Lan Shu

Bio: Lan Shu is an academic researcher from University of Electronic Science and Technology of China. The author has contributed to research in topics: Fuzzy number & Fuzzy set operations. The author has an hindex of 7, co-authored 11 publications receiving 160 citations.

Supremum metric on the space of fuzzy sets and common fixed point theorems for fuzzy mappings

Abstract: This paper generalizes a classical result about the space of bounded closed sets with the Hausdorff metric, and establishes the completeness of CB(X) with respect to the completeness of the metric space X, where CB(X) is the class of fuzzy sets with nonempty bounded closed @a-cut sets, equipped with the supremum metric d"~ which takes the supremum on the Hausdorff distances between the corresponding @a-cut sets. In addition, some common fixed point theorems for fuzzy mappings are proved and two examples are given to illustrate the validity of the main results in fixed point theory.

Common fixed point theorems for fuzzy mappings under Φ-contraction condition

Abstract: In this paper, under Φ-contraction condition, we prove common fixed point theorems for fuzzy mappings in the space of fuzzy sets on a compact metric space with the d ∞ -metric for fuzzy sets.

Notes on fuzzy complex analysis

Abstract: Several fuzzy complex analysis problems are discussed, pointing out some errors in literature and some weaknesses of introduced concepts. A modified approach to fuzzy complex analysis is proposed, and its impact is discussed.

On starshaped fuzzy sets

Abstract: In this paper we firstly define some new types of fuzzy starshapedness, discuss the relationships among the different types of fuzzy starshapedness, and then present some basic properties of them. Finally we develop several important results on the shadows of starshaped fuzzy sets.

Notes on “On the restudy of fuzzy complex analysis: Part I and Part II”

Abstract: In this note, we show by counterexamples that some results of Qiu and colleagues [On the restudy of fuzzy complex analysis: Part I The sequence and series of fuzzy complex numbers and their convergences, Fuzzy Sets and Systems 115 (2000) 445-450; On the restudy of fuzzy complex analysis: Part II The continuity and differentiation of fuzzy complex functions, Fuzzy Sets and Systems 120 (2001) 517-521] concerning the convergence of the series of fuzzy complex numbers and the differentiation of fuzzy complex functions are incorrect, and offer some of their modified versions We also show that the derivative introduced by them is inappropriate for the functions mapping complex numbers into fuzzy complex numbers

Complex Neurofuzzy ARIMA Forecasting—A New Approach Using Complex Fuzzy Sets

Abstract: A novel complex neurofuzzy autoregressive integrated moving average (ARIMA) computing approach is presented for the problem of time-series forecasting. The proposed approach integrates a complex neurofuzzy system (CNFS) using complex fuzzy sets (CFSs) and ARIMA models to form the proposed computing model, which is called the CNFS-ARIMA. The output of CNFS-ARIMA is complex-valued, of which the real and imaginary parts can be used for two different functional mappings. This is the so-called dual-output property. There is no fuzzy If-Then rule in the genesis of CNFS-ARIMA. For the formation of CNFS-ARIMA, structure learning and parameter learning are involved to self-organize and self-tune the CNFS-ARIMA. A class of CFSs is used to describe the premise parts of fuzzy If-Then rules, whose consequent parts are specified by ARIMA models. CFS is an advanced fuzzy set whose membership degrees are complex-valued within the unit disc of the complex plane. With the synergetic merits of CNFS and ARIMA, CNFS-ARIMA models have excellent nonlinear mapping capability for time-series forecasting. A number of benchmark time series are used to test the proposed approach, whose results are compared with those by other approaches. Moreover, real-world financial time series, such as the National Association of Securities Dealers Automated Quotation (NASDAQ), the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), and the Dow Jones Industrial (DJI) Average Index, are used for the proposed approach to perform the dual-output forecasting experiments. The experimental results indicate that the proposed approach shows excellent performance.

A Method for Multiple Periodic Factor Prediction Problems Using Complex Fuzzy Sets

Abstract: Multiple periodic factor prediction (MPFP) problems exist widely in multisensor data fusion applications. Development of an effective prediction method should integrate information for multiple periodically changing factors. Because the uncertainty and periodicity coexist in the information used, the prediction method should be able to handle them simultaneously. In this study, complex fuzzy sets are used to represent the information with uncertainty and periodicity. A product-sum aggregation operator (PSAO) is developed for a set of complex fuzzy sets, which is used to integrate information with uncertainty and periodicity, and a PSAO-based prediction (PSAOP) method is then proposed to generate a solution of MPFP problems. This study illustrates the details of the PSAOP method through two real applications in annual sunspot number prediction and bushfire danger rating prediction. Experiments indicate that the proposed PSAOP method effectively handles the uncertainty and periodicity in the information of multiple periodic factors simultaneously and can generate accurate predictions for MPFP problems.

Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mareš equivalence relation

Abstract: In this paper, we obtain some algebraic properties and topological properties of the quotient space of fuzzy numbers with respect to the equivalence relation defined by Mares: every fuzzy number has only one Mares core and equivalent fuzzy numbers have the same Mares core; in addition, equivalence classes of fuzzy numbers can be only expressed as the sum of its Mares core and the set of symmetric fuzzy numbers, which shows the notable difference between the equivalence classes of fuzzy numbers and the cosets of the normal subgroup in a group. Based on these results, we introduce a new concept of convergence under which the quotient space is complete. As an application of the main results, it is shown that if we identify every fuzzy number with the corresponding equivalence class, there would be more differentiable fuzzy functions than what is found in the literature.

On fuzzy differential equations in the quotient space of fuzzy numbers

Abstract: Since addition possesses an inverse in the quotient space of fuzzy numbers based on Mares equivalence relation, in this paper, we introduce a metric on the quotient space of fuzzy numbers, and then deal with fuzzy mappings of a real variable whose values are equivalence classes of fuzzy numbers. We study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation. Finally, some examples are given to illustrate the main theorems.

Fixed points of fuzzy contractive and fuzzy locally contractive maps

Abstract: We establish some fixed point theorems for fuzzy contractive and fuzzy locally contractive mappings on a compact metric space with the d ∞ -metric for fuzzy sets. Our results generalized well-known classical results of Edelstein.