Solving the interval type-2 fuzzy polynomial equation using the ranking method

2014 ◽  
Author(s):  
Nurhakimah Ab. Rahman ◽  
Lazim Abdullah
Keyword(s):  
Polynomial Equation ◽  
Ranking Method ◽  
Interval Type

Behavioral Risky Multiple Attribute Decision Making with Interval Type-2 Fuzzy Ranking Method and TOPSIS Method

2021 ◽  
pp. 1-41
Author(s):  
Wangwang Yu ◽  
Xinwang Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Ranking Method ◽  
Topsis Method ◽  
Multiple Attribute ◽  
Fuzzy Ranking ◽  
Interval Type ◽  
Evaluation Information

Considering the decision maker’s psychological state will influence their evaluation result in the risky multi-attribute decision-making problem, and the uncertainty of evaluation information. In this paper, we will propose a behavioral risky multiple attribute decision making with interval type-2 fuzzy ranking method and TOPSIS method. The interval type-2 fuzzy set is used to express the uncertainty of evaluation information, the prospect theory is applied to describe people’s psychological state in the processing of risk decision making. First, we define a new ranking method for interval type-2 fuzzy set to compare the interval type-2 fuzzy evaluation information and the expectation. Second, we give a relative distance for interval type-2 fuzzy set to get the distance between the interval type-2 fuzzy evaluation information and expectation. Third, we use the prospect theory, the new defined ranking method and the new defined distance formula to obtain the comprehensive prospect value. Fourth, we use the improved TOPSIS method and the comprehensive prospect value to rank the alternatives. Based on the above-mentioned steps, we give the solution for risky interval type-2 fuzzy multiple attribute decision-making problem, which named as the behavioral risky multiple attribute decision making with interval type-2 fuzzy ranking method and TOPSIS method. Finally, we use an example to show the rationality of this method.

A New Method for Solving Multi-Criteria Multi-Attributes Decision Making Based on the Ranking of Type-2 Fuzzy Variables

2021 ◽  
Vol 10 (1) ◽  
pp. 20-42
Author(s):  
Dhiman Dutta ◽  
Mausumi Sen ◽  
Ashok Deshpande ◽  
Biplab Singha
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Ranking Method ◽  
Ranking Methods ◽  
Fuzzy Variables ◽  
Decision Making Problem ◽  
Criteria Weights ◽  
Interval Type ◽  
Very High

In this paper, the authors have proposed the concept of interval type-2 triangular fuzzy variables. Then, they studied the concepts of value and ambiguity of interval type-2 triangular fuzzy variables and interval type-2 trapezoidal fuzzy variables. They introduced the concept of value and ambiguity in order to define the ranking method for the interval type-2 fuzzy variables. A comparative result of the various other ranking methods is also given in the tabular form. A multi-criteria multi-attributes decision-making problem is provided to explain the ranking method in which the evaluation ratings of the alternatives on the attributes, and the criteria weights as provided by the decision makers are expressed as linguistic terms (e.g., very high, medium, fair, and good). The multi-criteria multi-attributes decision-making problem is then worked out by applying the proposed algorithm.

Solutions of interval type-2 fuzzy polynomials using a new ranking method

2015 ◽  
Author(s):  
Nurhakimah Ab. Rahman ◽  
Lazim Abdullah ◽  
Ahmad Termimi Ab. Ghani ◽  
Noor ’Ani Ahmad
Keyword(s):  
Ranking Method ◽  
Fuzzy Polynomials ◽  
Interval Type

Influence of different fuzzy operators on analytical structure and variable gains of typical interval type-2 fuzzy PI controller

2020 ◽  
Vol 39 (3) ◽  
pp. 4319-4329
Author(s):  
Haibo Zhou ◽  
Chaolong Zhang ◽  
Shuaixia Tan ◽  
Yu Dai ◽  
Ji’an Duan ◽  
...  
Keyword(s):  
Pi Controller ◽  
Real Time Control ◽  
Fuzzy Operators ◽  
Fuzzy Operator ◽  
Analytical Structure ◽  
Product Operator ◽  
Pi Controllers ◽  
Fuzzy Pi Controller ◽  
Interval Type

The fuzzy operator is one of the most important elements affecting the control performance of interval type-2 (IT2) fuzzy proportional-integral (PI) controllers. At present, the most popular fuzzy operators are product fuzzy operator and min() operator. However, the influence of these two different types of fuzzy operators on the IT2 fuzzy PI controllers is not clear. In this research, by studying the derived analytical structure of an IT2 fuzzy PI controller using typical configurations, it is proved mathematically that the variable gains, i.e., proportional and integral gains of typical IT2 fuzzy PI controllers using the min() operator are smaller than those using the product operator. Moreover, the study highlights that unlike the controllers based on the product operator, the controllers based on the min() operator have a simple analytical structure but provide more control laws. Real-time control experiments on a linear motor validate the theoretical results.

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