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...

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...

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 ...

Environmental impact assessment (EIA) is the assessment of the possible impact that a proposed plan or project may have on the environment, together consisting of the natural, social and economic aspects. The aim of this paper is to propose an environmental impact assessment methodology based on an integrated fuzzy AHP–ELECTRE approach in the context of urban industrial planning. In the propose...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...