Intuitionistic fuzzy starshaped sets (i.f.s.) is a generalized model of fuzzy starshaped set. By the definition of i.f.s., the intuitionistic fuzzy general starshaped sets (i.f.g.s.), intuitionistic fuzzy quasi-starsh...Intuitionistic fuzzy starshaped sets (i.f.s.) is a generalized model of fuzzy starshaped set. By the definition of i.f.s., the intuitionistic fuzzy general starshaped sets (i.f.g.s.), intuitionistic fuzzy quasi-starshaped sets (i.f.q-s.) and intuitionistic fuzzy pseudo-starshaped sets (i.f.p-s.) are proposed and the relationships among them are studied. The equivalent discrimination conditions of i.f.q-s. and i.f.p-s. are presented on the basis of their properties which are meaningful for the research of the generalized fuzzy starshaped sets. Moreover, the invariance of the two given fuzzy sets under the translation transformation and linear reversible transformation are discussed.展开更多
Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuz...Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.展开更多
This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or obse...The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.展开更多
文摘Intuitionistic fuzzy starshaped sets (i.f.s.) is a generalized model of fuzzy starshaped set. By the definition of i.f.s., the intuitionistic fuzzy general starshaped sets (i.f.g.s.), intuitionistic fuzzy quasi-starshaped sets (i.f.q-s.) and intuitionistic fuzzy pseudo-starshaped sets (i.f.p-s.) are proposed and the relationships among them are studied. The equivalent discrimination conditions of i.f.q-s. and i.f.p-s. are presented on the basis of their properties which are meaningful for the research of the generalized fuzzy starshaped sets. Moreover, the invariance of the two given fuzzy sets under the translation transformation and linear reversible transformation are discussed.
基金Supported by the Aeronautical Science Foundation(20115868009)the Open Project Program of Key Laboratory of Intelligent Computing&Information Processing of Ministry of Education in Xiangtan University(2011ICIP04)+1 种基金the Program of 211 Innovation Engineering on Information in Xiamen University(2009-2011)the College Students Innovation Training Plan of Xianmen University~~
文摘Although the concept of interval fuzzy set and its properties have been defined, its three theorems and their effectiveness are not proved. Therefore, the knowledge presentation and its operation rules of interval fuzzy set are studied firstly, and then the cut set of interval fuzzy set is proposed. Moreover, the decomposition theo- rem, the representation theorem and the extension theorem of interval fuzzy set are presented. Finally, examples are given to demonstrate that the classical fuzzy set is a special case of interval fuzzy set and interval fuzzy set is an effective expansion of the classical fuzzy set.
基金Supported by the National Natural Science Foundation of China (No. 69803007)
文摘This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
文摘The system of linear equations plays a vital role in real life problems such as optimization, economics, and engineering. The parameters of the system of linear equations are modeled by taking the experimental or observation data. So the parameters of the system actually contain uncertainty rather than the crisp one. The uncertainties may be considered in term of interval or fuzzy numbers. In this paper, a detailed study of three solution techniques namely Classical Method, Extension Principle method and α-cuts and interval Arithmetic Method to solve the system of fuzzy linear equations has been done. Appropriate applications are given to illustrate each technique. Then we discuss the comparison of the different methods numerically and graphically.
