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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301 SJR: 0.531 SNIP: 0.8 CiteScore™: 1.52

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2017020585
pages 475-510

HESITANT TRAPEZOIDAL FUZZY AGGREGATION OPERATORS BASED ON ARCHIMEDEAN t-NORM AND t-CONORM AND THEIR APPLICATION IN MADM WITH COMPLETELY UNKNOWN WEIGHT INFORMATION

Xindong Peng
School of Information Sciences and Engineering, Shaoguan University, Shaoguan, 521005, China

ABSTRACT

In this paper, we investigate the multiple attribute decision-making (MADM) problems in which the attribute values take the form of hesitant trapezoidal fuzzy elements (HTFEs). The existing t-norms and t-conorms, including the algebraic, Einstein, Frank, and Hamacher t-norms and t-conorms, can be regarded as special cases of Archimedean t-norm and t-conorm. Firstly, we develop some new operational laws for HTFEs based on the Archimedean t-norm and t-conorm. Then, based on the operational laws, we define some hesitant trapezoidal fuzzy aggregation operators and their generalizations are also introduced, and some desirable properties and the relationships of these operators are discussed in detail. Meanwhile, we present two objective weight determination methods. Inspired by the idea of dependent aggregation, we propose some dependent hesitant trapezoidal fuzzy aggregation operators: the dependent hesitant trapezoidal fuzzy Frank ordered weighted average (DHTFFOWA) operator and the dependent hesitant trapezoidal fuzzy Frank ordered weighted geometric (DHTFFOWG) operator. Furthermore, we develop an approach to MADM under hesitant trapezoidal fuzzy environment. Finally, an illustrative example for software development project selection is given to verify the developed method and to demonstrate its applicability and validity.