Composition of fuzzy operators often appears and it is natural to ask when the order of composition does not change the result. In previous papers, we characterized permutability in the case of fuzzy consequence operators and fuzzy interior operators. We also showed the connection between the permutability of the fuzzy relations and the permutability of their induced fuzzy operators. In this wo...

Contrast to identical rationality, non-identical rationality is laid as the basis for option pricing, realized by a family of non-additive fuzzy measures mathematically, which naturally induces the new concept and analyzing methods, fuzzy options. Then as demonstration, the paper applies the fuzzy options to default risk analysis for municipal bonds in China.

A fuzzy context-free K-grammar is a fuzzy context-free grammar with a countable rather than a finite number of rules satisfying the following condition: for each symbol α, the set containing all right-hand sides of rules with left-hand side equal to α forms a fuzzy language that belongs to a given family K of fuzzy languages. In this paper we study the effect of the non-self-embedding restricti...

In this paper I will introduce the trapezoidal intuitionistic fuzzy numbers (IF numbers) and will prove some operations for them. Also I am going to propose a new ordering method for IF numbers in which I will consider two characteristic values of membership and non-membership functions for an IF number. These values are defined by the integral of the inverse fuzzy membership and non-membership...

The fuzzy extension principle has been widely used to extend the domain of mathematical functions and relations from elements of a referential set to fuzzy subsets of that referential set. However, there are restrictions associated with the fuzzy extension principle. This paper addresses the question how restricted is the family of “fuzzy set to fuzzy set mappings” obtained by the fuzzy extensi...

The main feature of a Takagi-Sugeno (T-S) fuzzy model is to express the local dynamics of each fuzzy implication (rule) by a linear system model. The overall fuzzy model of the system is achieved by fuzzy “blending” of the linear system models. Parallel or feedback connections of T-S fuzzy systems which preserve the properties of each system are possible [1]. Thus a simple and straightforward a...

A non-linear multi-objective transportation problem (NMOTP) refers to a special class of non-linear multi-objective problems. In this paper we review goal programming (GP) and fuzzy programming (FP) as two approaches for solving (NMOTP). Meanwhile, by extending Mohamed’s idea about fuzzy goal programming (FGP), we propose a fuzzy goal programming approach to solve the non-linear multi-objective...

In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, w...

In uncertainty decision making, experts can use interval-fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, linguistic 2tuple or linguistic indices to express their preferences. Using kernel function, the fuzzy numbers can be converted into fuzzy number range from 0 to 1. Thus, different fuzzy judgment matrix can be expressed in a unified style. A judging method for ordinal consis...

Data envelopment analysis (DEA) is a linear programming based non-parametric technique for evaluating the relative efficiency of homogeneous decision making units (DMUs) on the basis of multiple inputs and multiple outputs. There exist radial and non-radial models in DEA. Radial models only deal with proportional changes of inputs/outputs and neglect the input/output slacks. On the other hand, ...