To measure the fuzziness of fuzzy sets, this paper introduces a distance-based and a fuzzy entropybased measurements. Then these measurements are generalized to measure the fuzziness of fuzzy partition, namely partition fuzziness. According to the relationship between the validity of fuzzy partition and its partition fuzziness, a family of cluster validity functions is proposed based on the mod...

evaluative and comparative analysis among educational projects remains an issue for administration, program directors, instructors, and educational institutes. this study reports a fuzzy complexity model for educational projects, which has two primary aspects (technical aspects and transparency aspects). these aspects may not be measured precisely due to uncertain situations. therefore, a fuzzy...

Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. W...

In this paper we propose the concept of fuzzy projections on subspaces of F(R), obtained from Zadeh’s extension of canonical projections in R, and we study some of the main properties of such projections. Furthermore, we will review some properties of fuzzy projection solution of fuzzy differential equations. As we will see, the concept of fuzzy projection can be interesting for the graphical r...

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

In this paper, we axiomatically introduce fuzzy multi-measures on bounded lattices. In particular, we make a distinction between four different types of fuzzy set multi-measures on a universe X, considering both the usual or inverse real number ordering of this lattice and increasing or decreasing monotonicity with respect to the number of arguments. We provide results from which we can derive ...

Using the notion of a fuzzy point and its belongness to and quasicoincidence with a fuzzy subset, some new concepts of a fuzzy interior ideal in Abel Grassmann’s groupoids S are introduced and their interrelations and related properties are invesitigated. We also introduce the notion of a strongly belongness and strongly quasicoincidence of a fuzzy point with a fuzzy subset and characterize fuz...

The primary issue involved in image and signal processing is to efficiently remove noise from a digital color image while preserving its features. A fuzzy filter is presented for the reduction of additive noise for digital color images. The filter consists of two sub filters. The first sub filter computes fuzzy distances among the color components of the central pixel and its neighborhood. Thes...