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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| Format: | Thesis |
| Language: | English |
| Published: |
Universiti Sains Islam Malaysia
2015
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| Subjects: | |
| Online Access: | http://ddms.usim.edu.my/handle/123456789/8247 |
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| Summary: | 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. |
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