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International Journal of Mathematics and Mathematical Sciences
Volume 2018 (2018), Article ID 9209524, 13 pages
https://doi.org/10.1155/2018/9209524
Research Article

Fuzzy Triangular Aggregation Operators

National Advanced School of Engineering, University of Yaounde 1, 8390 Yaounde, Cameroon

Correspondence should be addressed to Ulrich Florian Simo

Received 29 June 2017; Accepted 28 November 2017; Published 1 February 2018

Academic Editor: Theodore E. Simos

Copyright © 2018 Ulrich Florian Simo and Henri Gwét. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a new class of fuzzy aggregation operators that we call fuzzy triangular aggregation operators. To do so, we focus on the situation where the available information cannot be assessed with exact numbers and it is necessary to use another approach to assess uncertain or imprecise information such as fuzzy numbers. We also use the concept of triangular norms (t-norms and t-conorms) as pseudo-arithmetic operations. As a result, we get notably the fuzzy triangular weighted arithmetic (FTWA), the fuzzy triangular ordered weighted arithmetic (FTOWA), the fuzzy generalized triangular weighted arithmetic (FGTWA), the fuzzy generalized triangular ordered weighted arithmetic (FGTOWA), the fuzzy triangular weighted quasi-arithmetic (Quasi-FTWA), and the fuzzy triangular ordered weighted quasi-arithmetic (Quasi-FTOWA) operators. Main properties of these operators are discussed as well as their comparison with other existing ones. The fuzzy triangular aggregation operators not only cover a wide range of useful existing fuzzy aggregation operators but also provide new interesting cases. Finally, an illustrative example is also developed regarding the selection of strategies.