With the emergence of the fundamental paper [5] by Zadeh in 1965 number of papers have appeared in literature featuring the application of fuzzy sets to pattern recognition, decision problems, function approximation, system theory, fuzzy logic, fuzzy algorithms, fuzzy automata, fuzzy grammars, fuzzy languages, fuzzy algebras, fuzzy topology, etc. [2], [7]. In this note, our interests are in the...

John Yen l;sc 1 Information Sciences Institute 46i6 Admiralty Way l\Iarina del Rey. CA. 90292 Dempster's rule of combination has been the most controversial part of the Dempster-Shafer (D-S) theory. In particular, Zadeh has reached a conjecture on the noncombinability of evidence from a relational model of the D-S theory. In this paper. we will describe another relational model where D-S masses...

We study graded properties (α–properties) of fuzzy relations, which are parameterized versions of fuzzy relation properties defined by L.A. Zadeh. Namely, we take into account fuzzy relations which are: α–reflexive, α– irreflexive, α–symmetric, α–antisymmetric, α–asymmetric, α–connected, α–transitive, where α ∈ [0, 1]. We also pay our attention to the composed versions of these basic properties...

Gilles CHAMPENOIS Collège Saint-André, Saint-Maur, France [email protected] ABSTRACT. A fuzzy mnesor space is a semimodule over the positive real numbers. It can be used as theoretical framework for fuzzy sets. Hence we can prove a great number of properties for fuzzy sets without refering to the membership functions. "Classical logic has erred in devoting so little attention to approx...

Based on the in-depth analysis of the essence and features of vague phenomena, this paper focuses on establishing the axiomatical foundation of membership degree theory for vague phenomena, presents an axiomatic system to govern membership degrees and their interconnections. On this basis, the concept of vague partition is introduced, further, the concept of fuzzy set introduced by Zadeh in 196...

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...

The problem of converting possibility measures into probability measures has received attention in the past, but not by so many scholars. This question is philosophically interesting as part of the debate between probability and fuzzy sets. The imbedding of fuzzy sets into random set theory as done by Goodman and Nguyen (1985), Wang Peizhuang (1983), among others, has solved this question in pr...

We contribute to the theory of implications and conjunctions related by adjointness, in multiple-valued logics. We suggest their use in Zadeh s compositional rule of inference, to interpret generalized modus ponens inference schemata. We provide new complete characterizations of implications that distinguish left arguments, implications that satisfy the exchange principle, divisible conjunction...

A fuzzy control system which is a typical system utilizing fuzzy model is mainly using the Max-Min CRI (Compositional Rule of Inference) method by Zadeh and Mamdani for fuzzy inference. But the Max-Min CRI method suffers from drawbacks including: error-prone weighting strategy, inefficient compositional rule of inference, and subjective formulation of membership functions. Because of these prob...

We consider equations of Müller–Israel–Stewart type describing a relativistic viscous fluid with bulk viscosity in four-dimensional Minkowski space. show that there exists class smooth initial data are localized perturbations constant states for which the corresponding unique solutions to Cauchy problem break down finite time. Specifically, we prove time such develop singularity or become unphy...