Ranking of Exponential Vague Sets With an Application to Decision Making Problems

 

Pushpinder Singh

 

Department of Computer Science, Palacky University, 17. listopadu 12, CZ-77146, Olomouc, Czech Republic. pushpindersnl@gmail.com

 

ABSTRACT

The main aim of this paper is to propose a new approach for the ranking of exponential vague sets. The concepts of exponential vague sets and arithmetic operations between two exponential vague sets are introduced. The shortcomings of some existing ranking approaches for the ranking of generalized fuzzy sets and intuitionistic fuzzy numbers are pointed out. The proposed method consider not only the rank but also the decision maker optimistic attitude and it is shown that proposed ranking approach is more intuitive and reasonable as compared to existing ranking approaches. Also the proposed ranking function satisfies the reasonable properties for the ordering of fuzzy quantity. For practical use, proposed ranking approach is applied to decision making problem.

Keywords: Fuzzy sets, vague sets, exponential vague sets, intuitionistic fuzzy numbers, ranking functions, decision making problems.

 

RESUMEN

El objetivo principal de este trabajo es proponer un nuevo enfoque para la clasificación de los conjuntos inciertos exponenciales. Se introducen los conceptos de conjuntos inciertos exponenciales y operaciones aritméticas entre dos conjuntos inciertos exponenciales. Se señalan las deficiencias de algunos enfoques de clasificación existentes para la clasificación de los conjuntos difusos generalizados y de los números difusos intuicionistas. El método propuesto toma en cuenta no sólo el rango, sino también el enfoque optimista para toma de decisiones y se muestra que el enfoque de clasificación propuesto es más intuitivo y razonable en comparación con los enfoques de clasificación existentes. Asimismo, la función de clasificación propuesta satisface las propiedades razonables para el ordenamiento de la cantidad difusa. Para usos prácticos, el enfoque de clasificación propuesto se aplica al problema de toma de decisiones.

 

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Acknowledgements

The author is very grateful to the Editor-in-Chief, and the anonymous referees, for their constructive comments and suggestions that led to an improved version of this paper. The author was supported by the Education for Competitiveness Operational Programme project "Encourage the creation of excellent research teams and intersectoral mobility at Palacky University in Olomouc" reg. no. CZ.1.07/2.3.00/30.0004, which is co-financed by the European Social Fund and the state budget of the Czech Republic.

 

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