lead to deviations in the final sorting results, which will cause certain economic losses to enterprises and individuals.

Method used

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  • Interval intuitionistic fuzzy multi-attribute decision making method based on improved entropy and score function
  • Interval intuitionistic fuzzy multi-attribute decision making method based on improved entropy and score function
  • Interval intuitionistic fuzzy multi-attribute decision making method based on improved entropy and score function

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Experimental program
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Effect test

Embodiment 1

[0078] Example 1, there are 5 candidate suppliers A i (i=1, 2, ..., 5), formulating 6 assessment indicators (attributes) are: service attitude (G 1 ), product quality (G 2 ), technical level (G 3 ), and product price (G 4 ), management system (G 5 ), supply capacity (G 6 ). The attribute weight vector is k=(0.20, 0.10, 0.25, 0.10, 0.15, 0.20) T , and then consulted and recommended by experts, evaluate the 5 candidate suppliers according to the above 6 indicators, and then conduct statistical processing. Assuming that the evaluation information of each supplier under each index is standardized, the interval intuitionistic fuzzy decision matrix is ​​shown in Table 1.

[0079] Table 1 Suppliers' interval information under each assessment index

[0080]

[0081]

[0082] Step 2: Utilize the calculation formula of the improved interval intuitionistic fuzzy entropy in the second step of the present invention to calculate the attribute weight vector as W=(0.064, 0.158, ...

Embodiment 2

[0094] Concepts related to interval intuitionistic fuzzy sets

[0095] 1. Interval intuitionistic fuzzy sets

[0096] Definition 1 Assume that int[0,1] represents the entire closed subset of the interval number [0,1], X is a non-empty set, A={A (x),v A (x)|x∈X>} is an intuitionistic fuzzy set. in,

[0097] mu A : X → Int[0, 1], v A : X → Int[0, 1] (1)

[0098] To meet the conditions

[0099]

[0100] also,

[0101] π A (x)=1-μ A (x)-v A (x) (3)

[0102] Indicates the degree of hesitation that element x in set X belongs to A. π A (x) is also called intuition index or hesitation index, 0≤π A (x)≤1. If π A (x)=0, the intuitionistic fuzzy set degenerates into a fuzzy set. make,

[0103]

[0104]

[0105] but is an interval intuitionistic fuzzy set, then

[0106]

[0107] if and Then interval intuitionistic fuzzy sets degenerate into intuitionistic fuzzy sets.

[0108] 2. Interval intuitionistic fuzzy entropy

[0109] After analyzing the axioma...

Embodiment 3

[0142] Embodiment 3, comparison of interval intuitionistic fuzzy numbers

[0143] For the multi-attribute decision-making problem where the attribute weights are completely unknown, after the weights of each attribute are determined by using the interval fuzzy entropy, the inter-intuitive fuzzy numbers should be sorted. The present invention lists three sorting functions. Let α=([a, b], [c, d]) be an interval intuitionistic fuzzy number.

[0144] 1. Analysis of the limitations of existing scoring functions

[0145] (1) Xu Zeshui defined the scoring function S(α)=(a-c+b-d) / 2 and the exact function h(α)=( a+b+c+d) / 2, the sorting rule is: the larger S(α), the better the interval intuitionistic fuzzy number, and when S(α) is equal, the larger the exact function is, the better the interval intuitionistic fuzzy number is. But for the score function and the exact function, some interval numbers cannot be sorted correctly.

[0146] Example 1α 1 =([0.2,0.3],[0.1,0.4]),α 2 =([0.15,...

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Abstract

The invention belongs to the field of multi-attribute decision making, and discloses a method and system for interval intuitionistic fuzzy multiple attribute decision-making base on improved entropy and score function. Aiming at the popular problem of supplier selection, the fuzzy entropy of uncertainty and hesitation is used to determine the weight of each index under the condition that the weight of supplier attribute is completely unknown, and the objective weighting method is used to correct the deviation caused by the agent preference. The new score function is used to sort the scheme set, and the final supplier selection scheme is obtained. The invention utilizes an improved method to calculate the attribute weight according to the contribution degree of the attribute to the decisionscheme. In view of the limitation of the existing score function, a new score function is proposed. The weight of the attribute is correctly and reasonably calculated, and the score function makes upthe problem the other sorting functions fail to sort certain interval numbers to a certain extent. When the invention selects suppliers for enterprises, the invention provides a more objective and reasonable method.

Description

technical field [0001] The invention belongs to the field of multi-attribute decision-making, in particular to an interval intuitionistic fuzzy multi-attribute decision-making method based on improved entropy and score function. Background technique [0002] At present, the existing technologies commonly used in the industry are as follows: [0003] The choice of suppliers is a multi-objective decision-making problem. Usually, the solutions to such problems include analytic hierarchy process, fuzzy comprehensive evaluation method, multi-attribute decision-making method, linear programming method, TOPSIS method, etc. The invention adopts an improved interval intuitionistic fuzzy multi-attribute decision-making method applied to the problem of supplier selection. [0004] The concept of interval intuitionistic fuzzy sets was first proposed by Atanassov. Considering the complexity and uncertainty of certain things, as well as the limitations of people's cognitive level, it is...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06Q10/04G06Q10/06
CPCG06Q10/04G06Q10/0639
Inventor 张仕斌杨敏刘宁甘建超赵杨张航张金全
Owner CHENGDU UNIV OF INFORMATION TECH
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