Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)-fuzzy subalgebras where α, β are any two of {∈, q, ∈∨ q, ∈ ∧ q} with α 6=∈ ∧ q is introduced, and related properties are

In this paper we investigate the System of fuzzy relation equations with inf → composition. We base on the knowledge of he system of fuzzy relation equations with sup−∗-composition. First, the general notions are explained and then are shown the smallest and maximal solutions. Finally is investigated a simple criterion of solvability for a special case of fuzzy sets.

Properties of sup-∗ compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider sup-∗ powers of fuzzy relations under diverse assumptions about ∗ operation. At first, we remind fundamental properties of sup-∗ composition. Then, ...

In this work we present a method for constructing an Atanassov’s intuitionistic fuzzy preference relation from a fuzzy preference relation that takes into account the ignorance of the expert when evaluating the preferences in the latter. Moreover, we present two algorithms that make use of this method for extending the weighted voting method to the Atanassov’s intuitionistic fuzzy setting in de...

In this paper, the multi-person decision making problems with various different types of incomplete linguistic preference relations are studied. Some new concepts, including incomplete uncertain linguistic preference relation, incomplete triangular fuzzy linguistic preference relation, incomplete trapezoid fuzzy linguistic preference relation, expected incomplete linguistic preference relation ...

In this paper we present a method of decomposing a neutrosophic database relation with Neutrosophic attributes into basic relational form. Our objective is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or vague relation can only handle incomplete information. Authors are taking the Neutrosophic Relational database [8], [2] to show how imprecise data can ...

Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces. Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of o...

Intuitionistic fuzzy sets theory which is the generalisation of fuzzy sets theory is more suitable tool for dealing with imprecise information. The information provided by the decision maker is imprecise in many situations. So, intuitionistic fuzzy preference relation is a suitable tool for such cases. The estimation of the priority vector of the intuitionistic fuzzy preference relation is an i...

Weighted aggregation of fuzzy preference relations on the set of alternatives by several criteria in decision-making problems is considered. Pairwise comparisons with respect to importance of the criteria are given in fuzzy preference relation as well. The aggregation procedure uses the composition between each two relations of the alternatives. The membership function of the newly constructed ...

Tool wear condition monitoring has the potential to play a critical role in ensuring the dimensional accuracy of the workpiece and prevention of damage to cutting equipment. It could also help in automating cutting processes. In this paper, the feed cutting force estimated with the aid of an inexpensive current sensor installed on the ac servomotor of a computerized numerical control turning ce...