In this paper, we introduce the concept of bipolar-valued fuzzification of ordered AG-groupoids and discuss some structural properties of bipolarvalued fuzzy two-sided ideals of an intra-regular ordered AG-groupoid.

We define an extended fuzzy equivalence relation, discuss some basic properties of extended fuzzy equivalence relations, find the extended fuzzy equivalence relation generated by a fuzzy relation in a set, and give some lattice theoretic properties of extended fuzzy equivalence relations.

In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

The paper dealswith systems of fuzzy relation equations known in the literature as eigen fuzzy set equations, aswell aswith systems of related fuzzy relation inequalities.Ourmain results are algorithms for computing the greatest and the smallest solutions to the considered systems of fuzzy relation inequalities, and algorithms for computing the greatest solutions to the considered systems of fu...

In this paper, we discussed about the intuitionistic fuzzy linear transformations (IFLT) and shown that the set of all linear transformations ) (V L defined over an intuitionistic fuzzy vector space V does not form an vector space. Here we determine the unique intuitionistic fuzzy matrix associated with an intuitionistic fuzzy linear transformation with respect to an ordered standard basis for ...

The basic paradigm of simulation is the probabilistic approach to describing real world uncertainty. However, in many cases we do not have an information that would be precise enough to build the corresponding probabilistic model or there are some human factors that prevent doing so. In such situations the mathematical tools of fuzzy set theory may be successfully used. It seems that the simple...

Inference mechanisms and interpretations of fuzzy rule bases are studied together from the point of view of systems of fuzzy relation equations. A proper use of an inference mechanism connected to a fuzzy relation interpreting a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations which are motiva...

Algebra of ordered fuzzy numbers (OFN) is defined to handle with fuzzy inputs in a quantitative way, exactly in the same way as with real numbers. Additional two structures: algebraic and normed (topological) are introduced to define a general form of defuzzyfication operators. A useful implementation of a Fuzzy Calculator allows counting with the general type membership relations.