scholarly journals General Complex-Valued Grouping Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ying Chen ◽  
Lvqing Bi ◽  
Bo Hu ◽  
Songsong Dai
Keyword(s):  
Fuzzy Sets ◽  
Special Kind ◽  
Aggregation Function ◽  
Construction Methods ◽  
General Complex ◽  
Complex Valued

Grouping function is a special kind of aggregation function which measures the amount of evidence in favor of either of the two choices. Recently, complex fuzzy sets have been successfully used in many fields. This paper extends the concept of grouping functions to the complex-valued setting. We introduce the concepts of complex-valued grouping, complex-valued 0-grouping, complex-valued 1-grouping, and general complex-valued grouping functions. We present some interesting results and construction methods of general complex-valued grouping functions.

scholarly journals General Complex-Valued Overlap Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Ying Chen ◽  
Lvqing Bi ◽  
Bo Hu ◽  
Songsong Dai
Keyword(s):  
Fuzzy Sets ◽  
Aggregation Function ◽  
Construction Methods ◽  
General Complex ◽  
Complex Valued

Overlap function is a special type of aggregation function which measures the degree of overlapping between different classes. Recently, complex fuzzy sets have been successfully applied in many applications. In this paper, we extend the concept of overlap functions to the complex-valued setting. We introduce the notions of complex-valued overlap, complex-valued 0-overlap, complex-valued 1-overlap, and general complex-valued overlap functions, which can be regarded as the generalizations of the concepts of overlap, 0-overlap, 1-overlap, and general overlap functions, respectively. We study some properties of these complex-valued overlap functions and their construction methods.

A method of constructing fuzzy implications from the FIφ-construction

2021 ◽  
pp. 1-14
Author(s):  
Yifan Zhao ◽  
Kai Li
Keyword(s):  
Specific Property ◽  
New Method ◽  
Aggregation Function ◽  
Fuzzy Implications ◽  
Construction Methods ◽  
Fuzzy Implication ◽  
New Construction

In the recent years, several new construction methods of fuzzy implications have been proposed. However, these construction methods actually care about that the new implication could preserve more properties. In this paper, we introduce a new method for constructing fuzzy implications based on an aggregation function with F (1,  0) =1, a fuzzy implication I and a non-decreasing function φ, called FIφ-construction. Specifically, some logical properties of fuzzy implications preserved by this construction are studied. Moreover, it is studied how to use the FIφ-construction to produce a new implication satisfying a specific property. Furthermore, we produce two new subclasses of fuzzy implications such as UIφ-implications and GpIφ-implications by this method and discuss some additional properties. Finally, we provide a way to generate fuzzy subsethood measures by means of FIφ-implications.

scholarly journals Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

Information ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 5 ◽  
Author(s):  
Liu ◽  
Mahmood ◽  
Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imaginary Part ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Membership Degree ◽  
The Real ◽  
Complex Valued

In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of complex-valued non‐membership degree is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we develop the score function, accuracy function and comparison method for two Cq-ROFNs. Based on Cq-ROFSs, some new aggregation operators are called complex q-rung orthopair fuzzy weighted averaging (Cq-ROFWA) and complex q-rung orthopair fuzzy weighted geometric (Cq-ROFWG) operators are investigated, and their properties are described. Further, based on proposed operators, we present a new method to deal with the multi‐attribute group decision making (MAGDM) problems under the environment of fuzzy set theory. Finally, we use some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

scholarly journals A Numerical Method for Computing the Roots of Non-Singular Complex-Valued Matrices

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 966
Author(s):  
Diego Caratelli ◽  
Paolo Emilio Ricci
Keyword(s):  
Numerical Method ◽  
Worked Examples ◽  
Higher Order ◽  
Singular Matrix ◽  
The Matrix ◽  
General Complex ◽  
Complex Valued

A method for the computation of the n th roots of a general complex-valued r × r non-singular matrix ? is presented. The proposed procedure is based on the Dunford–Taylor integral (also ascribed to Riesz–Fantappiè) and relies, only, on the knowledge of the invariants of the matrix, so circumventing the computation of the relevant eigenvalues. Several worked examples are illustrated to validate the developed algorithm in the case of higher order matrices.

scholarly journals Two Classes of Entropy Measures for Complex Fuzzy Sets

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 96 ◽  
Author(s):  
Lvqing Bi ◽  
Zhiqiang Zeng ◽  
Bo Hu ◽  
Songsong Dai
Keyword(s):  
Fuzzy Sets ◽  
Unit Circle ◽  
Type A ◽  
Rotational Invariance ◽  
The Other ◽  
Membership Functions ◽  
Type B ◽  
Invariance Properties ◽  
Entropy Measures ◽  
Complex Valued

Complex fuzzy sets are characterized by complex-valued membership functions, whose range is extended from the traditional fuzzy range of [0,1] to the unit circle in the complex plane. In this paper, we define two kinds of entropy measures for complex fuzzy sets, called type-A and type-B entropy measures, and analyze their rotational invariance properties. Among them, two formulas of type-A entropy measures possess the attribute of rotational invariance, whereas the other two formulas of type-B entropy measures lack this characteristic.

scholarly journals ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR(p) PROCESSES

1999 ◽  
Vol 15 (2) ◽  
pp. 184-217 ◽  
Author(s):  
Tjacco van der Meer ◽  
Gyula Pap ◽  
Martien C.A. van Zuijlen
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Limit Distribution ◽  
Continuous Time ◽  
Convergence Result ◽  
Likelihood Estimator ◽  
Characteristic Roots ◽  
Least Squares Estimators ◽  
General Complex ◽  
Complex Valued

In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behavior of the least-squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We apply the results for real-valued nearly unstable AR(p) models. In this case the limit distribution can be identified with the maximum likelihood estimator of the coefficients of the corresponding continuous time AR processes.

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