The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to mul...

This paper is a brief summary of “M.Takahashi, T.Murofushi, S.Asahina, A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory, Fuzzy Sets and Systems, to appear.” This paper states that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary an...

Many problems arise in practical applications when data is extracted from a group of experts, all of whom do not collectively agree. The theory of Type 2 Fuzzy Multisets is capable of modelling these types of uncertainties in decision making. The purpose of this paper is to introduce the study of various algebraic structures of Type 2 Fuzzy Multisets. As a beginning of this study, the concept o...

image segmentation is an essential issue in image description and classification. currently, in many real applications, segmentation is still mainly manual or strongly supervised by a human expert, which makes it irreproducible and deteriorating. moreover, there are many uncertainties and vagueness in images, which crisp clustering and even type-1 fuzzy clustering could not handle. hence, type-...

The Fuzzy Analytic Network Process (ANP) is generally used for solving multicriteria decision making (MCDM) problems by considering the pairwise comparison between criteria/sub-criteria, and inner/outer dependencies among criteria. Linguistic expressions are used for experts’ judgements, and these judgements are imprecise and vague. Hence, incorporating fuzziness with multi-criteria decision ma...

In this paper, we present a type-2 fuzzy logic based system for robustly extracting the human silhouette which is a fundamental and important procedure for advanced video processing applications, such as pedestrian tracking, human activity analysis and event detection. The presented interval type-2 fuzzy logic system is able to detach moving objects from extracted human silhouette in dynamic en...

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...

Two advanced controllers were developed in this paper, i.e., a type-1 and a type-2 fuzzy logic controller and their performances compared in simulation for a case study, i.e., a binary distillation column, which is characterized by high nonlinearities and parameter uncertainties in the underlying mathematical model. Priority was given to the type-2 fuzzy controller, with special attention to in...