‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a well-knownmetric, which preserves the expected interval of the fuzzy number, is completely solved. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Properties of this new trapezoidal approximation operator are studied. © 2007 Elsevier B.V. ...

Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind arithmetic sets using gradual number and From point view soft computing, this definition provides new way handling operations The is an important characterization set. also useful for analyses applications arithmetic. In paper, we present general conclusions crucial problems related to ranges induced by These indic...

Suppose S is a subset of a metric spaceM with a metric δ, and D a subset of positive real numbers. The distance graph G(S, D), with a distance set D, is the graph with vertex set S in which two vertices x and y are adjacent iff δ(x, y) ∈ D. Distance graphs, first studied by Eggleton et al. [7], were motivated by the well-known plane-coloring problem: What is the minimum number of colors needed ...

Sets and Intervals • An interval with round brackets such as (a, b) means all the numbers between a and b not including a and b. We call this interval an open interval. • An interval with square brackets such as [a, b] means all the numbers between a and b including a and b. We call this interval a closed interval. • An interval with one square bracket and one closed bracket is called a clopen ...

In view of multi-attribute decision-making problems with interval numbers in social economy and engineering system, this paper defines and analyzes the basic operational rule, normalized method, sequence comparison strategy, and the calculating formula for the distance of interval numbers and interval number sequence. It presents weighted TOPSIS decision-making model based on interval numbers o...