the concept of an $l$-bornology is introduced and the theory of $l$-bornological spacesis being developed. in particular the lattice of all $l$-bornologies on a given set is studied and basic properties ofthe category of $l$-bornological spaces and bounded mappings are investigated.

The fundamental concept of the fuzzy logic has been weakened by requiring a mere membership relation; consequently an ordered fuzzy number (OFN) arises as an ordered pair of continuous real functions defined on the interval [0, 1]. Four algebraic operations are constructed in a way that renders them an algebra. Further, a norm is introduced which makes them a Banach space. A class of linear def...

In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semig...

In this paper, we discuss the equivalent conditions of pretopological and topological $L$-fuzzy Q-convergence structures and define $T_{0},~T_{1},~T_{2}$-separation axioms in $L$-fuzzy Q-convergence space. {Furthermore, $L$-ordered Q-convergence structure is introduced and its relation with $L$-fuzzy Q-convergence structure is studied in a categorical sense}.

Ordered fuzzy numbers that make possible to deal with fuzzy inputs quantitatively, exactly in the same way as with real numbers, are defined together with four algebraic operations. For defuzzyfication operators that play the main role when dealing with fuzzy controllers and fuzzy inference systems an approximation formula is given. In order to determine it when a training set is given a dedica...

a central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. in this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. the main stages of the modeling process are represented as fuzz...

In this paper we introduce bipolar fuzzy subsemigroup, bipolar fuzzy left (right) ideals and bipolar fuzzy bi-ideal in ordered semigroups. We characterize different classes of ordered semigroups by the properties of their bipolar fuzzy ideals and bipolar fuzzy bi-ideals.

Traditional fuzzy logic uses real numbers as truth values. This description is not always adequate, so in intuitionistic fuzzy logic, we use pairs of real numbers to describe a truth value. Such pairs can be described either as pairs (t; f) for which t + f 1, or, alternatively, as pairs (t; 1 ? f) for which t 1 ?f. To make this description even more adequate, instead of using real numbers to de...

the pioneer work of image compression/reconstruction based onfuzzy relational equations (icf) and the related works are introduced. theicf regards an original image as a fuzzy relation by embedding the brightnesslevel into [0,1]. the compression/reconstruction of icf correspond to thecomposition/solving inverse problem formulated on fuzzy relational equations.optimizations of icf can be consequ...