Strict lower sections, strict upper sections and open order intervals (strict order intervals) are classical 9 notions associated to crisp orderings (crisp total preorders). In this paper, we extend these notions to fuzzy orderings. We determine all the fuzzy orderings (they contain all the crisp orderings) which make it possible 11 to compare two fuzzy strict lower sections and two fuzzy stric...

Due to the nature of real world problems, the collected data usually involve some kind of uncertainty. As a matter of fact, many parts of information cannot be quantified due to their nature. Incomplete information or partial ignorance is also another cause for resorting to fuzziness. In many decision making problems, fuzzy values are approximated by crisp data. This defuzzification leads to lo...

we present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with lr fuzzy variables. as solutions, notions of exact and approximate solutions are considered. we transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. if the corresponding crisp system is incompatible, then the fuzzy ...

We introduce the category NCSet consisting of neutrosophic crisp sets and morphisms between them. And we study NCSet in the sense of a topological universe and prove that it is Cartesian closed over Set, where Set denotes the category consisting of ordinary sets and ordinary mappings between them. 2010 AMS Classification: 03E72, 18B05

: Fried products derived from potato, particularly potato crisp have been widely included in food basket of the households in the recent years in Iran. Potato crisp, among other products, is of great importance and is considered as competitive products. This product is in the list of the food products with high acrylamide content. Therefore, due to the nutritional importance of this product and...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

This paper shows that the k-means quantization of a signal can be interpreted both as a crisp indicator function and as a fuzzy membership assignment describing fuzzy clusters and fuzzy boundaries. Combined crisp and fuzzy indicator functions are defined here as natural generalizations of the ordinary crisp and fuzzy indicator functions, respectively. An application to iris segmentation is pres...