Lech Schulz Department of Chemistry, Adam Mickiewicz University Poznan, Poland A preliminary notion of a complex system is regarded as a collection consisting of more elementary components such that they constitute a unified species with an increased complexity [1]. This concept comes from the contraposition of the whole and its elements. Constituting the whole members of a complex collection c...

using the notion of “belongingness ($epsilon$)” and “quasi-coincidence (q)” of fuzzy points with fuzzy sets, we introduce the concept of an ($ alpha, beta$)- fuzzyhv-ideal of an hv-ring, where , are any two of {$epsilon$, q,$epsilon$ $vee$ q, $epsilon$ $wedge$ q} with $ alpha$ $neq$ $epsilon$ $wedge$ q. since the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy hv-ideals is an important and ...

In many real decision situations, for each of the alternatives, we only have fuzzy information about the consequences of each action. This fuzzy information can be described by a fuzzy number, i.e., by a membership function with a single local maximum, or it can be described by a more complex fuzzy set, with several local maxima. We show that, from the viewpoint of decision making, it is suffic...

module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

Abshocr-Fuzzy modeling of complex systems is a challenging topic. This paper proposes an effective approach to data-based fuzzy optimizing fuzzy system structure and parameters. For this purpose, we cope with fuzzy clustering based on inclusion concept where the rule-base bas to be simplified. This simplification occurs in the sense that similar Membership Functions (MF) pertaining to the premi...