As for applications of fuzzy complex number theory, ramot et al. Complex fuzzy hyperring based on complex fuzzy spaces. In addition, we will prove that the derivative in 28 is only appropriate for very few functions mapping complex numbers into generalized complex fuzzy numbers. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial extension principle. Thamilmani abstract the objective of this paper is to investigate the a pplications of complex fuzzy sets. Fuzzy complex numbers and their application for classi.
Many thousand of papers, articles have published in di. Fuzzy complex numbers, proceedings of isfk, guangzhou, p. Complex fuzzy subgroups 2015 on other hand ax 1 r ax 1ei. In this paper some classical and measuretheoretical notions are extended to the case of complex fuzzy sets. Fuzzynumbers february 5, 2019 title tools to deal with fuzzy numbers type package description s4 classes and methods to deal with fuzzy numbers. Fuzzy number is expressed as a fuzzy set defining a fuzzy interval in the real number. A complex fuzzy process is a function from to the set of complex numbers.
Pdf multifuzzy complex numbers and multifuzzy complex. Section 2 is some preliminary notions including fuzzy complex number, real fuzzy distance between two fuzzy real numbers, and two fuzzy. The paper 2 defined the measurable functions of complex fuzzy, with its definition researching that it is the complex fuzzy decision theorem of measurable functions, and introduced the various convergences definition of its sequence, according to the definition we further studied the various convergence theorem of its sequence, it builds the certain foundation for the complex. In classical mathematics we are familiar with what we call crisp sets. They allow for computing any arithmetic operations e. The fixed point of fuzzy complex numbervalued mapping. A process is a complex fuzzy process if and only if there exist two fuzzy processes and such that.
Originally, the revolutionary theory of smarandache notions was born as a paradoxist movement that challenged the status quo of existing mathematics. If and are independent liu processes, then is called a complex liu process. Deducing the properties of fuzzy complex numl, ers under addition, multlica fion, etc. A modified approach to fuzzy complex analysis is proposed. Several fuzzy complex analysis problems are discussed, pointing out some errors in literature and some weaknesses of introduced concepts. Complex intuitionistic fuzzy power aggregation operators. Complex fuzzy hyperring based on complex fuzzy spaces aip conference proceedings 1691, 040009 2015. Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. They are fuzzy complex numbervalued distance on, fuzzy complex numbervalued measure on, and some related notions, such as nulladditivity, pseudonulladditivity, nullsubtraction, pseudonullsubtraction, autocontionuous from. The objective of this paper is to investigate the innovative concept of complex fuzzy sets. Fuzzy numbers fns, introduced by dubois and prade in 10.
Horizontal representation another representation is very often applied as follows. A novel framework of fuzzy complex numbers and its. When the fuzzy numbers represent linguistic concepts, e. The procedure of addition or subtraction is simple, but the procedure of multiplication or.
The concept of a fuzzy number plays fundamental role in formulating quantitative fuzzy variables. For example, the possible interferometric coherence g values are the set x of all real numbers between 0 and 1. Theory of complex fuzzy soft set and its applications ijirst. In this paper, we introduce the concepts of fuzzy complex number, the operations of fuzzy complex number, the concepts of convergence for fuzzy complex. The arithmetic operators on fuzzy numbers are basic content in fuzzy mathematics. This paper presents a method to construct more general fuzzy complex numbers and sets from ordinary fuzzy complex numbers by introduced the ordered sequences of membership functions. Multifuzzy complex numbers and multifuzzy complex sets. While in the final section we introduce function which play key role in the theory of fuzzy systems, specially sequence and series of nfuzzy complex numbers, now this work under validation.
The acut operation can be also applied to the fuzzy. Department of mathematics, hainan normal university. A fuzzy number is a generalization of a regular, real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. Complex fuzzy setvalued complex fuzzy measures and.
Pdf axiomatic of fuzzy complex numbers researchgate. However, this concept is different from fuzzy complex number introduced and discussed by buckley 25 and zhang. Tamir and others published complex number representation of intuitionistic fuzzy sets find, read and cite all. The novelty of the complex fuzzy set lies in the range of values its. In contrast to a traditional fuzzy membership function, this range is not limited to 0, 1, but extended to the unit circle in the complex plane. The results of this paper are linked with those presented in 1,p. The very basic notion of fuzzy systems is a fuzzy subset. Recently, zadeh introduced the concept of znumbers. Fuzzy arithmetic is based on two properties of fuzzy numbers each fuzzy set and also each fuzzy number can fully be represented by its 7cuts 7cuts of each fuzzy number are closed intervals of real numbers for all 7 0,1 arithmetic operations on fuzzy numbers are defined in terms of arithmetic operations on their 7cuts on closed. Since the boundary of this interval is ambiguous, the interval is also a fuzzy set. Then we investigate some characteristics of complex fuzzy soft group.
The domain of fuzzy numbers is a fuzzy set of the range of values of all fuzzy variables n and associate degrees of memberships n. In buckleys definition, the representation of fuzzy complex number in the polar form is quite unstable. Alteration, truncation or removal of conformationally heterogeneous regions impacts the activity of the corresponding complex. Fuzzy numbers map real values from r on to a closed interval 0,1.
These are variables whose states are fuzzy numbers. Pdf complex number representation of intuitionistic fuzzy sets. Fuzzy set theoryand its applications, fourth edition. It is concluded that multifuzzy complex set is an extension of buckley fuzzy complex set. Complex fuzzy sets and complex fuzzy logic an overview of. Let fa igbe a collection of complex fuzzy subgroups of a group gsuch that a j is homogeneous with a k for all j. Learn what complex numbers are, and about their real and imaginary parts. They are fuzzy complex numbervalued distance on fk, fuzzy complex numbervalued measure on fk, and some related notions, such as nulladditivity, pseudonulladditivity, nullsubtraction, pseudonullsubtraction, autocontionuous. A modification to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two. A guide to the fuzzynumbers package for r fuzzynumbers.
What is a fuzzy complex laboratory of monika fuxreiter. In this book, we study the subject of smarandache fuzzy algebra. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape. Fuzzy numbers fuzzy numbers are a special type of fuzzy sets which can be used to represent imprecise quantities such as about 0. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. In the second section display basic definitions and notations of nfuzzy complex numbers. It is shown that arithmetic of fuzzy complex numbers may be performed in terms of. Complex fuzzy numbers have been utilized in several numerical applications 4446. Yet, the concept of a complex fuzzy number is different from the concept of complex fuzzy sets or complex fuzzy classes. Complex fuzzy setvalued complex fuzzy measures and their. Request pdf on apr 1, 2015, asit dey and others published multifuzzy complex numbers and multifuzzy complex sets find, read and cite all the research you need on researchgate. Generally a fuzzy interval is represented by two end points a. The novelty of the complex fuzzy set lies in the range of values its membership function may attain.
Introduction in the last four decades, the fuzzy group theory was developed as follows. Fuzzy complex value measure and fuzzy complex value. The relationship between complex fuzzy soft group and fuzzy soft group is also investigated. Multiplication operation on fuzzy numbers is defined by the extension principle. A new theory of complex fuzzy group is introduced and developed. Pdf fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. This paper first defines fuzzy complex numbers and shows closure under the basic arithmetic operations. The idea of fuzzy sets based on real number system. Complex fuzzy space, complex fuzzy subspace, complex fuzzy binary operation, complex fuzzy group, complex fuzzy subgroup. Firstly, the definition of fuzzy complex measure is introduced, the properties of fuzzy complex measure is mainly discussed in details.
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