LR fuzzy numbers are quite common in real world applications involving the triangular fuzzy number, the Gaussian fuzzy number, and the Cauchy fuzzy number as special cases. In this paper, we first prove that a fuzzy number is an LR fuzzy number if and only if its credibility distribution is strictly increasing. After that, based on credibility measure, an operational law on independent LR fuzzy...

This paper presents a new class of fuzzy expectation data envelopment analysis (FEDEA) models with credibility constraints. Since the proposed model contains the credibility of fuzzy events in the constraints and the expected value of a fuzzy variable in the objective, the solution process is very complex. Thus, in the case when the inputs and outputs are mutually independent trapezoidal fuzzy ...

With reasonable control selections on the space of functions, various application models can take the shape of a well-defined control system on mathematics. In the credibility space, controlability management of fuzzy differential equation is as much important issue as stability. This paper addresses exact controllability for abstract fuzzy differential equations in the credibility space in the...

The objective of this paper is to study some new analytical properties of credibility functions. We first discuss the continuity of credibility functions, and establish the sufficient and necessary conditions for the right continuity and left continuity of credibility functions. Furthermore, we study the absolute continuity of credibility functions and obtain some sufficient conditions for the ...

There are various types of uncertainty in the real world. This is a motivation to investigate the behavior of uncertain phenomena. Random phenomena is one class of objective uncertain phenomena which has been well studied. Probability theory is an efficient tool to study the behavior of random phenomena. Besides randomness, fuzziness is a basic type of subjective uncertainty initiated by Zadeh....

The purpose of this paper is to provide an algorithm for commercial banks in Taiwan to evaluate the credibility of their potential debtors from the default probability viewpoint under fuzzy environment. The fundamental concepts we have adopted include the eigenvector method, fuzzy Delphi method, fuzzy set theory, and multi-criteria decision making method. By coordinating the concept of internal...

Classic inverse minimum spanning tree problem is to make the least edge weight modification such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. Although many applications can be formulated into this problem, fuzzy parameters are met in some real-world applications. In this paper, a type of inverse minimum spanning tree problem with fuzzy edge...

uncertainty inherent in the financial market was usually consid- ered to be random. however, randomness is only one special type of uncer- tainty and appropriate when describing objective information. for describing subjective information it is preferred to assume that uncertainty is fuzzy. this paper defines the expected payoof trading strategies in a fuzzy financial market within the framewor...

Fuzziness plays an essential role in the real world. Fuzzy set theory has been developed very fast since it was introduced by Zadeh (1965) [1]. A fuzzy set was characterized with its membership function by Zadeh. The term fuzzy variable was fist introduced by Kaufmann (1975) [2], and then appeared in Zadeh (1978) [3] and Nahmias (1978) [4] as a fuzzy set of real numbers. In order to establish t...

The coordination of two-echelons supply chain by buyback contract under the imperfect product quality and fuzzy demand environment is investigated in this paper. The mathematical models are built based on credibility theory, and the optimal parameters of buyback contract are obtained. In addition, the influence of the imperfect product rate on the parameters of buyback contract is analyzed. Fin...