Hedge algebras: An algebraic approach to structure of sets of linguistic truth values

Fuzzy Sets and SystemsPublished 1 May 1990

Nguyễn Cát Hồ, Wolfgang Wechler

DOI10.1016/0165-0114(90)90002-n

Source URL

Citations212

SJR quartileQ1

SJR score0.75

SNIP1.25

Abstract

It is shown that any sets of linguistic values of linguistic variables can be axiomatized, which leads to a notion of hedge algebras. Some intuitive properties of linguistic hedges, which are a basis of the axiomatization of the hedge algebras, are discussed informally. The characteristics of the hedge algebras depend on such a discussion and they seem to reflect the natural structure of sets of linguistic values of linguistic variables. Some fundamental properties of hedge algebras are examined. They constitute a foundation of further development of our theory of hedge algebras and of some kind of fuzzy logic.

Keywords

Computer ScienceDecision Sciences

Information SciencesThe concept of a linguistic variable and its application to approximate reasoning-III

12,148 Citations1975L. A. Zadeh

Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.

Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—I

12,036 Citations1975Lotfi A. Zadeh

It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc.

Information SciencesThe concept of a linguistic variable and its application to approximate reasoning—II

2,509 Citations1975Lotfi A. Zadeh

The nonrestricted nonfuzzy variable u constitutes the base variable for X and R(X;u) is a fuzzy subset of U which represents a fuzzy restriction on the values of u imposed by X.

SyntheseFuzzy logic and approximate reasoning

1,598 Citations1975Lotfi A. Zadeh

F fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc.

Hedges: A Study in Meaning Criteria and the Logic of Fuzzy Concepts

1,579 Citations1975George Lakoff

Journal of CyberneticsA Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges

1,022 Citations1972L. A. Zadeh

A basic idea suggested in this paper is that a linguistic hedge such as very, more or less, much, essentially, etc. may be viewed as an operator which acts on the fuzzy set representing the meaning of its operand.

International Journal of Man-Machine StudiesŁukasiewicz logic and fuzzy set theory

246 Citations1976R. G. F. GILES

A new form of logic is described, originally developed for the formalization of physical theories, the essential feature being a “fuzzification” of the concept of a proposition, which corresponds closely to the infinitevalued logic Ł α, of Łukasiewicz.

International Journal of Approximate ReasoningImplication in fuzzy logic

236 Citations1987Philippe Smets, Paul Magrez

Fuzzy Sets and SystemsOn many-valued logics, fuzzy sets, fuzzy logics and their applications

43 Citations1978Heinz J. Skala

A survey of some aspects of many-valued logics and the theory of fuzzy sets and fuzzy reasoning, as advocated in particular by Zadeh, and shows that their definition is sound if some acceptable rationality requirements are demanded.