Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral

The theory of complex dual type-2 hesitant fuzzy sets (CDT-2HFSs) is a blend of two different modifications of fuzzy sets (FSs), called complex fuzzy sets (CFSs) and dual type-2 hesitant fuzzy sets (DT-2HFSs). CDT-2HFS is a proficient technique to cope with unpredictable and awkward information in realistic decision problems. CDT-2HFS is composed of the grade of truth and the grade of falsity, and the grade of truth (also for grade of falsity) contains the grade of primary and secondary parts in the form of polar coordinates with the condition that the sum of the maximum of the real part (also for the imaginary part) of the primary grade (also for the secondary grade) cannot exceed the unit interval [0, 1]. The aims of this manuscript are to discover the novel approach of CDT-2HFS and its operational laws. These operational laws are also justified with the help of an example. Additionally, based on a novel CDT-2HFS, we explored the correlation coefficient (CC) and entropy measures (EMs), and their special cases are also discussed. TOPSIS method based on CDT-2HFS is also explored. Then, we applied our explored measures based on CDT-2HFSs in the environment of the TOPSIS method, medical diagnosis, pattern recognition, and clustering algorithm to cope with the awkward and complicated information in realistic decision issues. Finally, some numerical examples are given to examine the proficiency and validity of the explored measures. Comparative analysis, advantages, and graphical interpretation of the explored measures with some other existing measures are also discussed.

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Hazard identification, risk assessment and control for dam construction safety using an integrated BWM and MARCOS approach under interval type-2 fuzzy sets environment

Automation in Construction ◽

10.1016/j.autcon.2021.103699 ◽

2021 ◽

Vol 127 ◽

pp. 103699

Author(s):

Erkan Celik ◽

Muhammet Gul

Keyword(s):

Risk Assessment ◽

Fuzzy Sets ◽

Construction Safety ◽

Hazard Identification ◽

Dam Construction ◽

Interval Type ◽

And Control

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An interval type-2 hesitant fuzzy best-worst method

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202801 ◽

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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