Interval Type-2 Fuzzy Aggregation Operations Based on Maclaurin Means and Its Extensions

2019 ◽  
pp. 27-56
Author(s):  
Jindong Qin ◽  
Xinwang Liu
Keyword(s):  
Fuzzy Aggregation ◽  
Interval Type ◽  
Aggregation Operations

scholarly journals MULTIPLE CRITERIA DECISION ANALYSIS USING PRIORITISED INTERVAL TYPE-2 FUZZY AGGREGATION OPERATORS AND ITS APPLICATION TO SITE SELECTION

2017 ◽  
Vol 23 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Ting-Yu CHEN
Keyword(s):  
Decision Making ◽  
Decision Analysis ◽  
Site Selection ◽  
Aggregation Operator ◽  
Multiple Criteria ◽  
Multiple Criteria Decision Analysis ◽  
Landfill Site Selection ◽  
Fuzzy Aggregation ◽  
Interval Type

The theory of interval type-2 fuzzy sets provides an intuitive and computationally feasible method of addressing uncertain and ambiguous information in decision-making fields. This paper aims to develop a prioritised interval type-2 fuzzy aggregation operator and apply it to multiple criteria decision analysis with prioritised criteria. This paper considers situations in which a relationship between the criteria exists such that a lack of satisfaction by the higher priority criteria cannot be readily compensated by the satisfaction of lower priority criteria. This paper introduces the developed prioritised interval type-2 fuzzy aggregation operator to address the problem of criteria aggregation in this environment. To demonstrate the feasibility of the proposed operator, this paper provides a multiple criteria decision-making method that uses the prioritised interval type-2 fuzzy aggregation operator, and the method is illustrated with a practical application to landfill site selection.

scholarly journals Interval type-2 fuzzy aggregation operator in decision making and its application

2021 ◽  
Author(s):  
M. Lathamaheswari ◽  
D. Nagarajan ◽  
J. Kavikumar ◽  
Said Broumi
Keyword(s):  
Fuzzy Controller ◽  
Aggregation Operator ◽  
Climate Conditions ◽  
Real World Application ◽  
Operational Laws ◽  
Internal Parameters ◽  
Fuzzy Aggregation ◽  
Effective System ◽  
Interval Type

AbstractType-2 fuzzy sets (T2FSs) can deal with higher modeling and uncertainties which exist in the real-world application, specifically in the control systems. Particularly the climate changes are always uncertain and thus, the type-2 fuzzy controller is an effective system to handle those situations. Polyhouse is a methodology used to cultivate the plants. It breaks the seasonal hurdle of the formulation and it is also suitable for the conflictive climate conditions. Controlling and directing internal parameters of the polyhouse play an essential role in the growth of the plant. Among those, humidity is an important element when one deals with the growth of the plant in polyhouse. It affects the weather, as well as the global change of the climate and hence, the inner climate of the polyhouse will be disturbed. In this paper, operational laws for triangular interval type-2 fuzzy numbers and derived triangular interval type-2 weighted geometric (TIT2WG) operator with their desired mathematical properties using Dombi triangular norms. Also, humidity control is analyzed using interval type-2 fuzzy controller (IT2FC) with the use of derived aggregation operator which is the aim of the paper. Further stability of the system has been analyzed by applying four different defuzzification methods and the method is recommended which gives a better response.

scholarly journals Retreat: Fuzzy Multi-Criteria Decision Making Based on Pros And Cons

2019 ◽  
Vol 8 (2) ◽  
pp. 6072-6079
Keyword(s):  
Decision Making ◽  
Final Decision ◽  
Multi Criteria Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Aggregation ◽  
Life Issues ◽  
Decision Environment ◽  
Pros And Cons ◽  
Interval Type

We introduce a new fuzzy multi-criteria decision making method using interval type-2 pentagonal fuzzy numbers. We propose to incorporate pros and cons of an issue to arrive at better decision. The necessary concepts and terminologies are defined. The proposed decision method consists of three stages. We use a prioritized interval type-2 pentagonal fuzzy aggregation operator to arrive at a tentative decision in the second stage. We use the existing concept of synthesis value and define a new suitable formula in order to accommodate fuzzy decision environment with pros and cons of an issue. A formula to combine the de-fuzzified pro-value and con-value of an alternative is proposed and the same is used to rank the alternatives. We further introduce concept of consolation score to align the final decision with the gut level of a decision maker. The fuzzy concepts such as fuzzy relations and fuzzy trace theory are employed to arrive at consolation score. This newly proposed fuzzy multi-criteria decision making method is a comprehensive and complete approach to a decision problem particularly concerning life-issues.

scholarly journals Symmetric Triangular Interval Type-2 Intuitionistic Fuzzy Sets with Their Applications in Multi Criteria Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 401 ◽  
Author(s):  
Sukhveer Singh ◽  
Harish Garg
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Numerical Illustration ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Aggregation ◽  
Important Extension ◽  
Interval Type

Type-2 intuitionistic fuzzy set (T2IFS) is a powerful and important extension of the classical fuzzy set, intuitionistic fuzzy set to measure the vagueness and uncertainty. In a practical decision-making process, there always occurs an inter-relationship among the multi-input arguments. To deal with this point, the motivation of the present paper is to develop some new interval type-2 (IT2) intuitionistic fuzzy aggregation operators which can consider the multi interaction between the input argument. To achieve it, we define a symmetric triangular interval T2IFS (TIT2IFS), its operations, Hamy mean (HM) operator to aggregate the preference of the symmetric TIT2IFS and then shows its applicability through a multi-criteria decision making (MCDM). Several enviable properties and particular cases together with following different parameter values of this operator are calculated in detail. At last a numerical illustration is to given to exemplify the practicability of the proposed technique and a comparative analysis is analyzed in detail.

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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