Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots

Abstract

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

Cumulative Prospect Theory: Performance Evaluation of Government Purchases of Home-Based Elderly-Care Services Using the Pythagorean 2-tuple Linguistic TODIM Method

“…Xu and Yager [33] designed several geometric aggregation operators for IFSs. Zhou et al [34] defined normalized weighted Bonferroni harmonic mean-based intuitionistic fuzzy operators for the sustainability of search and rescue robots. Cavallaro et al [35] assessed the technologies of concentrated solar power (CSP) by using the IF-TOPSIS and trigonometric entropy weights.…”

Multi-Criteria Decision-Making Techniques for Improvement Sustainability Engineering Processes

“…Distribution of papers according to authors' affiliations is presented in Table 1. Authors and coauthors from Lithuania contributed 12 papers, five papers without international collaboration [1][2][3][4][5] and seven papers with international cooperation: Bosnia and Herzegovina-Lithuania-Serbia-Malaysia [6], Lithuania-Bosnia and Herzegovina-Serbia [7], Iran-Lithuania [8], China-Lithuania [9], Malaysia-Lithuania [10], Serbia-South Africa-Lithuania-Bosnia and Herzegovina [11] and Chile- The largest number of authors were from Serbia (29 authors). China has 21 authors, while 18 researches come from Lithuania and 17 from India.…”

Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making

“…Bonferroni mean (BM), which reflects the correlations of input arguments, was originally presented by Bonferroni 22 and then interpreted by Yager 23 as joined averaging and “anding” operator, which allows replacing the average operator by other means, such as Choquet integral 24 and ordered weighted average operator 25 . By reason of the fact that BM does not only consider importance of each criterion but also reflects interrelation of the individual criterion, it has received more attention and many aggregation operators have been developed based on BM for MCDM 12,26–32 . Xu and Yager 30 investigated BM under the intuitionistic fuzzy environment and developed intuitionistic fuzzy Bonferroni mean (IFBM) operator and also defined weighted intuitionistic fuzzy Bonferroni mean (WIFBM) operator.…”

“…25 By reason of the fact that BM does not only consider importance of each criterion but also reflects interrelation of the individual criterion, it has received more attention and many aggregation operators have been developed based on BM for MCDM. 12,[26][27][28][29][30][31][32] Xu and Yager 30 investigated BM under the intuitionistic fuzzy environment and developed intuitionistic fuzzy Bonferroni mean (IFBM) operator and also defined weighted intuitionistic fuzzy Bonferroni mean (WIFBM) operator. Xia et al 29 generalized classical BM, which ignores the weight vector of aggregating arguments and introduced generalized intuitionistic fuzzy weighted Bonferroni mean (GIFWBM) and generalized intuitionistic fuzzy weighted Bonferroni geometric mean (GWGBM) and also proposed an approach to MCDM.…”