22 research outputs found
Bi-ideals of ordered semigroups based on the interval-valued fuzzy point
Interval-valued fuzzy set theory (advanced generalization of Zadeh’s fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, we introduce the notion of generalized quasi-coincident with (q(Formula Presented)) relation of an interval-valued fuzzy point with an interval-valued fuzzy set. In fact, this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. Applying this newly defined idea, the notion of an interval-valued (∈,∈vq(Formula Presented)) -fuzzy bi-ideal is introduced. Moreover, some characterizations of interval-valued (∈,∈vq(Formula Presented)) -fuzzy bi-ideals are described. It is shown that an interval-valued (∈,∈vq(Formula Presented)) -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. Finally, the concept of implication-based interval-valued fuzzy bi-ideals, characterizations of an interval-valued fuzzy bi-ideal and an interval-valued (∈,∈vq(Formula Presented)) - fuzzy bi-ideal are considered
Semantics of fuzzy quantifiers
The aim of this thesis is to discuss the semantics of FQs (fuzzy quantifiers),
formal semantics in particular. The approach used is fuzzy semantic based
on fuzzy set theory (Zadeh 1965, 1975), i.e. we explore primarily the denotational
meaning of FQs represented by membership functions. Some empirical
data from both Chinese and English is used for illustration.
A distinguishing characteristic of the semantics of FQs like about 200 students and many students as opposed to other sorts of quantifiers like every
student and no students, is that they have fuzzy meaning boundaries. There
is considerable evidence to suggest that the doctrine that a proposition is either true or false has a limited application in natural languages, which raises
a serious question towards any linguistic theories that are based on a binary
assumption. In other words, the number of elements in a domain that must
satisfy a predicate is not precisety given by an FQ and so a proposition con¬
taining one may be more or less true depending on how closely numbers of
elements approximate to a given norm.
The most significant conclusion drawn here is that FQs are compositional in
that FQs of the same type function in the same way to generate a constant
semantic pattern. It is argued that although basic membership functions are
subject to modification depending on context, they vary only with certain
limits (i.e. FQs are motivated—neither completely predicated nor completely
arbitrary), which does not deny compositionality in any way. A distinctive
combination of compositionality and motivation of FQs makes my formal
semantic framework of FQs unique in the way that although some specific
values, such as a norm, have to be determined pragmatically, semantic and
inferential patterns are systematic and predictable.
A number of interdisciplinary implications, such as semantic, general linguistic, logic and psychological, are discussed. The study here seems to be
a somewhat troublesome but potentially important area for developing theories (and machines) capable of dealing with, and accounting for, natural
languages
Fuzzy Multiattribute Utility Analysis for Collective Choice
An extension of multiattribute utility analysis for the multiple-agents decision problem is presented. Although multiattribute utility analysis is concerned with decisionmaking under uncertainty, assessment of parameters of the multiattribute utility functions is actually performed deterministically by the single decisionmaker. This paper is concerned with fuzzy evaluation of the multiattribute utility function, which is based on a fuzzy preference ordering and scaling constants using membership functions of the fuzzy set theory. The fuzzy approach treats a conceptual imprecision that accrues from a multiplicity of evaluation. A fuzzy multiattribute utility function with multiple-agents evaluation is derived. A computer package ICOPSS/FR for assuring the transitivity of collective preference ordering in an agreement level is demonstrated for assessment of the fuzzy multiattribute utility functions