Interval-valued fuzzy soft topology and its applications in group decision-making problems

Interval-valued fuzzy soft sets are an extension of fuzzy soft sets, which are used in decision-making to indicate insufficient evaluation, uncertainty, and vagueness. Lower membership degree and upper membership degree are two types of information considered by interval-valued fuzzy soft sets. In the literature, there are various interval-valued fuzzy soft set-based decision-making algorithms. However, these algorithms are unable to overcome the issue of comparable alternatives, and as a result, they might well be ignored due to a lack of a comprehensive model. In addition, generalizing preorder and equivalence of interval-valued fuzzy soft sets have been proposed. This generalization shows a deeper insight into the decision-making processed based on preference relationship. In this thesis, we develop two multi algorithms based on the interval-valued fuzzy soft topology to overcome different situations in decision-making problems. In the first step, we present the interval-valued fuzzy soft topology concept as the basic framework of this work and we study some topological properties. This includes interior, closure, and continuity. Quasi-separation axioms in an intervalvalued fuzzy soft topology, known as q-Ti spaces for i = 0;1;2;3;4; together with several of their basic properties are investigated. In the second phase, we consider two crisp topological spaces, known as a lower topology induced by the interval-valued fuzzy soft topology (IVFST); denoted as tl e;b and an upper topology induced by the interval-valued fuzzy soft topology (IVFST); denoted as tu e;a: Some properties of these topologies are also studied. The induced topologies and quasi-separation axioms in interval-valued fuzzy soft topology are discussed. In the third phase, we introduce two preorder relations and two equivalence relations over X for the two topological structures tl e;b and tu e;a: We also present some properties of these preorder and equivalence relations, and links between them are studied. The links between two preorder and equivalence relations and interval-valued fuzzy soft quasi-separation axioms are studied. In the application phase of this thesis, we provide a representation of the results acquired in the previous steps in order to compute and define various algorithms that assist group decision-making using interval-valued fuzzy soft sets. The weighted interval-valued fuzzy soft set presented is applied to solve group decision-making using interval-valued fuzzy soft sets.

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