Soft sets and their variants
Michael Voskoglou; Said Broumi
Abstract
Much of a person’s cognitive activity depends on the ability to reason analogically. Analogical reasoning (AR) compares the similarities between new and past knowledge and uses them to obtain an understanding of the new knowledge. The mechanisms, however, under which the human mind works are not ...
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Much of a person’s cognitive activity depends on the ability to reason analogically. Analogical reasoning (AR) compares the similarities between new and past knowledge and uses them to obtain an understanding of the new knowledge. The mechanisms, however, under which the human mind works are not fully investigated and as a result AR is characterized by a degree of fuzziness and uncertainty. Probability theory has been proved sufficient for dealing with the cases of uncertainty due to randomness. During the last 50-60 years, however, various mathematical theories have been introduced for tackling effectively the other forms of uncertainty, including fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, rough sets, etc. The combination of two or more of those theories gives frequently better results for the solution of the corresponding problems. A hybrid assessment method of AR skills under fuzzy conditions is developed in this work using Grey Numbers (GN) and soft sets as tools, which is illustrated by an application on evaluating student analogical problem solving skills.
Soft sets and their variants
Mujahid Abbas; Yanhui Guo; Ghulam Murtaza
Abstract
The aim of this paper is to investigate different definitions of soft points in the existing literature on soft set theory and its extensions in different directions. Then limitations of these definitions are illustrated with the help of examples. Moreover, the definition of soft point in the setup of ...
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The aim of this paper is to investigate different definitions of soft points in the existing literature on soft set theory and its extensions in different directions. Then limitations of these definitions are illustrated with the help of examples. Moreover, the definition of soft point in the setup of fuzzy soft set, intervalvalued fuzzy soft set, hesitant fuzzy soft set and intuitionistic soft set are also discussed. We also suggest an approach to unify the definitions of soft point which is more applicable than the existing notions.
Soft sets and their variants
Somen Debnath
Abstract
Hypersoft set is an extension of the soft set where there is more than one set of attributes occur and it is very much helpful in multi-criteria group decision making problem. In a hypersoft set, the function F is a multi-argument function. In this paper, we have used the notion of Fuzzy Hypersoft Set ...
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Hypersoft set is an extension of the soft set where there is more than one set of attributes occur and it is very much helpful in multi-criteria group decision making problem. In a hypersoft set, the function F is a multi-argument function. In this paper, we have used the notion of Fuzzy Hypersoft Set (FHSS), which is a combination of fuzzy set and hypersoft set. In earlier research works the concept of Fuzzy Soft Set (FSS) was introduced and it was applied successfully in various fields. The FHSS theory gives more flexibility as compared to FSS to tackle the parameterized problems of uncertainty. To overcome the issue where FSS failed to explain uncertainty and incompleteness there is a dire need for another environment which is known as FHSS. It works well when there is more complexity involved in the parametric data i.e the data that involves vague concepts. This work includes some basic set-theoretic operations on FHSSs and for the reliability and the authenticity of these operations, we have shown its application with the help of a suitable example. This example shows that how FHSS theory plays its role to solve real decision-making problems.
Soft sets and their variants
Renukadevi Vellapandi; Sangeetha Gunasekaran
Abstract
We introduce a new concept of certainty and coverage of a parameter of the soft set and present a new decision making approach for the soft set over the universe using the certainty of a parameter. Also, we point out the drawbacks of the reduct definition by pointing out the delusion of Proposition 14 ...
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We introduce a new concept of certainty and coverage of a parameter of the soft set and present a new decision making approach for the soft set over the universe using the certainty of a parameter. Also, we point out the drawbacks of the reduct definition by pointing out the delusion of Proposition 14 given by Herawan et al. [20] and provide the revised definition of the reduct of the multi soft set.
