On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.<br /

Using linear programming for weights identification of generalized bonferroni means in R

The generalized Bonferroni mean is able to capture some interaction effects between variables and model mandatory requirements. We present a number of weights identification algorithms we have developed in the R programming language in order to model data using the generalized Bonferroni mean subject to various preferences. We then compare its accuracy when fitting to the journal ranks dataset

A Comprehensive Analysis of Neutrosophic Bonferroni Mean Operator

The Neutrosophic Bonferroni operator is a novel operator that we provide in this paper. Then the arithmetic operations for Neutrosophic Bonferroni operator is developed which tells the existence of Neutrosophic Bonferroni operator. Then its properties were discussed with special cases. To group decision-making issues with several attributes, arithmetic ranking operations and the Neutrosophic approach are used. The result is compared with the existing methodology. The suggested approach will more accurately give the decision maker the ideal attribute than the existing system does. Neutrophic multicriteria is a method of decision-making that makes use of ambiguity to integrate various criteria or factors—often with imprecise or ambiguous data—to reach a result. The neutrosophic multicriteria analysis enables the assessment of subjective and qualitative factors, which can assist in resolving conflicting goals and preferences. In Neutrosophic Multi-Attribute Group Decision Making (NMAGDM) problems, all the data supplied by the decision makers (DMs) is expressed in single-value Neutrosophic triangular and trapezoidal numbers, which are studied in this work and can improve the flexibility and precision of capturing uncertainty and aggregating preferences