Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection

Abstract

Picture fuzzy numbers (PFNs), as the generalization of fuzzy sets, are good at fully expressing decision makers’ opinions with four membership degrees. Since aggregation operators are simple but powerful tools, this study aims to explore some aggregation operators with PFNs to solve practical decision-making problems. First, new operational rules, the interaction operations of PFNs, are defined to overcome the drawbacks of existing operations. Considering that interrelationships may exist only in part of criteria, rather than all of the criteria in reality, the partitioned Heronian aggregation operator is modified with PFNs to deal with this condition. Then, desirable properties are proved and several special cases are discussed. New decision-making methods with these presented aggregation operators are suggested to process hotel selection issues. Last, their practicability and merits are certified by sensitivity analyses and comparison analyses with other existing approaches. The results indicate that our methods are feasible to address such situations where criteria interact in the same part, but are independent from each other at different parts.

Dynamic Multi-Attribute Decision-Making Based on Interval-Valued Picture Fuzzy Geometric Heronian Mean Operators

“…Liu and Chen [26] proposed the intuitionistic fuzzy Archimedean Heronian aggregation (IFAHA) operator and the intuitionistic fuzzy weight Archimedean Heronian aggregation (IFWAHA) operator. Luo and Xing [27] combined the partitioned HM operator with the PFN to deal with the problem of hotel selection. Liu [28] proposed some new intuitionistic uncertain language HM operators to deal with the situation where both the attribute weights and the expert weights take the form of crisp numbers, and attribute values take the form of intuitionistic uncertain linguistic variables.…”

Some Picture Fuzzy Aggregation Operators based on Frank t-norm and t-conorm: Application to MADM Process

“…Zeng et al [50] proposed the exponential Jensen PF divergence measure and applied it in multi-criteria group decision making. Several researchers proposed information aggregation operators under the PF environment [3,16,17,22,30,32,43,51]. Garg [14] presented some PF aggregation operators and applied them to multi-criteria decision making.…”

Power Improved Generalized Heronian Mean Operators Utilizing Hamacher Operations with Picture Fuzzy Information

“…Ates and Akay [41] expanded some Bonferroni mean (BM) to picture fuzzy set to handle MADM, including PFBM, PFNWBM, and PFOWBM operators. Luo and Xing [42] proposed picture fuzzy interaction partitioned Heronian (PFIPH) operator for selecting hotel. Qin et al [43] introduced the Dempster-Shafer theory to PFS and proposed power Muirhead mean (PMM) operators utilizing the proposed operational rules.…”