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Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications

Molodtsov (1999) introduced the concept of a soft set as a general mathematical tool for dealing with uncertainty as a mapping from a set of parameters to a power set of the universe. Moreover, Maji, Biswas and Roy (2001) have introduced the concept of fuzzy soft set and Majumdar and Samanta (2010)...

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Main Author: Ayman Abdelkarim Mohammad Hazaymeh
Format: Thesis
Language:English
Published: Universiti Sains Islam Malaysia 2015
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FST
Online Access:http://ddms.usim.edu.my/handle/123456789/8247
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spelling my.usim-82472017-03-02T07:20:58Z Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications Ayman Abdelkarim Mohammad Hazaymeh FST Molodtsov (1999) introduced the concept of a soft set as a general mathematical tool for dealing with uncertainty as a mapping from a set of parameters to a power set of the universe. Moreover, Maji, Biswas and Roy (2001) have introduced the concept of fuzzy soft set and Majumdar and Samanta (2010) have introduced the concept of generalized fuzzy soft sets and their operations and application of generalized fuzzy soft sets in decision making problem. In 1975 Zadeh introduced a concept of an interval-valued fuzzy set. After Zadeh’s work, Yang et al. (2009) defined a hybrid model called the interval-valued fuzzy soft sets and investigated some of their basic properties. Cagman et al. (2010) defined a fuzzy parameterized fuzzy soft set in which the approximate functions are defined from a set of fuzzy parameters to the fuzzy subsets of the universal set. The question here: are all the parameters of this type of problems has no time value for previous information which means why we didn’t take the component time value of the information in our consideration when we are making decision. To solve the problem with time as parameters and as a generalization of Molodtsov’s soft set we shall introduce the concept of a time-fuzzy soft set (T-FSS), and study some of its properties and basic operations. Namely complement, union, intersection, AND and OR, and we shall elaborate the concept of time in decision making through some hypothetical application problem. Most of these models came through one expert, to solve this problem, Alkhazaleh (2012) considered a collection of experts and generalized soft set to soft expert set and fuzzy soft expert with two opinions, where they study some of its properties and explained the application of this concept in decision making problem. In some problems, may be two opinions are insufficient for decision making problem. Therefore we need to enrich the state with multi opinions, which makes it possible to make better decisions and learn more to make better decisions. To enrich this concept to be more effective and useful we shall consider a collection set of opinions and generalize the concept of fuzzy soft expert set with multi opinions and explain the application of this concept in decision making problem. Then we shall introduce an algorithm to convert the fuzzy soft expert set with multi opinions to fuzzy soft set and find the decision. By a combination the previous concepts we shall introduce the concept of a time-fuzzy soft expert set (T-FSES) and the concept of a fuzzy parameterized fuzzy soft expert set (FPFSES) and the concept of interval-valued fuzzy soft expert set (IV-FSES). Finally, we introduce the concept of generalized fuzzy soft expert set (GFSES), and study some of its properties and its basic operations namely, complement, union, intersection, AND and OR. Then we shall present two hypothetical applications in decision making problem of our previous concepts ((T-FSES, FPFSES, IVFSES and GFSES). Finally for the last two of our concepts (IVFSES, GFSES)we shall introduce the mapping of the classes of the concepts and study their properties. 2015-05-26T02:52:57Z 2015-05-26T02:52:57Z 2013-11 Thesis http://ddms.usim.edu.my/handle/123456789/8247 en Universiti Sains Islam Malaysia
institution Universiti Sains Islam Malaysia
building USIM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universit Sains Islam i Malaysia
content_source USIM Institutional Repository
url_provider http://ddms.usim.edu.my/
language English
topic FST
spellingShingle FST
Ayman Abdelkarim Mohammad Hazaymeh
Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications
description Molodtsov (1999) introduced the concept of a soft set as a general mathematical tool for dealing with uncertainty as a mapping from a set of parameters to a power set of the universe. Moreover, Maji, Biswas and Roy (2001) have introduced the concept of fuzzy soft set and Majumdar and Samanta (2010) have introduced the concept of generalized fuzzy soft sets and their operations and application of generalized fuzzy soft sets in decision making problem. In 1975 Zadeh introduced a concept of an interval-valued fuzzy set. After Zadeh’s work, Yang et al. (2009) defined a hybrid model called the interval-valued fuzzy soft sets and investigated some of their basic properties. Cagman et al. (2010) defined a fuzzy parameterized fuzzy soft set in which the approximate functions are defined from a set of fuzzy parameters to the fuzzy subsets of the universal set. The question here: are all the parameters of this type of problems has no time value for previous information which means why we didn’t take the component time value of the information in our consideration when we are making decision. To solve the problem with time as parameters and as a generalization of Molodtsov’s soft set we shall introduce the concept of a time-fuzzy soft set (T-FSS), and study some of its properties and basic operations. Namely complement, union, intersection, AND and OR, and we shall elaborate the concept of time in decision making through some hypothetical application problem. Most of these models came through one expert, to solve this problem, Alkhazaleh (2012) considered a collection of experts and generalized soft set to soft expert set and fuzzy soft expert with two opinions, where they study some of its properties and explained the application of this concept in decision making problem. In some problems, may be two opinions are insufficient for decision making problem. Therefore we need to enrich the state with multi opinions, which makes it possible to make better decisions and learn more to make better decisions. To enrich this concept to be more effective and useful we shall consider a collection set of opinions and generalize the concept of fuzzy soft expert set with multi opinions and explain the application of this concept in decision making problem. Then we shall introduce an algorithm to convert the fuzzy soft expert set with multi opinions to fuzzy soft set and find the decision. By a combination the previous concepts we shall introduce the concept of a time-fuzzy soft expert set (T-FSES) and the concept of a fuzzy parameterized fuzzy soft expert set (FPFSES) and the concept of interval-valued fuzzy soft expert set (IV-FSES). Finally, we introduce the concept of generalized fuzzy soft expert set (GFSES), and study some of its properties and its basic operations namely, complement, union, intersection, AND and OR. Then we shall present two hypothetical applications in decision making problem of our previous concepts ((T-FSES, FPFSES, IVFSES and GFSES). Finally for the last two of our concepts (IVFSES, GFSES)we shall introduce the mapping of the classes of the concepts and study their properties.
format Thesis
author Ayman Abdelkarim Mohammad Hazaymeh
author_facet Ayman Abdelkarim Mohammad Hazaymeh
author_sort Ayman Abdelkarim Mohammad Hazaymeh
title Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications
title_short Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications
title_full Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications
title_fullStr Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications
title_full_unstemmed Fuzzy Soft Set And Fuzzy Soft Expert Set: Some Generalizations And Hypothetical Applications
title_sort fuzzy soft set and fuzzy soft expert set: some generalizations and hypothetical applications
publisher Universiti Sains Islam Malaysia
publishDate 2015
url http://ddms.usim.edu.my/handle/123456789/8247
_version_ 1645152375039590400
score 13.222552

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