Picture fuzzy Dombi aggregation operators: Application to MADM process

• Published in: Applied soft computing Vol. 74; pp. 99 - 109
• Main Authors: Jana, Chiranjibe, Senapati, Tapan, Pal, Madhumangal, Yager, Ronald R.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.2019
• Subjects: Dombi operations; MADM; Picture fuzzy Dombi arithmetic aggregation operators; Picture fuzzy Dombi geometric aggregation operators; Picture fuzzy numbers; Picture fuzzy numbers; Picture fuzzy Dombi arithmetic aggregation operators; Picture fuzzy Dombi geometric aggregation operators; MADM; Dombi operations
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2018.10.021

The operations of t-norm and t-conorm, developed by Dombi, were generally known as Dombi operations which may have a better expression of application if they are presented in a new form of flexibility within the general parameter. To the best of our knowledge, Dombi operations are yet to be applied in exhibiting picture fuzzy sets in an appropriate form and shape. Inspired by the established theory of Dombi operations and by applying picture fuzzy numbers (PFNs), in the present study, we propose picture fuzzy Dombi weighted average (PFDWA) operator, picture fuzzy Dombi order weighted average (PFDOWA) operator, picture fuzzy Dombi hybrid weighted average (PFDHWA) operator, picture fuzzy Dombi weighted geometric (PFDWG) operator, picture fuzzy Dombi order weighted geometric (PFDOWG) operator and picture fuzzy Dombi hybrid weighted geometric (PFDHWG) operator in a new light. These aforesaid operators are enormously used in the operational parameter to help a successful solution of the given problem. Here in our endeavored study, we develop a model for picture fuzzy Dombi aggregation operators to solve multiple attribute decision making (MADM) methods in an updated way. And at the end of our study a practical application of the deducted decision over investment alternatives is reported in accordance with the enjoyment or utility of the proposed work. •Present Dombi t-norm and Dombi t-conorm operations of the picture fuzzy set.•Define picture fuzzy Dombi arithmetic/ geometric aggregation operators.•Study some desired properties of these aggregation operators.•Develop a model for these operators to solve multiple attribute decision making method.•One numerical example is provided to illustrate the proposed approach.