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KINEMATIC AND KINETIC ANALYSIS OF THE 30-S CHAIR STAND TEST WITH A TRI-AXIAL INERTIAL MAGNETIC SENSOR
Abstract
This paper provides a generalization of known results about fuzzy finite state machines, fuzzy transformation semigroups and their relationship by broading the truth values domain from the interval [0,1] to a complete lattice endowed with a t-norm and a t-conorm. So, we deal with the concepts of L-fuzzy finite state machines and L-fuzzy transformation semigroups and we prove that the cited generalization is possible if and only if the t-norm and the t-conorm satisfy a distributive property. If we consider the complete lattice of the closed intervals inside the original lattice L, we give methods to obtain an interval lattice-valued finite state machine and an interval lattice-valued transformation semigroup from two L-fuzzy finite state machines or two L-fuzzy transformation semigroups, respectively. Conversely, we show two different ways to build a faithful L-fuzzy transformation semigroup from an interval lattice-valued state machine. In fact, both methods give the same result.
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July 2015
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The existence of isomorphism between the category of fuzzy automata and the category of chains of non-deterministic automata
is proved and some relationships between output fuzzy sets of these systems are investigated.
Uninorms are an important generalization of triangular norms and conorms, having a neutral element lying anywhere in the unit interval. In this paper we introduce the notion of uninorm in interval-valued fuzzy set theory, or equivalently in intuitionistic fuzzy set theory in the sense of Atanassov, and investigate its properties.
A generalization of the notion of intuitionistic fuzzy set is given in the spirit of ordinary interval valued fuzzy sets. The new notion is called interval valued intuitionistic fuzzy set (IVIFS). Here we present the basic preliminaries of IVIFS theory.
Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued "intuitionistic" sets, "intuitionistic" fuzzy sets and topologies Abstract This paper demonstrates two meta-mathematical propositions concerning the increasingly popular "intuitionistic" (= vague) approaches to fuzzy sets and fuzzy topology, as well as the closely related interval-valued (= grey) sets and interval-valued "intuitionistic" sets: (1) the term "intuitionistic" in these contexts is historically inappropriate given the standard mathematical usage of "intuitionistic"; and (2), at every level of existence—powerset level, topo-logical fibre level, categorical level—interval-valued sets, interval-valued "intuitionistic" sets, and "intuitionistic" fuzzy sets and fuzzy topologies are redundant and represent unnecessarily complicated, strictly special subcases of standard fixed-basis set theory and topology. It therefore follows that theoretical workers should stop working in these restrictive and complicated programs and instead turn their efforts to substantial problems in the simpler and more general fixed-basis and variable-basis set theory and topology, while applied workers should carefully document the need or appropriateness of interval-valued or "intuitionistic" notions in applications.
In this paper we prove that, under suitable conditions, Atanassov’s Kα operators, which act on intervals, provide the same numerical results as OWA operators of dimension two. On one hand, this allows us to recover OWA operators from Kα operators. On the other hand, by analyzing the properties of Atanassov’s operators, we can generalize them. In this way, we introduce a class of aggregation functions – the generalized Atanassov operators – that, in particular, include two-dimensional OWA operators. We investigate under which conditions these generalized Atanassov operators satisfy some properties usually required for aggregation functions, such as bisymmetry, strictness, monotonicity, etc. We also show that if we apply these aggregation functions to interval-valued fuzzy sets, we obtain an ordered family of fuzzy sets.
In this paper, we study in-depth certain properties of interval-valued fuzzy sets and Atanassov's intuitionistic fuzzy sets (A-IFSs). In particular, we study the manner in which to construct different interval-valued fuzzy connectives (or Atanassov's intuitionistic fuzzy connectives) starting from an operator. We further study the law of contradiction and the law of excluded middle for these sets. Furthermore, we analyze the following properties: idempotency, absorption, and distributiveness. We conclude relating idempotency with the capacity that some of the connectives studied have for maintaining, in certain conditions, the amplitude (or Atanassov's intuitionistic index) of the intervals on which they act. © 2008 Wiley Periodicals, Inc.
Intuitionistic fuzzy sets [K.T. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia (deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84), 1983 (in Bulgarian)] are an extension of fuzzy set theory in which not only a membership degree is given, but also a non-membership degree, which is more or less independent. Considering the increasing interest in intuitionistic fuzzy sets, it is useful to determine the position of intuitionistic fuzzy set theory in the framework of the different theories modelling imprecision. In this paper we discuss the mathematical relationship between intuitionistic fuzzy sets and other models of imprecision.
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The idea of (faithful) intuitionistic fuzzy transformation semigroup, intuitionistic admissible relation, and intuitionistic (strong) homomorphism are introduced and their basic properties are examined.
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In this paper the Archimedean prop- erty and the nilpotency of t-norms on the lattice LI is investigated, where LI is the underlying lattice of interval-valued fuzzy set theory (Sam- buc, 1975) and intuitionistic fuzzy set theory (Atanassov, 1983). We give some characterizations of contin- uous t-norms on LI which satisfy the residuation principle, T (D,D) ⊆ D, the Archimedean property and nilpo- tency. Keywords: interval-valued fuzzy set, intuitionistic fuzzy set, t- norm, Archimedean, nilpotent, strict, representation.
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