Theory of Fuzzy Sets: The Case of Subnormality
نویسنده
چکیده
The theory of fuzzy sets with reference to subnormality needs to be properly explained. We shall in this article put forward the actual mathematical explanation of subnormal partial presence of an element in a set, better known as subnormal fuzziness. We shall first show that every law of subnormal fuzziness can be expressed in terms of two Lebesgue-Stieltjes measures. Thereafter we would define the complement of a subnormal fuzzy set in such a way that subnormal fuzzy numbers form a field.
منابع مشابه
FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES
The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...
متن کاملGeneral definitions for the union and intersection of ordered fuzzy multisets
Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...
متن کاملComprehensive analysis of a new fuzzy rule interpolation method
The first published result in fuzzy rule interpolation was the α-cut based fuzzy rule interpolation, termed as KH fuzzy rule interpolation, originally devoted for complexity reduction. Some deficiencies of this method was presented later, such as subnormal conclusion for certain configuration of the involved fuzzy sets. However, since that several conceptually different fuzzy rule interpolation...
متن کاملPOWERSET OPERATORS OF EXTENSIONAL FUZZY SETS
Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...
متن کاملPOWERSET OPERATOR FOUNDATIONS FOR CATALG FUZZY SET THEORIES
The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...
متن کامل