g e y w o r d s F u z z y numbers, Convexity, Continuity, Convex fuzzy mappings, Linear ordering, Fuzzy Weirstrass theorem, Fuzzy optimization. 1. I N T R O D U C T I O N Let R n denote the n-dimensional Eucl idean space. The suppor t , supp(#) , of a fuzzy set # : R ~ I = [0, 1] is defined as supp(/~) = {x • R n I #(x) > 0}. A fuzzy set # : R n --~ I is called fuzzy convex if #(Ax + (1 A)y) _>...

In this paper, a quantum neuro-fuzzy classifier (QNFC) for classification applications is proposed. The proposed QNFC model is a five-layer structure, which combines the compensatory-based fuzzy reasoning method with the traditional Takagi–Sugeno–Kang (TSK) fuzzy model. The compensatory-based fuzzy reasoning method uses adaptive fuzzy operations of neuro-fuzzy systems that can make the fuzzy lo...

Fuzzy differential equation is an important tool to deal with dynamic systems in fuzzy environments. However, it is difficult to find the solutions to all fuzzy differential equations. In this paper, methods to solve linear fuzzy differential equations and reducible fuzzy differential equations are given. Moreover, existence and uniqueness theorem for homogeneous fuzzy differential equations ar...

In this paper, we construct fuzzy renewal processes involving fuzzy random variables. We first extend the renewal processes to the fuzzy renewal processes where interarrival times, rewards, and stopping times are all fuzzy random variables. According to these fuzzy renewal processes, we then extend some theorems of renewal processes to those in fuzzy renewal processes. These are elementary rene...

in this paper, a location allocation (la) problem in construction and demolition (c&d;) waste management (wm) is studied. a bi-level model for this problem under a fuzzy random environment is presented where the upper level is the governments who sets up the processing centers, and the lower level are the administrators of different construction projects who control c&d; waste and the after tre...

Abstract-This paper presents a general approach to fuzzy clustering methods. A generalised fuzzy objective function is used to combine fuzzy c-means clustering, fuzzy entropy clustering, and their extended versions into a generalised fuzzy clustering method. Some new extended versions of the above-mentioned clustering methods are proposed from this general approach. Several cluster data sets we...

The stochastic ordering of random variables is extended to the cases where the available data are imprecise quantities, rather than crisp. To do this, using some elements of fuzzy set theory, we suggest the fuzzy reversed hazard rate and fuzzy mean inactivity time functions and apply them to construct some new fuzzy stochastic orders for ranking fuzzy random variables. In addition, we study the...

A hybrid unsupervised learning algorithm, termed as rough-fuzzy c-means, is proposed in this paper. It comprises a judicious integration of the principles of rough sets and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in class definition, the membership function of fuzzy sets enables efficient handling of ove...

Firefly algorithm is a swarm-based algorithm that can be used for solving optimization problems. In this paper, we focus on image clustering algorithm using the fuzzy set of possible solution is incorporated into the original firefly to improve the performance. The movement of the firefly still follows the original pattern but they are updated according fuzzy c-means algorithm. All method, k-me...

In this paper, we propose a Context-based Gustafson-Kessel (CGK) clustering that builds Information Granulation (IG) in the form of fuzzy set. The fundamental idea of this clustering is based on Conditional Fuzzy C-Means (CFCM) clustering introduced by Pedrycz. The proposed clustering develops clusters preserving homogeneity of the clustered patterns associated with the input and output space. ...