Are grades of membership probabilities?
Fuzzy Sets and Systems - Interpretations of Grades on Membership
Correlation of interval-valued intuitionistic fuzzy sets
Fuzzy Sets and Systems
Some remarks on distances between fuzzy numbers
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Type 2 fuzzy sets: an appraisal of theory and applications
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
On the compatibility between defuzzification and fuzzy arithmetic operations
Fuzzy Sets and Systems
Fuzzy measures for correlation coefficient of fuzzy numbers
Fuzzy Sets and Systems
Correlation coefficient for type-2 fuzzy sets: Research Articles
International Journal of Intelligent Systems
T-sum of bell-shaped fuzzy intervals
Fuzzy Sets and Systems
Investors' preference order of fuzzy numbers
Computers & Mathematics with Applications
A new approach for ranking of trapezoidal fuzzy numbers
Computers & Mathematics with Applications
An interval arithmetic based fuzzy TOPSIS model
Expert Systems with Applications: An International Journal
Expert Systems with Applications: An International Journal
Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method
Expert Systems with Applications: An International Journal
Information Sciences: an International Journal
Concave type-2 fuzzy sets: properties and operations
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Fuzzy decision making with immediate probabilities
Computers and Industrial Engineering
Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers
Expert Systems with Applications: An International Journal
A new approach for ranking of L-R type generalized fuzzy numbers
Expert Systems with Applications: An International Journal
Computers and Industrial Engineering
Computers and Industrial Engineering
A theoretical development on a fuzzy distance measure for fuzzy numbers
Mathematical and Computer Modelling: An International Journal
Information Sciences: an International Journal
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Fuzzy set theory (FST), since its introduction in the 1960s, has been continuously developed. Theory development for FST is highly challenging. For instance, various researchers have devoted substantive efforts in developing methodologies for many fundamental tasks, such as ranking type-1 fuzzy numbers, defining arithmetic and logical operations on type-1 and type-2 fuzzy numbers, and defining correlation measure on type-1 and type-2 numbers, resulting in a multitude of approaches, many of which based on differing postulates and assumptions. On the other hand, by interpreting the membership function of a linguistic concept based on a probabilistic framework, and by abandoning Zadeh's extension principle in favor of relying on probabilistic arguments, many of the technical difficulties in developing theory involving ''type-1'' like linguistic concepts and variables can be bypassed, with the resulting probabilistic linguistic framework enabling a uniform approach for theory development for a wide range of elementary operations and measures. In this article, the probabilistic linguistic framework is extended to type-2 linguistic sets that allows, with as few postulates as possible, uniform approach for developing methodologies for fundamental tasks such as taking the union and intersection of and performing arithmetic operations on type-2 linguistic numbers. Furthermore, we demonstrate the resulting methodology by applying it to an industrial data set concerning multi-criteria decision making.