Constructing interval-valued generalized partitioned Bonferroni mean operator with several extensions for MAGDM
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ORIGINAL ARTICLE
Constructing interval-valued generalized partitioned Bonferroni mean operator with several extensions for MAGDM Debasmita Banerjee1 • Bapi Dutta3 • Debashree Guha2 • Mark Goh3 Received: 16 June 2018 / Accepted: 28 January 2020 Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In group decision making, each expert’s background and the level of knowledge and ability differ, which makes the expert’s information inputs to the decision-making process heterogeneous. Such heterogeneity in the information can affect the outcome of the selection of the decision alternatives. This paper therefore attempts to partition the heterogeneous information into homogeneous groups to elicit similar (related) and dissimilar (unrelated) data using a clustering algorithm. We then develop an aggregation approach to gather the collective opinions from the homogeneous clusters to accurately model the decision problem in a group setting. The proposed aggregation approach, labeled as the generalized partitioned Bonferroni mean (GPBM), is studied to investigate the characteristics of the aggregation operator. Further, we extend the GPBM concept to an interval-valued fuzzy set context using the additive generators of the strict t-conorms and we develop two other new aggregation operators: the interval-valued GPBM (IVGPBM) and the weighted IVGPBM (WIVGPBM). We analyze the aggregation of fuzzy numbers by the IVGPBM operator using interval arithmetic involving a-cuts and the acut-based decomposition principle of fuzzy numbers. Two practical examples are presented to illustrate the applicability of these operators, and a comparison is conducted to highlight the effects of the confidence level and the sensitivity of the parameters chosen, analyzing the results with the parameterized strict t-conorm. Finally, we compare the experimental results of the proposed method with existing methods. Keywords Group decision making Partitioned Bonferroni mean Interval-valued fuzzy sets Fuzzy numbers Clustering
1 Introduction
& Debashree Guha [email protected]; [email protected] Debasmita Banerjee [email protected] Bapi Dutta [email protected] Mark Goh [email protected] 1
Department of Mathematics, Indian Institute of Technology, Patna 801106, India
2
School of Medical Science and Technology, Indian Institute of Technology, Kharagpur 721302, India
3
The Logistics Institute—Asia Pacific, National University of Singapore, 21 Heng Mui Keng Terrace, Singapore 119613, Singapore
Multiattribute group decision making (MAGDM), integral to modern decision science, involves selecting the best alternative(s) from a set of alternatives based on multiple quantitative and qualitative attributes, relying on a group of decision-makers to make the selection decision. The MAGDM problem has gained traction due to its extensive use in disciplines such as management, finance, engineering, and technology. There has been considerable research interest in t
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