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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 concept of complex intuitionistic fuzzy subrings based on the notion of complex intuitionistic fuzzy subspace, This concept generalize the concept of intuitionistic fuzzy space from the real range of membership function and non-membership, [0,1], to complex range of membership function and, non-membership unit disc in the complex plane. This generalization leads us to introduce and study the approach of complex intuitionistic fuzzy subrings. [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]

The present paper, introduces a complex vague relation (CVR) as a generalization of avague relation by extending the range of truth-membership and false-membership functions from the closed unit interval [0, 1] to the unit circle in the complex plane. Then we introduce the basic operations on CVRs, namely complement, union and intersection. Some examples are given. [ABSTRACT FROM AUTHOR]

This paper conceptually defines and studies the complex fuzzy hyperring, which relies on the notion that complex fuzzy spaces are a direct generalization of fuzzy hyperring. [ABSTRACT FROM AUTHOR]

In this paper, we continue the study of complex fuzzy groups by introducing the notion of complex fuzzy normal subgroup based on complex fuzzy space as a generalisation of fuzzy normal subgroup in the sense of Dib. [ABSTRACT FROM AUTHOR]

In this paper we combine two definitions, namely fuzzy soft multiset and complex fuzzy set to construct the definition of a complex fuzzy soft multiset and study its properties. In other words, we study the extension of a fuzzy soft multiset from real numbers to complex numbers. We also introduce its basic operations, namely complement, union and intersection. Some examples are given. [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]

Soft set is a general mathematical tool for dealing with uncertainties and imprecision. Many complicated problems in economics, engineering, environment, social science, medical science and other fields involve uncertain data. These problems cannot be solved using existing classical methods such as fuzzy set theory and rough set theory. Hence the concept of soft sets was introduced as a new mathematical tool for dealing with uncertainties that is free from the difficulties affecting the existing methods. The theory of hyperstructures and hyperalgebra on the other hand, was introduced as an extension of the classical theory of sets as well as the theory of abstract algebra. This theory states that in an algebraic hyperstructure, the composition of two elements is a set. The study of soft hyperstructures which is an extension of the theory of soft sets and the theory of algebraic hyperstructures began with the introduction of the notion of soft hypergroupoids and soft subhypergroupoids. In this paper, we study the theory of soft hyperalgebra by introducing the notion of soft hypergroups and soft subhypergroups as an extension of the notion of soft sets, algebraic hyperstructures and soft hyperstructures. This is followed by the introduction of the notion of soft homomorphism of hypergroups. Furthermore the basic properties and structural characteristics of these notions are studied and discussed. [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]

Complex fuzzy sets and its accompanying theory although at its infancy, has proven to be superior to classical type-1 fuzzy sets, due its ability in representing time-periodic problem parameters and capturing the seasonality of the fuzziness that exists in the elements of a set. These are important characteristics that are pervasive in most real world problems. However, there are two major problems that are inherent in complex fuzzy sets: it lacks a sufficient parameterization tool and it does not have a mechanism to validate the values assigned to the membership functions of the elements in a set. To overcome these problems, we propose the notion of complex fuzzy soft expert sets which is a hybrid model of complex fuzzy sets and soft expert sets. This model incorporates the advantages of complex fuzzy sets and soft sets, besides having the added advantage of allowing the users to know the opinion of all the experts in a single model without the need for any additional cumbersome operations. As such, this model effectively improves the accuracy of representation of problem parameters that are periodic in nature, besides having a higher level of computational efficiency compared to similar models in literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce new classes of functions called totally-continuous functions and its variants totally semi-continuous functions and semi totally-continuous functions in double fuzzy topological spaces. Their characterizations, examples and relationship with other notions of continuous functions in this space are provided. [ABSTRACT FROM AUTHOR]

In this paper, numerical algorithm is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. In order to enhance the order of accuracy of the solutions, a developed fourth order Runge-Kutta method is apply for solving fuzzy differential equations. The purpose of this study is to explore the explicit methods which we believe that most of the explicit methods can be improved and modified to cater and solve fuzzy differential equations. This paper is divided into six sections. In the first section, some basic definitions and theorem are reviewed. The numerical examples are given to illustrate the efficiency of the method and the comparison with the existing method is discussed. [ABSTRACT FROM AUTHOR]

In this paper a three stage Runge Kutta method based Contraharmonic Mean is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore an explicit method which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. A numerical example is given to illustrate the accuracy of the method. The comparison with the existing method is also discussed. The proposed method gives better numerical results and suitable for solving fuzzy differential equations. [ABSTRACT FROM AUTHOR]

This paper presents the ASKE-Risk method, coupled with Fuzzy Inference Systems, and Monte Carlo Risk Simulation to measure and prioritize Individual Technical Competence of a value chain to assess changes in the human capital of a company. ASKE is an extension of the method Knowledge Value Added, which proposes the use of a proxy variable for measuring the flow of knowledge used in a key process, creating a relationship between the company's financial results and the resources used in each of the business processes. [ABSTRACT FROM AUTHOR]