Recall that a structure M is minimal if every definable (with parameters) subset of M is either finite or cofinite. The study of minimal partially ordered structures was initiated by Tanović in [4, 5]. The results from [4, 5] were essential in the proof by Tanović of the Pillay’s conjecture [1], which states that every countable structure in a countable language has infinitely many nonisomorphi...

This paper presents an original definition of data representativeness. The representativeness of each datum in a dataset is a meaningful notion quantified by a degree computed by aggregating fuzzy subsets. These fuzzy subsets are obtained by fuzzifying data in a robust way. We illustrate the usefulness of the representativeness by presenting applications for statistical location estimation,and ...

In this paper, the fuzzy nonlinear programming problem is discussed. In order to obtain more accurate solution, the properties of fuzzy set and fuzzy number with linear membership function and fuzzy maximum decision maker is utilized to fuzzifying the crisp problem . An example is provided to show the effectiveness of the proposed method.

Ralph Freese Department of Mathematics University of Hawaii at Manoa Honolulu, Hawaii 96822 In this paper we look at some of the problems on free lattices and free modular lattices which are of an order theoretic nature. We review some of the known results, give same new results, and present several open problems. Every countable partially ordered set can be order embedded into a countable free...

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...

After dropping the implication-like operation and reversing the order, an MTL-algebra becomes a partially ordered structure (L;≤,⊕, 0, 1) based on the single addition-like operation ⊕. Furthermore, ⊕ may be restricted to a partial, but cancellative addition + without loss of information. We deal in this paper with the case that the resulting partial algebra (L;≤,+, 0, 1) is embeddable into the ...

Previous work has shown a relation between L-valued extensions of FCA and the spectra of some matrices related to L-valued contexts. We investigate the spectra of reducible matrices over completed idempotent semifields in the framework of dioids, naturally-ordered semirings, that encompass several of those extensions. Considering special sets of eigenvectors also brings out complete lattices in...