In this paper, we first generalize the products of two fuzzy soft matrices. Through these generalizations, three or more fuzzy soft matrices in the different types can be multiplied. Furthermore, we introduce the mean operators and normalized fuzzy weighted mean operators of the fuzzy soft matrices. We discuss the theoretical aspects of these operators. We describe the multicriteria group decision making (MCGDM) problem with different evaluation criterion sets, and then we create two algorithms using the mean operators and generalized products of fuzzy soft matrices to deal with such problems. To show the advantages of the proposed ones, we present the comparison results with some of the preexisting decision making algorithms of fuzzy soft sets. Finally, we create Scilab codes of our algorithms to expedite and facilitate the decision making process.
The traditional picture hesitant fuzzy aggregation operators are generally suitable for aggregating information acquired in the form of picture hesitant fuzzy numbers, but they will fail in dealing with interval-valued picture hesitant fuzzy information. In this paper, we describe the notion of interval-valued picture hesitant fuzzy set and the operational laws of interval-valued picture hesitant fuzzy variables. Moreover, we derive some dynamic interval-valued picture hesitant fuzzy aggregation operators (based on Einstein operators) to aggregate the interval-valued picture hesitant fuzzy information collected at different periods. Some desirable properties of these aggregation operators are discussed in detail. In addition, we develop the approaches to tackle the multi-period decision-making problems, where all decision information takes the form of interval-valued picture hesitant fuzzy information collected at different periods. In an attempt to illustrate the applications of the proposed approaches, two numerical examples are given to measure the impact of Coronavirus Disease 2019 (COVID-19) in daily life and to identify the optimal investment opportunity. Finally, a comparative analysis of the proposed and existing studies are conducted to demonstrate the effectiveness of the proposed approaches. The presented interval-valued picture hesitant fuzzy operations, aggregation operators, and decision-making approaches can widely apply to dynamic decision analysis and multi-stage decision analysis in real life.
In this paper, we focus on the matrices representing the inverse fuzzy soft sets over both the universal object set and the universal parameter set. Some basic operations and properties of these inverse fuzzy soft matrices are investigated. Moreover, two adjustable approaches to multi-criteria group decision making (MCGDM), namely inverse fuzzy soft sum-product decision making (IFSSPDM) and inverse fuzzy soft distributive If-difference decision making (IFSDIf-dDM), are proposed. The IFSSPDM approach achieves the optimal choice for the MCGDM problem based on the inverse fuzzy soft structures consisting of multiple-discrete parameter sets and common universal object sets. The objective of IFSDIf-dDM approach is to present a solution for the MCGDM problem based on the inverse fuzzy soft structures consisting of a common universal parameter set and two discrete universal object sets. Thus, the solutions can be obtained using the practicality of inverse fuzzy soft matrices for two different types of decision making problems. Besides, the comparisons are presented showing that the proposed approaches produce more convincing outputs than the current fuzzy soft approaches.
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