Preprint Article Version 1 This version is not peer-reviewed

Heronian Means as Aggregation Operators for Multi-Attribute Decision Making Applications

Version 1 : Received: 21 July 2018 / Approved: 23 July 2018 / Online: 23 July 2018 (05:29:46 CEST)

How to cite: Shang, X.; Wang, J.; Nanda, A.; Li, W. Heronian Means as Aggregation Operators for Multi-Attribute Decision Making Applications. Preprints 2018, 2018070405 (doi: 10.20944/preprints201807.0405.v1). Shang, X.; Wang, J.; Nanda, A.; Li, W. Heronian Means as Aggregation Operators for Multi-Attribute Decision Making Applications. Preprints 2018, 2018070405 (doi: 10.20944/preprints201807.0405.v1).

Abstract

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

Subject Areas

interval-valued intuitionistic fuzzy set; aggregation operator; Heronian mean; geometric Heronian mean; multi-attribute decision making

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