Abstract
Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for decision makers in order to select the optimal alternative under an uncertain environment. Currently, there are three interval-valued fuzzy soft set-based decision-making algorithms in the literature. However, these algorithms are not able to overcome the issue of comparable alternatives and, in fact, might be ignored due to the lack of a comprehensive priority approach. In order to provide a partial solution to this problem, we present a group decision-making solution which is based on a preference relationship of interval-valued fuzzy soft information. Further, corresponding to each parameter, two crisp topological spaces, namely, lower topology and upper topology, are introduced based on the interval-valued fuzzy soft topology. Then, using the preorder relation on a topological space, a score function-based ranking system is also defined to design an adjustable multi-steps algorithm. Finally, some illustrative examples are given to compare the effectiveness of the present approach with some existing methods.
Highlights
Dealing with vagueness and uncertainty, rather than exactness, in most real-world situations is the main problem in data-analysis sciences and decision-making
Yang et al [25] developed the method presented in [7] for an interval-valued fuzzy soft set and applied the concept of interval-valued fuzzy choice values to propose an approach for solving decision-making problems
The methods in [25,43,44], rank the objects based on a linear ordering system, while the present method ranks the objects based on preorder relation and a preference relationship, which allows one to have some incomparable objects
Summary
Dealing with vagueness and uncertainty, rather than exactness, in most real-world situations is the main problem in data-analysis sciences and decision-making. Soft sets theory contributes to a vast range of applications, in decision-making In this regard, many important results have been achieved, from parameter reduction to new ranking models. Yang et al [25] developed the method presented in [7] for an interval-valued fuzzy soft set and applied the concept of interval-valued fuzzy choice values to propose an approach for solving decision-making problems. Ma et al [43] introduced an average and an antitheses table for intervalvalued fuzzy soft sets and selected an optimal option for group decision-making problems through the score value. Proposing a novel score function of interval-valued fuzzy soft sets that selects an optimal option for group decision-making problems. A real-life example is given to compare the effectiveness of this approach with some existing methods
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