FMIAT: Frequency Matrix Inclusion Analysis Technique for MCDM

Authors

  • Madiha Qayyum Department of Mathematics, COMSATS University Islamabad, Pakistan
  • Etienne E. Kerre Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Belgium
  • Shazia Rana Department of Mathematics, COMSATS University Islamabad, Pakistan

DOI:

https://doi.org/10.7546/CRABS.2023.07.03

Keywords:

intuitionistic fuzzy set (IFS), weighted average cardinality measure (WACM), fuzzy inclusion measure for intuitionistic fuzzy sets, MCDM (multi criteria decision making), FMIAT (frequency matrix inclusion analysis technique)

Abstract

The wider applicability of inclusion measures as well as the diversity of data existing in real life situations has motivated most of the researchers to introduce a two degree inclusion indicator within the intuitionistic fuzzy framework. Although these measures are capable of portraying the level of inclusion as well as a non inclusion relation existing between objects under consideration yet, they lose their practical application due to their computational complexity in many decision making situations. In our view, a single fuzzy degree intuitionistic inclusion measure will serve the purpose more effectively rather than a two degree inclusion measure for intuitionistic fuzzy sets. Therefore, in this research work we present a new yet effective technique to solve the Multi-Criteria Decision Making problems in intuitionstic fuzzy environment based on single degree inclusion measures called The Frequency Matrix Inclusion Analysis Technique (FMIAT). This new technique is much simpler than any of the previously introduced techniques for MCDM in literature which makes it economically viable. The technique utilizes the Parametric family of Fuzzy Inclusion Measures for IFS's introduced in [Qayyum M. (2017) New Measures of intuitionistic inclusion and similarity with applications, PhD Thesis, COMSATS University Islamabad, Lahore Campus] as fundamental tool of analysis whose members in their own construction are based on variety of t-norms and t-conorms. This possible variation of t-norms and t-conorms gives our technique a clear advantage over other techniques as it becomes more flexible and can deal with all the three different states of mind (being Pessimist, Optimist and Neutral) of a decision maker by use of different operators in the respective inclusion indicators. Finally, an application of this technique is made in the field of Organizational Management.

Author Biographies

Madiha Qayyum, Department of Mathematics, COMSATS University Islamabad, Pakistan

Mailing Address:
Department of Mathematics,
COMSATS University Islamabad
Lahore Campus
Lahore 54000, Pakistan

E-mail: mqayyum@cuilahore.edu.pk

Etienne E. Kerre, Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Belgium

Mailing Address:
Department of Applied Mathematics, Computer Science and Statistics,
Ghent University
Krijgslaan 281, S9
B-9000 Ghent, Belgium

E-mail: Etienne.Kerre@ugent.be

Shazia Rana, Department of Mathematics, COMSATS University Islamabad, Pakistan

Mailing Address:
Department of Mathematics,
COMSATS University Islamabad
Lahore Campus
Lahore 54000, Pakistan

E-mail: shaziarana@cuilahore.edu.pk

Downloads

Published

31-07-2023

How to Cite

[1]
M. Qayyum, E. Kerre, and S. Rana, “FMIAT: Frequency Matrix Inclusion Analysis Technique for MCDM”, C. R. Acad. Bulg. Sci. , vol. 76, no. 7, pp. 999–1007, Jul. 2023.

Issue

Section

Mathematics