Comparison between interval type-2 fuzzy sets based on a fuzzy preference relation with probability degree

2011 ◽  
Author(s):  
Feng Zhang ◽  
Ignatius Joshua ◽  
Chee-Peng Lim
Keyword(s):  
Fuzzy Sets ◽  
Preference Relation ◽  
Fuzzy Preference Relation ◽  
Interval Type ◽  
Fuzzy Preference

scholarly journals An Approach for Achieving Consistency for Symmetric Trapezoidal Interval Type-2 Fuzzy Sets

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Jiuping Xu ◽  
Kang Xu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Preference Relation ◽  
Mapping Method ◽  
Linguistic Terms ◽  
Actual Case ◽  
Preference Relations ◽  
Interval Type

Interval type-2 fuzzy sets (IT2 FSs) are powerful tools for dealing with linguistic information in decision making. However, there is a dearth of research regarding the consistency of preference relations based on IT2 FSs. In this paper, symmetric IT2 FSs and IT2 additive preference relations are defined, whilst at the same time a mapping method is proposed to convert IT2 numbers into the corresponding linguistic terms based on the ranking values for IT2 FSs, and some properties for symmetric IT2 FSs are proved. Then, we discuss the process for achieving consistency for IT2 additive preference relations. An algorithm is developed for the IT2 additive preference relation process for achieving consistency, and some desired algorithmic properties are proved. Finally, an actual case study is used in order to demonstrate the effectiveness of the proposed approach.

Soft Computing Based on an Interval Type-2 Fuzzy Decision Model for Project-Critical Path Selection Problem

2018 ◽  
Vol 5 (1) ◽  
pp. 1-24
Author(s):  
Y. Dorfeshan ◽  
S. Meysam Mousavi
Keyword(s):  
Fuzzy Sets ◽  
Critical Path ◽  
Preference Relation ◽  
Path Selection ◽  
Analysis Model ◽  
Relative Preference ◽  
Critical Path Selection ◽  
Fuzzy Decision Model ◽  
Interval Type

This article describes how project managers are faced with the conflicting criteria to make their decisions. In many real-world conditions, it may be difficult to get certain information about activities attributes, including time, cost, risk, and quality. In this case, interval type-2 fuzzy sets (IT2FSs) which consider more uncertainty than type-1 fuzzy sets (T1FSs) are used. In this article, a new group multi-criteria analysis model is expressed based on new compromise solution and relative preference relation (RPR) concept under IT2FSs environment. Also, a new version of the evaluation on distance from average solution (EDAS) method is introduced to specify the weight of each expert under IT2FSs. Furthermore, the RPR is more reasonable than the defuzzification approach. In fact, the RPR not only can provide preference degree between two fuzzy numbers but also can keep some information. Finally, an application from literature is adopted and solved to demonstrate the applicability of proposed method.

An interval type-2 hesitant fuzzy best-worst method

2021 ◽  
pp. 1-28
Author(s):  
Ashraf Norouzi ◽  
Hossein Razavi hajiagha
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Fuzzy Ahp ◽  
Uncertain Data ◽  
Interval Type ◽  
Best Worst Method

Multi criteria decision-making problems are usually encounter implicit, vague and uncertain data. Interval type-2 fuzzy sets (IT2FS) are widely used to develop various MCDM techniques especially for cases with uncertain linguistic approximation. However, there are few researches that extend IT2FS-based MCDM techniques into qualitative and group decision-making environment. The present study aims to adopt a combination of hesitant and interval type-2 fuzzy sets to develop an extension of Best-Worst method (BWM). The proposed approach provides a flexible and convenient way to depict the experts’ hesitant opinions especially in group decision-making context through a straightforward procedure. The proposed approach is called IT2HF-BWM. Some numerical case studies from literature have been used to provide illustrations about the feasibility and effectiveness of our proposed approach. Besides, a comparative analysis with an interval type-2 fuzzy AHP is carried out to evaluate the results of our proposed approach. In each case, the consistency ratio was calculated to determine the reliability of results. The findings imply that the proposed approach not only provides acceptable results but also outperforms the traditional BWM and its type-1 fuzzy extension.

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