Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we deal with the algebraic structure of soft sets. The lattice structures of soft sets are constructed. The concept of soft equality is introduced and some related properties are derived. It is proved that soft equality is a congruence relation with respect to some operations and the soft quotient algebra is established. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
Information Sciences,2009年179(14):2325-2332 ISSN：0020-0255
[Pei, Zheng] Xihua Univ, Sch Math & Comp Engn, Chengdu 610039, Sichuan, Peoples R China.;[Xu, Yang; Qin, Keyun] SW Jiaotong Univ, Dept Math, Chengdu 610031, Sichuan, Peoples R China.;[Ruan, Da] CEN SCK, Belgian Nucl Res Ctr, B-2400 Mol, Belgium.;[Ruan, Da] Univ Ghent, B-9000 Ghent, Belgium.
[Pei, Zheng] Xihua Univ, Sch Math & Comp Engn, Chengdu 610039, Sichuan, Peoples R China.
Linguistic data summary;Personnel database;Fuzzy statement;The LOWA operator;Genetic algorithms;The 2-tuple linguistic representation model
A linguistic data summary of a given data set is desirable and human consistent for any personnel department. To extract complex linguistic data summaries, the LOWA operator is used from fuzzy logic and some numerical examples are also provided in this paper. To obtain a complex linguistic data summary with a higher truth degree, genetic algorithms are applied to optimize the number and membership functions of linguistic terms and to select a part of truth degrees for aggregations, in which linguistic terms are represented by the 2-tuple linguistic representation model. Crown Copyright (C) 2009 Published by Elsevier Inc. All rights reserved.
Fuzzy Sets and Systems,2014年234:46-60 ISSN：0165-0114
[Li, Yingfang; Qin, Keyun] Southwest Jiaotong Univ, Sch Math, Chengdu 610031, Sichuan, Peoples R China.;[Qin, Keyun; He, Xingxing] Southwest Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Sichuan, Peoples R China.
[He, Xingxing] Southwest Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Sichuan, Peoples R China.
Similarity measure;Fuzzy equivalence;Biresiduation;Fuzzy set
The purpose of this paper is threefold. Firstly, based on the concept of fuzzy equivalence given by Fodor and Roubens, we propose different methods for the construction of fuzzy equivalencies from biresiduations, automorphisms, fuzzy negations, t-norms and t-conorms. Secondly, we give two manners of generating similarity measures of P.Z. Wang from fuzzy equivalencies. Finally, some properties of the two kinds of similarity measures are discussed and compared. (C) 2013 Elsevier B.V. All rights reserved.
Soft set theory and interval set theory are all mathematical tools for dealing with uncertainties. This paper is devoted to the discussion of soft interval set and its application. The notion of soft interval sets is introduced by combining soft set and interval set. Several operations on soft interval sets are presented in a manner parallel to that used in defining operations on soft sets and the lattice structures of soft interval sets are established. In addition, a soft interval set based decision making problem is analyzed.
This paper addresses on the robust exponential admissibility of uncertain switched descriptor systems with time-varying delays. Firstly, an easily verified condition is presented to check the switching-impulsive-free which ensures the consistent of algebraic equations. Moreover, a novel type of piecewise Lyapunov functions which are decreasing at switching times is introduced. This type of delicately constructed Lyapunov functions can efficiently eliminate the switching jump of adjacent Lyapunov functions at switching instants. By this type of Lyapunov functions and Razumikhin-type technique, the delay-independent minimum dwell time criteria of robust exponential admissibility are established under switching-impulsive-free. Two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results. (C) 2013 Elsevier Inc. All rights reserved.