Hongxing Li

Fuzzy Set-Valued Similarity Measure and its Application to Pattern Recognition

In paper [1], the definition of fuzzy set similarity measure and it’s application to fuzzy inference are given. So we introduce similarity measure of fuzzy set-valued, which is called fuzzy similarity measure. Fuzzy similarity measure is a generalized similarity measure, the axiomatic description is given, and some examples of fuzzy similarity measure are proposed, meanwhile its application to pattern recognition is shown.

A fuzzy similarity inference method for fuzzy reasoning

In this paper, Fuzzy Similarity Inference (FSI) is investigated. First, the axiomatic definition of the fuzzy similarity measure is introduced. It is a generalization of the similarity measure. Some formulas are given to compute the fuzzy similarity of two fuzzy sets. Second, a novel fuzzy reasoning, called fuzzy similarity inference, is proposed. Computational formulas for both fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) are obtained. Based on the theory of partial valuations, FSI method is put under the framework of logic semantically. Furthermore, the generalized problem of FSI is investigated. Computational formulas for @a-FSI FMP and @a-FSI FMT are obtained. At last, reversibility properties of FSI are proved.

Three new cut sets of fuzzy sets and new theories of fuzzy sets

Three new cut sets are introduced from the view points of neighborhood and Q-neighborhood in fuzzy topology and their properties are discussed. By the use of these cut sets, new decomposition theorems, new representation theorems, new extension principles and new fuzzy linear mappings are obtained. Then inner project of fuzzy relations, generalized extension principle and new composition rule of fuzzy relations are given. In the end, we present axiomatic descriptions for different cut sets and show the three most intrinsic properties for each cut set.

On the definition of the intuitionistic fuzzy subgroups

Abstract In this paper, a new kind of intuitionistic fuzzy subgroup theory, which is different from that of Ma, Zhan and Davvaz (2008)xa0 [22] , [23] , is presented. First, based on the concept of cut sets on intuitionistic fuzzy sets, we establish the neighborhood relations between a fuzzy point x a and an intuitionistic fuzzy set A . Then we give the definitions of the grades of x a belonging to A , x a quasi-coincident with A , x a belonging to and quasi-coincident with A and x a belonging to or quasi-coincident with A , respectively. Second, by applying the 3-valued Lukasiewicz implication, we give the definition of ( α , β ) -intuitionistic fuzzy subgroups of a group G for α , β ∈ { ∈ , q , ∈ ∧ q , ∈ ∨ q } , and we show that, in 16 kinds of ( α , β ) -intuitionistic fuzzy subgroups, the significant ones are the ( ∈ , ∈ ) -intuitionistic fuzzy subgroup, the ( ∈ , ∈ ∨ q ) -intuitionistic fuzzy subgroup and the ( ∈ ∧ q , ∈ ) -intuitionistic fuzzy subgroup. We also show that A is a ( ∈ , ∈ ) -intuitionistic fuzzy subgroup of G if and only if, for any a ∈ ( 0 , 1 ] , the cut set A a of A is a 3-valued fuzzy subgroup of G , and A is a ( ∈ , ∈ ∨ q ) -intuitionistic fuzzy subgroup (or ( ∈ , ∈ ∨ q ) -intuitionistic fuzzy subgroup) of G if and only if, for any a ∈ ( 0 , 0.5 ] (or for any a ∈ ( 0.5 , 1 ] ), the cut set A a of A is a 3-valued fuzzy subgroup of G . At last, we generalize the ( ∈ , ∈ ) -intuitionistic fuzzy subgroup, ( ∈ , ∈ ∨ q ) -intuitionistic fuzzy subgroup and ( ∈ ∧ q , ∈ ) -intuitionistic fuzzy subgroup to intuitionistic fuzzy subgroups with thresholds, i.e.,xa0 ( s , t ] -intuitionistic fuzzy subgroups. We show that A is a ( s , t ] -intuitionistic fuzzy subgroup of G if and only if, for any a ∈ ( s , t ] , the cut set A a of A is a 3-valued fuzzy subgroup of G . We also characterize the ( s , t ] -intuitionistic fuzzy subgroup by the neighborhood relations between a fuzzy point x a and an intuitionistic fuzzy set A .

