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The connection of the 3-dimensional fuzzy sets with topos theory is considered. The category TFuz of the 3-dimensional fuzzy sets is constructed. It is shown that the category TFuz has all topos properties except Sub object Classifiers. It is also proved that the category TFuz has a middle object, and consequently forms a weak topos.
In this paper, the connection of the 4-valued inverse order nested sets and topos theory is considered. The category QNS of the 4-valued inverse order nested sets is constructed. It is shown that in the category QNS exist Equalizers, Finite Products, Terminal Objects, Exponentials and Subobject Classifiers. Consequently the category QNS forms a topos.
The aim of this article is to study the cut sets of interval valued intuitionistic fuzzy sets. By considering the cut sets of an interval-valued intuitionistic fuzzy set as five valued fuzzy sets, the definitions of four cut sets on interval-valued intuitionistic fuzzy sets are given, which are the generalizations of cuts sets on Zadeh fuzzy sets and the intuitionistic fuzzy sets. It is pointed that...
In this paper, a new method of ranking the fuzzy number is proposed. Firstly, a new concept of the satisfaction degree of the fuzzy number is presented and its properties are discussed. Secondly, the interaction between the parameters, ??- levels and ranking result is studied. Thirdly the method of the ranking is generalized to more fuzzy numbers. Finally, a numerical example illustrates the merits...
In order to describe complicated concepts, the concept of Y-N set is introduced. Firstly, the operations on Y-N sets such as union, intersection, difference and complement of Y-N sets are presented. Secondly, the definitions of image and preimage of a Y-N set under a mapping are given and the properties of the image and preimage are discussed. Finally, a category YNSet of Y-N sets is established and...
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