In this paper, the existing definition of the group-based generalized intuitionistic fuzzy soft set is clarified and redefined by merging intuitionistic fuzzy soft set over the set of alternatives and a group of intuitionistic fuzzy sets on parameters. In this prospect, two new subsets of the group-based generalized intuitionistic fuzzy soft set are proposed and several operations are contemplated. The two new aggregation operators called generalized group-based weighted averaging and generalized group-based weighted geometric operator are introduced. The related properties of proposed operators are discussed. The recent research is emerging on multi-attribute decision making methods based on soft sets, intuitionistic fuzzy soft sets, and generalized intuitionistic fuzzy soft sets. An algorithm is structured and two case studies of multi-attribute decision makings are considered using proposed operators. Further, we provide the comparison and advantages of the proposed method, which give superiorities over recent major existing methods.

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Molodtsov [25] proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Sabir and Naz [30] defined notion of bipolar soft set in 2013. In this paper, we redefine concept of bipolar soft set and bipolar soft set operations as more functional than former. Also we study on their basic properties and we present a decision making method with application.

KEYWORDSInterval trapezoidal neutrosophic set; ITNNWAA operator; ITNNWG operator; Multi-attribute decision making.Abstract. The aim of this paper is to introduce an interval trapezoidal neutrosophic set, which is a combination of trapezoidal fuzzy numbers, and an interval neutrosophic set. This paper presents some operational rules and the score and accuracy functions of interval trapezoidal neutrosophic numbers. Then, some aggregation operators based on interval trapezoidal neutrosophic information are proposed: the Interval Trapezoidal Neutrosophic Number Weighted Arithmetic Averaging (ITNNWAA) operator and the Interval Trapezoidal Neutrosophic Number Weighted Geometric Averaging (ITNNWGA) operator; in addition, the properties of these operators are investigated in detail. Furthermore, a multi-attribute decision-making method is developed based on the operators. Finally, a numerical example is presented to illustrate the applicability and e ectiveness of the proposed method.

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