• Korean Journal of Mathematics
• /
• v.25 no.1
• /
• pp.71-85
• /
• 2017

This paper introduces a novel extension of soft rough fuzzy set so-called modified soft rough fuzzy set model in which new lower and upper approximation operators are presented together their related properties that are also investigated. Eventually it is shown that these new models of approximations are finer than previous ones developed by using soft rough fuzzy sets.

• The Pure and Applied Mathematics
• /
• v.20 no.2
• /
• pp.117-127
• /
• 2013

As a generalization of fuzzy subsemigroups, the notion of ${\varepsilon}$-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ${\varepsilon}$-generalized fuzzy subsemigroups are established, and we show that the intersection of two ${\varepsilon}$-generalized fuzzy subsemigroups is also an ${\varepsilon}$-generalized fuzzy subsemigroup. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be ${\varepsilon}$-fuzzy idempotent is discussed. Using a given ${\varepsilon}$-generalized fuzzy subsemigroup, a new ${\varepsilon}$-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ${\varepsilon}$-generalized fuzzy subsemigroup is considered.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.12a
• /
• pp.29-32
• /
• 2002

We consider the question whether, for given fuzzy numbers, there are different Pairs of f-norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.2
• /
• pp.161-170
• /
• 2009

For various fuzzy numbers, many operations have been calculated. We generalize about triangular fuzzy number and calculate four operations based on the Zadeh's extension principle, addition A(+)B, subtraction A(-)B, multiplication A(${\cdot}$)B and division A(/)B for two generalized triangular fuzzy sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2002.12a
• /
• pp.5-8
• /
• 2002

In this paper, we introduce a simple new method on calculating the entropy of the image fuzzy set gotten by the extension principle without calculating its membership function.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.8 no.4
• /
• pp.69-72
• /
• 1998

We introduce a concept of a 'fuzzy' map between sets by modifying the concetp of the extension principle introduced by Dubois and Prade in [1] and by using this we generalize Goguen's and Zadeh's extension principles in [2] and [3].

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.161-167
• /
• 2009

Category Fuz of fuzzy sets has a similar function to the Category Set. We study injective, absolute retract, enough injectives, injective hulls and essential extension in the Category Fuz of fuzzy sets.

• Proceedings of the KIEE Conference
• /
• 1993.07a
• /
• pp.489-491
• /
• 1993

Many optimization problem or multiple attribute, multiple alternative decision making problem may have fuzzy evaluation factors. In this case, fuzzy number operation technique is needed to evaluate and compare object functions which become fuzzy sets. Generally, fuzzy number operations can be defined by extension principle of fuzzy set theory, but it is tedious to do fuzzy number operations by using extension principle when the membership functions are defined by complex functions. Many fast methods which approximate the membership functions such as triangle, trapezoidal, or L-R type functions are proposed. In this paper, a fast fuzzy number operation method is proposed which do not simplify the membership functions of fuzzy numbers.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.20 no.4
• /
• pp.592-595
• /
• 2010

The extended algebraic operations are defined by applying the extension principle to normal algebraic operations. And these operations are calculated for some kinds of fuzzy numbers. In this paper, we get exact membership function as a results of calculation of these operations for generalized quadratic fuzzy sets.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.7 no.1
• /
• pp.85-89
• /
• 2007

Many authors considered the computational aspect of sup-min convolution when applied to weighted average operations. They used a computational algorithm based on a-cut representation of fuzzy sets, nonlinear programming implementation of the extension principle, and interval analysis. It is well known that $T_W$(the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. In this paper, we consider the computational aspect of the extension principle by the use of $T_W$ when the principle is applied to fuzzy weighted average operations. We give the exact solution for the case where variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources.