Mathematical Morphology is a theory concerned with the processing and analysis of images or signals using filters and other operators that modify them. This paper studies how the original images and signals can be retrieved using fuzzy property-oriented concept lattices and fuzzy relation equations.

Fuzzy relation equations (FRE) are associated with the composition of binary fuzzy relations. In the present work FRE are used as a tool for studying the process of learning a new subject matter by a student class. A classroom application and other suitable examples connected to the student learning of the derivative are also presented illustrating our results and useful conclusions are obtained.

Fuzzy inference systems are studied from the point of view of systems of fuzzy relation equations. A fundamental interpolation condition is considered to be a crucial point of study in choosing proper inference method as well as a proper interpretation of a fuzzy rule base. The paper aims at additive interpretations and investigates their utilization from a theoretical point of view while their...

Recently, two types of simulations (forward and backward simulations) and four types of bisimulations (forward, backward, forward-backward, andbackward-forwardbisimulations) between fuzzyautomatahavebeen introduced. If there is at least one simulation/bisimulation of some of these types between the given fuzzy automata, it has been proved that there is the greatest simulation/bisimulation of th...

This paper presents some novel theoretical results as well as practical algorithms and computational procedures on fuzzy relation equations (FRE). These results refine and improve what has already been reported in a significant manner. In the previous paper, the authors have already proved that the problem of solving the system of fuzzy relation equations is an N P-hard problem. Therefore, it i...

in this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. we transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters value, ambiguity and fuzziness.

in this paper, a new method based on parametric form for approximate solu-tion of fuzzy linear matrix equations (flmes) of the form ax = b; where ais a crisp matrix, b is a fuzzy number matrix and the unknown matrix x one,is presented. then a numerical example is presented to illustrate the proposedmodel.

in a recent paper, de baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. in this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. the reasoninglargely ...