The information content of fuzzy relations and fuzzy rules

The appraisement of fuzzy relations is a significant problem in fuzzy theory. The related literatures done before almost focused on the similarity or equivalence fuzzy relations with a probability distribution preassigned. In this paper, a new measure named the information content of fuzzy relations is proposed, which estimates the information conveyed by a general fuzzy relations defined on multiple-domain without probability distribution preassigned. When fuzzy relation is taken as fuzzy set, the information content of fuzzy relation is compared with fuzzy entropy and specificity of fuzzy sets. Based on this new measure, a new concept, the information content of fuzzy rules, is defined, which focuses on the corresponding relation between input domain and output domain and can be used to appraise and choose fuzzy rules in rule mining.

The set-valued mapping based on ample fields

Ample fields play an important role in possibility theory. Based on the ample fields in possibility theory, two new concepts such as possibilistic set and possibility mapping are presented. A theoretical approach to define operations and implication operations of fuzzy sets based on the theory of falling shadows of possibilistic sets is established, and the category PosM of ample spaces and possibility mappings and the category @X(@W,A) of possibilistic sets are built up respectively. It is proved that the category @X(@W,A) is a topos.

Cut Sets on Interval-Valued Intuitionistic Fuzzy Sets

The aim of this article is to study the cut sets of interval valued intuitionistic fuzzy sets. By considering the cut sets of an interval-valued intuitionistic fuzzy set as five valued fuzzy sets, the definitions of four cut sets on interval-valued intuitionistic fuzzy sets are given, which are the generalizations of cuts sets on Zadeh fuzzy sets and the intuitionistic fuzzy sets. It is pointed that the cuts sets of interval-valued intuitionistic fuzzy sets have the same properties as that of the intuitionistic fuzzy sets and Zadeh fuzzy sets. These works provide a powerful tool to study interval-valued intuitionistic fuzzy sets.

Center of gravity fuzzy system based on regular fuzzy implication and it's probability representation

In this paper, we consider a fundamental theoretical question: why cannot regular fuzzy implication operator meeting logical properties construct fuzzy system? Through the appropriate choice of the aggregation operator, the center of gravity fuzzy system (COGFS) based on regular fuzzy implication is studied in detail in the paper. Numerical characteristics of the random vector corresponding to the above system have more normative format. Which is important to do the further research on unified theory of uncertain systems. Finally, we also discuss the universal approximation of the system. It proves that the system has higher approximation accuracy for nonlinear function, and the simulation result also illustrates the effective of conclusion.

Fuzzy Probabilistic Sets and r-Fuzzy Sets

In this paper, a connection between the fuzzy probabilistic set and the r-fuzzy set is established. Firstly, a new concept of r-fuzzy nested set is presented and it is pointed that a fuzzy probabilistic set is an equivalent class of a r-fuzzy nested set. Secondly, the concepts of fuzzy probabilistic subgroup and r-fuzzy subgroup of a group are given respectively, the relations between fuzzy probabilistic subgroups and fuzzy subgroups presented by Rosenfeld and the properties of r-fuzzy subgroups are discussed. Finally, the membership function of fuzzy probabilistic sets and r-fuzzy subgroups are defined, the properties of membership function of r-fuzzy subgroups are studied.

The probability distribution and fuzzy system based on bounded product implication

In this paper, a method of constructing joint probability density function and fuzzy system using non-singleton fuzzifier is proposed based on a set of input-output data. Firstly, we create fuzzy relations using bounded product implication operator. With the fuzzy relations, we get the joint probability density function of binary random variable. Secondly, the marginal density functions and numerical characteristics of bounded product distribution are discussed separately. Finally, the regression function is obtained based on the probability distribution. It is actually the center of gravity fuzzy system, which further reveals the probability sense of fuzzy systems with center of gravity method. Meanwhile, the sufficient condition for the fuzzy system as an universal approximator is given.