This paper attempts to present the new approach to design sufficient number of systematic fuzzy linguistics in matrix form and map the Fuzzy Linguistic Variable Matrix, which contains linguistic terms, into numeric domain using Fuzzy Normal Distribution based on the Parabola-based Membership Function. Existing fuzzy set theory is difficult to design the systematic and sufficient fuzzy linguisti...

Fuzzy set theory is a useful tool to describe situations in which the data are imprecise or vague. Fuzzy sets handle such situation by attributing a degree to which a certain object belongs to a set. The idea of fuzzy norm was initiated by Katsaras in [1984]. Felbin [1992] defined a fuzzy norm on a linear space whose associated fuzzy metric is of Kaleva and Seikkala type [1984]. Cheng and Morde...

Popper’s Logic of Scientific Discovery and Kuhn’s Structures of Scientific Revolutions are enormous important concepts on theories and their dynamic in 20 th century history and philosophy of science. How-ever, the works of the two have been criticized in the last half century and new views on theory nets and theory evolution appeared. In the last decades also new scientific methods and tools s...

A core tool for granular modeling is the use of linguistic rules, e.g. in fuzzy control approaches. We provide the reader with basic mathematical tools to discuss the behavior of system of such linguistic rules. These mathematical tools range from fuzzy logic and fuzzy set theory, through the consideration of fuzzy relation equations, up to discussions of interpolation strategies and to the use...

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second ...

A set $S subseteq V(G)$ is a semitotal dominating set of a graph $G$ if it is a dominating set of $G$ andevery vertex in $S$ is within distance 2 of another vertex of $S$. Thesemitotal domination number $gamma_{t2}(G)$ is the minimumcardinality of a semitotal dominating set of $G$.We show that the semitotal domination problem isAPX-complete for bounded-degree graphs, and the semitotal dominatio...

With the arrival of the information age, information acquisition and communication have become more and more important in the field of information technology. This paper uses the concept of homomorphism as a basic tool to study the communication between fuzzy information systems. The concepts of consistent and compatible mappings with respect to fuzzy sets are firstly defined and their basic pr...

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...

Dealing with notions of health, illness and disease contains dealing with fuzziness. As the paper will demonstrate, states of these notions do not only exist or not exist. The medical philosopher and physician SadeghZadeh introduced the notions of fuzzy health, fuzzy illness and fuzzy disease. A closer look will be taken on the concept of fuzzy disease. Because there are different possibilities...

Multisets alias bags are similar to fuzzy sets but essentially different in basic concepts and operations. We overview multisets together with basics of fuzzy sets in order to observe differences between the two. We then introduce fuzzy multisets and the combination of the both concepts. There is another concept of real-valued multisets as a generalization of multisets. Rough approximations of ...