Interval valued intuitionistic fuzzy sets
Fuzzy Sets and Systems
More on intuitionistic fuzzy sets
Fuzzy Sets and Systems
New operations defined over the intuitionistic fuzzy sets
Fuzzy Sets and Systems
Structures on intuitionistic fuzzy relations
Fuzzy Sets and Systems
On the relationship between some extensions of fuzzy set theory
Fuzzy Sets and Systems - Theme: Basic notions
Information Sciences: an International Journal
Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making
Expert Systems with Applications: An International Journal
Aggregation Functions: A Guide for Practitioners
Aggregation Functions: A Guide for Practitioners
On generalized Bonferroni mean operators for multi-criteria aggregation
International Journal of Approximate Reasoning
Choquet integrals of weighted intuitionistic fuzzy information
Information Sciences: an International Journal
Fuzzy Sets and Systems
Generalized Bonferroni mean operators in multi-criteria aggregation
Fuzzy Sets and Systems
On averaging operators for Atanassov's intuitionistic fuzzy sets
Information Sciences: an International Journal
Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets
Fuzzy Sets and Systems
Intuitionistic Fuzzy Bonferroni Means
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Intuitionistic Fuzzy Aggregation Operators
IEEE Transactions on Fuzzy Systems
Using linear programming for weights identification of generalized bonferroni means in r
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
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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 , 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.