Group Decision-Making Problems Based on Mixed Aggregation Operations of Interval-Valued Fuzzy and Entropy Elements in Single- and Interval-Valued Fuzzy Environments

Fuzzy sets and interval-valued fuzzy are two kinds of information expression forms in real uncertain vague environments. Their mixed multivalued operational problems very challenging indispensable issues group decision-making (GDM) problems. To solve single- hybrid expression, operations, GDM issues, this study first presents the notion a set/element (SIVFMS/SIVFME) with identical and/or different values. effectively for various SIVFME lengths, SIVFMS/SIVFME is converted into entropy (IVFES/IVFEE) based on mean SIVFME. Then, relationships IVFEEs expected value function sorting rules defined. Next, IVFEE weighted averaging geometric operators their mixed-weighted-averaging operation proposed. In terms IVFEEs, method developed to multicriteria environment SIVFMSs. Finally, proposed was utilized supplier selection problem supply chain as an actual sample show rationality efficiency Through comparative analysis relative methods, we found superiority that not only compensates defects existing but also makes process more reasonable flexible.