Inverse Fuzzy Research Articles

Fuzzy transforms: Theory and applications

The technique of direct and inverse fuzzy (F-)transforms of three different types is introduced and approximating properties of the inverse F-transforms are described. All three types of the direct F-transform are transformations from a function space to a finite dimensional vector space. The first (ordinary) F-transform is constructed on the basis of the ordinary algebra of reals, while the other two types of the F-transform are constructed on the basis of residuated lattice. The core idea of the technique of F-transforms is a fuzzy partition of a universe into fuzzy subsets (factors, clusters, granules etc.). We claim that for a sufficient representation of a function defined on this universe, we may consider its average values over fuzzy subsets from the partition. Thus, a function can be associated with a mapping from a set of fuzzy subsets to the set of its thus obtained average values. A number of theorems establishing best approximation properties of the inverse F-transforms are proved. In fact, three types of the inverse F-transform are the best approximations in average, from below, and from above respectively. As one of many possible applications, we present a method of image compression and reconstruction on the basis of the F-transform.

Is the class of all fuzzy rings a fuzzy HSP-class?

The aim of this paper is to generalize, the notion of fuzzy subring of a crisp ring to that of a fuzzy ring and the notion of crisp homomorphism between crisp rings with fuzzy direct image and fuzzy inverse image to that of a fuzzy homomorphism between fuzzy rings with truth values in different complete lattices, with fuzzy direct and inverse images, in such a way that the class of all fuzzy rings is in fact a fuzzy HSP-Class. In the process several elementary but important properties that naturally extended, are recorded including Correspondence and Isomorphism Theorems.

Fuzzy control of a three-tank system

Fuzzy inverse reasoning performed using fuzzy relational equations can be employed to deduce control actions appropriate for a desired process output. The three-tank plant to be controlled has two inputs and hence the fuzzy relational equation describing the dynamics of the plant is a two-decision variable equation. Algorithms are only available for solving equations that have a single decision variable. A method is proposed in this paper to decompose the two-decision-variable fuzzy relational equation into single-decision-variable equations so that existing algorithms can be applied to produce control actions for the plant.

ニューラルネットで統合するファジィ逆推論を用いた自動車デザイン支援システム

デザイナーの負担を軽減し, さらにデザイナーの発想を刺激するため, いろいろな造形支援システムが研究されている.システムはデザイナーの思考過程をモデル化し, そのモデルを用いて推論する.しかし往々にしてこれらのシステムはつぎの二つの問題を含むことが多い.すなわち, 1)変数に計測尺度と感覚尺度が混在する, 2)推論過程がデザイナーの思考のような柔軟性に欠ける.これらの問題に対して, 筆者らは本研究において, 1)造形対象の形態要素に関する計測尺度変数をファジィ集合によって感覚尺度化, 2)推論過程にファジィ逆推論を利用して造形解に幅をもたせた柔軟なモデルを提案する.さらに, デザイン問題の性質としてのファジィ関係式のあいまい性を包括するために, ニューラルネットワークモデルによる推論をシステムに導入する.本研究では自動車の外観イメージからスタイルの造形解を求める過程を事例に選んで造形支援システムを構築し, 実際のデータを使ってモデルの有効性を確かめた.

ファジィ関係逆問題における解の存在性判別

ファジィ関係逆問題における解の存在性判別