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Type-2 fuzzy sets allow us to incorporate the uncertainties about the membership functions into fuzzy sets, thereby overcoming a problem that is inherent in type-1 fuzzy sets, which does not allow for any uncertainty in assigning values to the membership functions. Complex fuzzy sets are type-1 fuzzy sets with complex-valued grades of membership and are characterized by an additional phase term which enables it to better represent and capture the timeperiodic and seasonal aspects of fuzziness that are prevalent in many real world problems and time-series applications. However, similar to type-1 fuzzy sets, the membership functions of complex fuzzy sets are difficult to enumerate, as they are subject to individual preferences and bias. To overcome this problem, we propose the concept of interval-valued complex fuzzy soft sets which combines complex fuzzy sets with type-2 fuzzy sets and soft sets. This adaption of complex fuzzy sets assigns an interval-based membership to each element and adequate parameterization, which betters corresponds to the intuition of representing fuzzy data. Subsequently this paper is concerned with the concepts related to this model, verifying the algebraic properties and demonstrating the utility of this model. [ABSTRACT FROM AUTHOR]

In this paper we present a new formulation of complex intuitionistic fuzzy rings based on the notion of complex intuitionistic fuzzy space. [ABSTRACT FROM AUTHOR]

Several innovative uncertainty sets were introduced recently. Complex Atanassov's intuitionistic fuzzy set (CAIFS) is one of these uncertainty sets, where Atanassov's intuitionistic fuzzy membership and non-membership functions take values in the unit circle in the complex plane. In this paper, some operations are generalised to the case of CAIFS. Two main operations  and ◇ are introduced and various properties are investigated. Also, we conclude the advantage from generalising these two operations to the realm of complex numbers, by finding out a relationship between the concepts of CAIFS and complex fuzzy sets (CFS). [ABSTRACT FROM AUTHOR]

In this paper we define the notation of mapping on intuitionistic fuzzy soft classes and we have studied some properties of intuitionistic fuzzy soft images and inverse images. Finally we give examples and counterexamples for these concepts. [ABSTRACT FROM AUTHOR]

This paper presents a new concept of complex intuitionistic fuzzy set (CIFS) which is generalized from the innovative concept of a complex fuzzy set (CFS) by adding the non-membership term to the definition of CFS. The novelty of CIFS lies in its ability for membership and non-membership functions to achieve more range of values. The ranges of values are extended to the unit circle in complex plane for both membership and non-membership functions instead of [0, 1] as in the conventional intuitionistic fuzzy functions. We define basic operations namely complement, union, and intersection on CIFSs. Properties of these operations are derived. [ABSTRACT FROM AUTHOR]