**m-Polar Fuzzy Soft Weighted Aggregation Operators and Their Applications in Group Decision-Making**

#### **Azadeh Zahedi Khameneh 1 and Adem Kiliçman 1,2,\***


Received: 26 October 2018; Accepted: 6 November 2018; Published: 13 November 2018

**Abstract:** Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers' behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreemen<sup>t</sup> scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreemen<sup>t</sup> affect the final outcome.

**Keywords:** m-polar fuzzy soft set; m-polar fuzzy soft preference relationship; aggregation operator; multi-attribute group decision-making
