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Q-Neutrosophic Soft Relation and Its Application in Decision Making
Majdoleen Abu Qamar1, Nasruddin Hassan1
1School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces Q-neutrosophic soft relations, a novel generalization of existing soft relation types. These relations effectively handle imprecise and inconsistent data, offering a new approach for decision-making problems.
Area of Science:
- Fuzzy Mathematics
- Set Theory
- Decision Science
Background:
- Traditional soft relations struggle with imprecise, indeterminate, and inconsistent data.
- Existing generalizations like fuzzy, intuitionistic fuzzy, and neutrosophic soft relations have limitations.
- Real-world problems often involve complex data requiring advanced modeling.
Purpose of the Study:
- To introduce and define Q-neutrosophic soft relations as a generalization of existing soft relations.
- To explore fundamental properties and operations of Q-neutrosophic soft relations.
- To develop and validate an algorithm for decision-making using these new relations.
Main Methods:
- Definition of Q-neutrosophic soft relations based on Cartesian products.
- Introduction of concepts such as inverse, composition, reflexivity, symmetry, and transitivity.
- Development of an algorithm for decision-making problems.
Main Results:
- Q-neutrosophic soft relations are defined as subsets of Cartesian products of Q-neutrosophic soft sets.
- Properties of inverse, composition, and various relation types (reflexive, symmetric, transitive, equivalence) are established.
- An algorithm is presented and verified with an example, demonstrating practical applicability.
Conclusions:
- Q-neutrosophic soft relations offer a powerful framework for handling complex, multi-dimensional uncertain data.
- The developed algorithm provides an efficient method for decision-making in scenarios with imprecise information.
- This research extends the theory of soft relations and opens avenues for future applications.
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