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
Some generalizations of the result proved by S.P. Singh [J. Approx. Theory 25（1979）, 89-90] are presented in convex metric spaces. The results proved contain several known results on the subject.
The paper deals with the exponential stability problem of a variable coefficient star-shaped network,whose strings are coupled at a common end in a star-shaped configuration and the common connection of all strings ca...The paper deals with the exponential stability problem of a variable coefficient star-shaped network,whose strings are coupled at a common end in a star-shaped configuration and the common connection of all strings can be moved.Two kinds of media materials with a component of viscous and another simply elastic are distributed on each string.Under suitable hypothesis on the coefficient functionsμj(x)of damping terms and the kernelsηj(s)of distributed delay terms,the well-posedness of the system is obtained by means of resolvent family theory.In addition,the allocation proportion of the two parts and the property of the material character functions are discussed when the starshaped network is exponentially stable.Meanwhile,the sufficient condition of exponential stability is established.Numerical simulations are also included to verify the main results.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This research is partially supported by University Grants Commission, India (F30-238/2004(SR)).
文摘Some generalizations of the result proved by S.P. Singh [J. Approx. Theory 25（1979）, 89-90] are presented in convex metric spaces. The results proved contain several known results on the subject.
基金the National Natural Science Foundation of China under Grant Nos.61773277 and 62073236。
文摘The paper deals with the exponential stability problem of a variable coefficient star-shaped network,whose strings are coupled at a common end in a star-shaped configuration and the common connection of all strings can be moved.Two kinds of media materials with a component of viscous and another simply elastic are distributed on each string.Under suitable hypothesis on the coefficient functionsμj(x)of damping terms and the kernelsηj(s)of distributed delay terms,the well-posedness of the system is obtained by means of resolvent family theory.In addition,the allocation proportion of the two parts and the property of the material character functions are discussed when the starshaped network is exponentially stable.Meanwhile,the sufficient condition of exponential stability is established.Numerical simulations are also included to verify the main results.
