Finding the numerical compensation in multiple criteria decision-making problems under fuzzy environment

ABSTRACT

In this paper, we have developed a methodology to derive the level of compensation numerically in multiple criteria decision-making (MCDM) problems under fuzzy environment. The degree of compensation is dependent on the tranquility and anxiety level experienced by the decision-maker while taking the decision. Higher tranquility leads to the higher realisation of the compensation whereas the increased level of anxiety reduces the amount of compensation in the decision process. This work determines the level of tranquility (or anxiety) using the concept of fuzzy sets and its various level sets. The concepts of indexing of fuzzy numbers, the risk barriers and the tranquility level of the decision-maker are used to derive his/her risk prone or risk averse attitude of decision-maker in each criterion. The aggregation of the risk levels in each criterion gives us the amount of compensation in the entire MCDM problem. Inclusion of the compensation leads us to model the MCDM problem as binary integer programming problem (BIP). The solution to BIP gives us the compensatory decision to MCDM. The proposed methodology is illustrated through a numerical example.

KEYWORDS:

• Multiple criteria analysis
• fuzzy sets
• tranquility
• risk prone
• degree of compensation

Acknowledgment

We are thankful to anonymous referees whose comments have substantially improved our work.

Additional information

Notes on contributors

Mahima Gupta

Mahima Gupta is currently working as an Assistant Professor, at the Institute of Management Technology, Ghaziabad, India. She received her MSc in Operations Research from Delhi University and FPM (Fellow Program in Management, equivalent to PhD) from IIM Lucknow, India. Her area of research interest include MCDM, Fuzzy logic and its applications, etc. To her credit she got publications in Expert Systems with applications, Computers and Industrial Engineering, Journal of Game Theory Review, etc.

B. K. Mohanty

B. K. Mohanty is a Professor in the Decision Science Group at Indian Institute of Management, Lucknow, India. He received MSc in Mathematics from Berhampur University, Orissa, and PhD in Operations Research from IIT Kharagpur, India. Prior to joining IIM, Lucknow, he served in Tata Research Development and Design centre, Pune as Member, Technical Staff, as an Associate Professor at Xavier Institute of Management Bhuanewar, India and as a Scientist at CFTRI Mysore India. His research interest include the areas such as; fuzzy logic applications in MCDM, Fuzzy logic applications in DSS, etc. He has some publications in the journals like, Fuzzy Sets and Systems, Computers and Operations Research, International Journal of Production Research, Decision Support Systems, Expert Systems Applications, etc.