Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, is given by linguistic values. It very awkward for the CFS describe this type of information. To overcome limitation, we first propose novel concept called complex set (LCFS) serve as an extension CFS. Then put forward some basic operational laws LCFSs. After t...

A conjunction T ties an implication operator A if the identity A(a,A(b, z)) = A(T (a, b), z) holds [A.A. Abdel-Hamid, N.N. Morsi, Associatively tied implications, Fuzzy Sets and Systems 136 (2003) 291–311]. We study the class of tied adjointness algebras (which are five-connective algebras on two partially ordered sets), in which the implications are tied by triangular norms. This class contain...

The lattice Lu of upper semicontinuous convex normal functions with convolution ordering arises in studies of type-2 fuzzy sets. In 2002, Kawaguchi and Miyakoshi [Extended t-norms as logical connectives of fuzzy truth values, Multiple-Valued Logic 8(1) (2002) 53–69] showed that this lattice is a complete Heyting algebra. Later, Harding et al. [Lattices of convex, normal functions, Fuzzy Sets an...

This study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by...

Based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. Further...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...

Type-2 fuzzy sets and complex fuzzy sets are both three dimensional extensions of type-1 fuzzy sets. Complex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, ap...

in this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. we then define products of $fs$-matrices andstudy their properties. we finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.