Search results for "Fuzzy Logic."

JH-Operators and Occasionally Weakly g-Biased Pairs in Fuzzy Symmetric Spaces

2013

We introduce the notions of $\mathcal{JH}$-operators and occasionally weakly $g$-biased mappings in fuzzy symmetric spaces to prove common fixed point theorems for self-mappings satisfying a generalized mixed contractive condition. We also prove analogous results for two pairs of $\mathcal{JH}$-operators by assuming symmetry only on the set of points of coincidence. These results unify, extend and complement many results existing in the recent literature. We give also an application of our results to product spaces.

Quantum Finite Automata and Logics

2006

The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindstrom quantifier is shown.

Extremal problems of approximation theory in fuzzy context

1999

Abstract The problem of approximation of a fuzzy subset of a normed space is considered. We study the error of approximation, which in this case is characterized by an L -fuzzy number. In order to do this we define the supremum of an L -fuzzy set of real numbers as well as the supremum and the infimum of a crisp set of L -fuzzy numbers. The introduced concepts allow us to investigate the best approximation and the optimal linear approximation. In particular, we consider approximation of a fuzzy subset in the space L p m of differentiable functions in the L q -metric. We prove the fuzzy counterparts of duality theorems, which in crisp case allows effectively to solve extremal problems of the…

Conditioning for Boolean Subsets, Indicator Functions and Fuzzy Subsets

2016

This chapter deals with measure-free conditioning. It starts with the mean value based definition of conditional fuzzy subsets which again gives a fuzzy subset. Applying this general construction to indicator functions, it is proved that these conditionals form an MV-algebra and that this is isomorphic to the already known MV-algebra of the interval based conditional Boolean subsets. In the following, the problem of iteration is completely solved with the result that there are exactly two types of iteration, called the blurred resp. the sharper one, which remain in the corresponding MV-algebras. Moreover, the general concept of conditional operators plays a significant role. Finally, the pr…

On another approach to the definition of an L-fuzzy valued integral

2011

We continue to develop a construction of an L-fuzzy valued measure extending a crisp measure defined on a σ-algebra of crisp sets to an L-fuzzy valued measure defined on a T M -tribe. We describe two equivalent approaches to define an L-fuzzy valued integral of non-negative measurable functions.

Upper and lower general aggregation operators based on a strong fuzzy metric

2018

L-fuzzy syntopogenous structures, Part I: Fundamentals and application to L-fuzzy topologies, L-fuzzy proximities and L-fuzzy uniformities

2013

Abstract We introduce the concept of an L-fuzzy syntopogenous structure where L is a complete lattice endowed with an implicator ↦ : L × L → L satisfying certain properties (in particular, as L one can take an MV-algebra). As special cases our L-fuzzy syntopogenous structures contain classical Csaszar syntopogenous structures, Katsaras–Petalas fuzzy syntopogenous structures as well as fuzzy syntopogeneous structures introduced in the previous work of the second named author (A. Sostak, Fuzzy syntopogenous structures, Quaest. Math. 20 (1997) 431–461). Basic properties of the category of L-fuzzy syntopogenous spaces are studied; categories of L-fuzzy topological spaces, L-fuzzy proximity spac…

A Decomposition Theorem for the Fuzzy Henstock Integral

2012

We study the fuzzy Henstock and the fuzzy McShane integrals for fuzzy-number valued functions. The main purpose of this paper is to establish the following decomposition theorem: a fuzzy-number valued function is fuzzy Henstock integrable if and only if it can be represented as a sum of a fuzzy McShane integrable fuzzy-number valued function and of a fuzzy Henstock integrable fuzzy number valued function generated by a Henstock integrable function.

Some dissenting views on the transitivity of individual preference

1990

(1) The transitivity property is not a necessary condition for the rationality of all individual preference relations. (2) A weakened definition of the transitivity is not necessarily relevant. (3) The non-transitivity of fuzzy preference relations is not inconsistent with a fuzzy total preorder structure on the set of alternatives.

Ranking fuzzy interval numbers in the setting of random sets – further results

1999

Abstract We present some new properties of several fuzzy order relations, defined on the set of fuzzy numbers, from among those introduced in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217]. The main result is proving that four from among the relations considered in [S. Chanas, M. Delgado, J.L. Verdegay, M.A. Vila, Information Sciences 69 (1993) 201–217] are strongly transitive (s-transitive).