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On some methods of study of states on interval valued fuzzy sets
Notes on Intuitionistic Fuzzy Sets, 2018
In this paper the state on interval valued fuzzy sets is studied. Two methods are considered: a representation of a state by a Kolmogorov probability and an embedding to an M V-algebra. The Butnariu-Klement representation theorem for interval valued fuzzy sets as a relation between probability measure and state is presented.
Lukasiewicz Operations in Fuzzy Set and Many-Valued Representations of Quantum Logics
Found Phys, 2000
It, is shown that Birkhoff von Neumann quantum logic (i.e., an orthomodular lattice or poset) possessing an ordering set of probability measures S can be isomorphically represented as a family of fuzzy subsets of S or, equivalently, as a family of propositional functions with arguments ranging over S and belonging to the domain of infinite-valued Fukasiewicz logic. This representation endows BvN quantum logic with a new pair of partially defined binary operations, different from the order-theoretic ones: Fukasiewicz intersection and union of fuzzy sets in the first case and Fukasiewicz conjunction and disjunction in the second. Relations between old and new operations are studied and it is shown that although they coincide whenever new operations are defined, they are not identical in general. The hypothesis that quantum-logical conjunction and disjunction should be represented by Fukasiewicz operations, not by order-theoretic join and meet is formulated and some of its possible consequences are considered.
Łukasiewicz Operations in Fuzzy Set and Many-Valued Representations of Quantum Logics
2000
It, is shown that Birkhoff von Neumann quantum logic (i.e., an orthomodular lattice or poset) possessing an ordering set of probability measures S can be isomorphically represented as a family of fuzzy subsets of S or, equivalently, as a family of propositional functions with arguments ranging over S and belonging to the domain of infinite-valued Fukasiewicz logic. This representation endows BvN quantum logic with a new pair of partially defined binary operations, different from the order-theoretic ones: Fukasiewicz intersection and union of fuzzy sets in the first case and Fukasiewicz conjunction and disjunction in the second. Relations between old and new operations are studied and it is shown that although they coincide whenever new operations are defined, they are not identical in general. The hypothesis that quantum-logical conjunction and disjunction should be represented by Fukasiewicz operations, not by order-theoretic join and meet is formulated and some of its possible consequences are considered.
Algebraic properties of fuzzy sets
Journal of Mathematical Analysis and Applications, 1972
Some new algebraic properties of the class _Lp(I) of the "fuzzy sets" are stressed; in particular it is pointed out that the class of the generalized characteristic functions furnished with the lattice operations proposed by Zadeh is a Brouwerian lattice. The possibility of inducing other different lattice operations to the whole class s(I) or to a suitable subclass of it is considered. The problem of the relationship between "fuzzy sets" and classical set theory is finally remarked. A qualitative comparison with similar situations appearing in the axiomatic formulation of quantum mechanics and in the classical theory of probability is made. * This paper is a slightly revised version of the report LC50 of the Laboratorio di Cibemetica de1 C.N.R.
On algebras for interval-valued fuzzy logic
2019
This work aims to introduce other approaches to the interval-valued fuzzy logic. These new approaches were inspired by Lodwick and Chalco's works on constraint intervals. These constraint intervals were used in this thesis to extend the fuzzy operators into two modes, named Single-Level Constrained Interval Operators and Constrained Interval Operators and studied their properties. A new algebra, called SBCI algebra, which arises from the intervalization of BCI-algebras, is also introduced. These algebras aims to be the algebraic model for intervalvalued fuzzy logics, which take into account the notion of correctness. A new class of fuzzy implications, called (T, N)-implications has also been studied. The author investigated the behavior of the BCI/SBCI algebras and (T, N)-implications.
Fuzzy logical algebras and their applications
TheScientificWorldJournal, 2015
It is well known that an important task of the artificial intelligence is to make a computer simulate a human being in dealing with certainty and uncertainty in information. Logic gives a technique for laying the foundations of this task. Information processing dealing with certain information is based on the classical logic. Nonclassical logic including many-valued logic and fuzzy logic takes the advantage of the classical logic to handle information with various facets of uncertainty, such as fuzziness and randomness. Therefore, nonclassical logic has become a formal and useful tool for computer science to deal with fuzzy information and uncertain information.
Some Results on Interval-Valued Fuzzy Matrices
atlantis-press.com
In this paper, we introduced intervalvalued fuzzy matrices (IVFMs) as the generalization of interval-valued fuzzy sets. Some essential unary and binary operations of IVFM and some special types of IVFMs ie, symmetric, reflexive, transitive and idempotent, ...
Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP), 2021
In this work, we provide a study on the representability of interval-valued fuzzy connectives considering partial and admissible orders. Our approach considers those orders based on injective aggregation functions which allowed the construction of intervalvalued operators. An immediate result is the construction of the implication used in the Quantum Logic, known as QL-implication, that in our proposal is generalised for intervals, given by means of interval-valued t-(co)norms and interval-valued fuzzy negations.
Fuzzy set ideas in quantum logics
International Journal of Theoretical Physics, 1992
Fuzzy set theory language and ideas are used to express basic quantum logic notions. The possibility of replacing probabilistic interpretation of quantum mechanics by interpretation based on infinite-valued logics and fuzzy set theory is outlined. Short review of various structures encountered in the fuzzy set approach to quantum logics is given.