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Title:	Soft sets and fuzzy soft sets : some generalisations
Authors:	Shawkat Mahmoud Rasheed Alkhazaleh (P44003)
Supervisor:	Abdul Razak Salleh, Prof. Dato' Dr.
Keywords:	Dissertations, Academic -- Malaysia Fuzzy sets Set theory Universiti Kebangsaan Malaysia -- Dissertations
Issue Date:	20-Jun-2012
Description:	In 1999 Molodtsov 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. The question here is: Are all the problems of this type consist of one set of parameters and one universe? The answer is definitely no. To solve problem with multiset of parameters and as a generalisation of Molodtsov's soft set we introduce the concept of a multiparameterized soft set, its properties and basic operations, namely complement, union, intersection, AND and OR. By considering a collection of universes we introduce the concept of a soft multiset, its basic operations such as complement, union and intersection. We give an application of soft multiset in decision making problem. Some researchers have created some models to solve problems in decision-making and medical diagnosis but most of these models come through one expert and if we want to take the opinion of more than one expert, we need to do some operations like union, intersection etc. This causes a problem with the users, especially with those who use questionnaires in their work and studies. To solve this problem we consider a collection of experts and generalize soft set to soft expert set, study some of its properties and explain its application in decision making problem. Maji, Biswas and Roy in 2001 introduced the concept of fuzzy soft set and in 2010 Majumdar and Samanta generalised the concept of fuzzy soft set where a degree is attached to the parameterization of fuzzy sets while defining a fuzzy soft set. We generalise the concept of fuzzy soft set to possibility fuzzy soft set where a possibility of each element in the universe is attached to the parameterization of fuzzy sets while defining a fuzzy soft set. We give an application of possibility fuzzy soft set in decision making problem and by considering dengue fever as a case study we give its application in medical diagnosis. Then we present an application of this theory to solve a decision making problem and medical diagnosis. In 2010 C¸aˇgman, C¸itak and Enginoglu 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. By using this definition we introduce the concept of fuzzy parameterized interval-valued fuzzy soft set (fpivfss) in which the approximate functions are defined from the set of fuzzy parameters to the interval-valued fuzzy subsets of the universal set. We also study its properties and operations. Likewise, to form fpivfss-decision making we define the fpivfss-aggregation operator and employ some numerical examples. We then introduce the concept of generalised interval-valued fuzzy soft set where a degree is attached to the parameterization of fuzzy sets while defining an interval-valued fuzzy soft set and study some of its properties. At the end of each of the above concepts we introduce the mapping of the classes of the concept and study its properties. In addition, we generalise the concept of soft expert set to the concept of fuzzy soft expert set and give its application in decision making problem. Finally, we define a fuzzy soft multiset and study its basic operations and apply the concept to solve a decision making problem.,Certification of Master's/ Doctorial Thesis" is not available
Pages:	244
Call Number:	QA248.5.K485 2012 tesis
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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