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. I...
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my-upm-ir.1040702023-07-07T02:37:17Z Interval-valued fuzzy soft topology and its applications in group decision-making problems 2022-04 Altwer, Mabruka Ali Juma 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. Fuzzy topology Decision making - Mathematical models 2022-04 Thesis http://psasir.upm.edu.my/id/eprint/104070/ http://psasir.upm.edu.my/id/eprint/104070/1/FS%202022%2038%20IR.pdf text en public doctoral Universiti Putra Malaysia Fuzzy topology Decision making - Mathematical models Kılıc¸man, Adem |
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Universiti Putra Malaysia |
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PSAS Institutional Repository |
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English |
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Kılıc¸man, Adem |
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Fuzzy topology Decision making - Mathematical models |
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Fuzzy topology Decision making - Mathematical models Altwer, Mabruka Ali Juma Interval-valued fuzzy soft topology and its applications in group decision-making problems |
description |
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. |
format |
Thesis |
qualification_level |
Doctorate |
author |
Altwer, Mabruka Ali Juma |
author_facet |
Altwer, Mabruka Ali Juma |
author_sort |
Altwer, Mabruka Ali Juma |
title |
Interval-valued fuzzy soft topology and its applications in group decision-making problems |
title_short |
Interval-valued fuzzy soft topology and its applications in group decision-making problems |
title_full |
Interval-valued fuzzy soft topology and its applications in group decision-making problems |
title_fullStr |
Interval-valued fuzzy soft topology and its applications in group decision-making problems |
title_full_unstemmed |
Interval-valued fuzzy soft topology and its applications in group decision-making problems |
title_sort |
interval-valued fuzzy soft topology and its applications in group decision-making problems |
granting_institution |
Universiti Putra Malaysia |
publishDate |
2022 |
url |
http://psasir.upm.edu.my/id/eprint/104070/1/FS%202022%2038%20IR.pdf |
_version_ |
1776100404113702912 |