Two principal semantics have been assigned to the division of fuzzy relations. In the first one, the weights of the divisor are seen as thresholds and in the other, they act as grades of importance. This paper discusses a third approach in which the weights play the role of ideal values. In this context, the notion of a graded inclusion between (fuzzy) sets moves to that of a graded equality. I...

In this paper we introduce an application of intervalvalued systems to the segmentation of prostate ultrasound images. The system classifies each pixel as prostate or background. The input variables are the values of each pixel in different processed images as proximity, edginess and enhanced image. The system has 20 rules and is trained with ideal images segmented by an expert. Interval-valued...

Neuro-fuzzy networks revealed their proficiency in learning from data, while offering a transparent and somehow interpretable rule-based model. Recent research focused either on the interpretability of the chosen model or on the system performance. Regarding the interpretability, here an index to control the trade-off between complexity and performance, some insights into fuzzy partitions prope...

Supplier selection is a multi-criterion decision making problem under uncertain environments. Hence, it is reasonable to hand the problem in fuzzy sets theory (FST) and Dempster Shafer theory of evidence (DST). In this paper, a new MCDM methodology, using FST and DST, based on the main idea of the technique for order preference by similarity to an ideal solution (TOPSIS), is developed to deal w...

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...

Our aim in this paper is to introduce and study a new sort of fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal) of a ternary semigroup, called interval-valued (α,β )-fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal). We also characterize regular ternary semigroups in terms of these interval-valued fuzzy ideals.

Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy le...

maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem. in this paper, we apply fuzzy soft sets to  -hyperrings. the concept of ( , q )       -fuzzy soft  -hyperideals of  -hyperrings is first introduced. some new characterizations are investigated. in particular, a...

although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-newtonian calculus. the important point to note is that the non-newtonian calculus is a self-contained system independent of any other system of calculus. since this self-contained work is intended for a wide audience, inc...