Let A be a finite matrix with rational entries. We say that A is doubly image partition regular if whenever the set N of positive integers is finitely coloured, there exists ~x such that the entries of A~x are all the same colour (or monochromatic) and also, the entries of ~x are monochromatic. Which matrices are doubly image partition regular? More generally, we say that a pair of matrices (A,...

The class of the s-transitive (resp. w-transitive) fuzzy matrices contains properly the class of the max-min transitive fuzzy matrices for which reduction models are already known. It is shown that some basic properties of these models remain valid also for s-transitive (resp. w-transitive)fuzzy matrices.

In this paper, we investigate the algebraic properties of intuitionistic fuzzy matrices under the new operations and . The properties of intuitionistic fuzzy matrices are also obtained in the case where these new operations are combined with the well known operations of intuitionistic fuzzy matrices.

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

Li and Pedrycz [Y. M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005) 68–92] have proved fundamental results that provide different equivalentways to represent fuzzy languageswithmembership values in a lattice-orderedmonoid, and generalize the well-known results of the classical theory of fo...

fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. the purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. to provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...

‎this paper deals with one problem that needs to be addressed in the emerging field known under the name computing with perceptions‎. ‎it is the problem of describing‎, ‎approximately‎, ‎a given fuzzy set in natural‎ ‎language‎. ‎this problem has lately been referred to as the problem of retranslation‎. ‎an approaches to ‎dealing with the retranslation problem is discussed in the paper‎, ‎that ...

In this paper, we present the concepts of a fuzzy soft left (right) ideal and fuzzy soft interior ideal over an ordered semigroup S . Some basic results of fuzzy soft left (right) ideals and fuzzy soft interior ideals are investigated and the supported examples are provided. Different classes, regular, intra-regular, and simple ordered semigroups are characterized by means of fuzzy soft left (r...