Fuzzy Symmetric Functions with Don't‐care Conditions and Applications

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Line-oriented two-dimensional grammars (LOTDGs), region-oriented two-dimensional grammars (ROTDGs) and parallel productions are introduced. The relationships between LOTDGs and ROTDGs are stated. Examples of LOTDGS for generating all possible 458 rightangled triangles, all possible squares, all possible 458 isosceles trapezoids, and all possible 458 parallelograms using parallel productions are presented. A new concise representation of a derivation chain is also introduced and illustrated by examples. LOTDGs and ROTDGs are compared. Generally speaking, LOTDGs require less terminal variables and non-terminal variables, require less storage space, and require less derivation steps. Seven challenging problems for future research are also included. In addition, parallel production is an effective tool to model parallel computers as well as parallel processing. The results have useful applications in robot vision interpretation, robot pictorial communication, artificial intelligence, visual languages, software engineering, medical expert systems, and fuzzy logic functions.

Section: Discussionmentioning

confidence: 81%

Line‐oriented two‐dimensional parallel computer languages

Lee

2002

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“…For example, if the max-product rule is used, the optimum solution may not be the same. The invariance property may have useful applications in fuzzy languages [8] and fuzzy logics [18,19] in term of saving computation time. It is particularly useful in real time and large scale system applications.…”

Section: Discussionmentioning

confidence: 99%

The invariance of optimum solution in a multi‐objective fuzzy environment

Zhang

Chung²,

Lee³

1996

Defines the order preservation and operator uniqueness assumption and the active assumption. Under these assumptions, presents the invariance of optimum solution in a multi‐objective fuzzy environment and gives illustrative examples. Presents applications, including in the heat transfer area, illustrated by numerical results and three dimensional figures. The results may have useful applications in fuzzy languages, fuzzy logics and other related areas.

“…Fuzzy logic functions (Dickerson and Kosko, 1993a, b, 1996; Lee, 1993; Lee and Chou, 1995, 2001) have attracted growing attention as promising avenues in fuzzy engineering (Kosko, 1997) and other related areas. More specifically, fuzzy monotone functions (Lee and Chou, 2001), fuzzy threshold functions (Lee and Chou, 1995) fuzzy symmetric functions (Lee, 1993) have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy symmetric threshold functions and applications

Lee

2003

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A fuzzy symmetric threshold (ST) function is defined to be a fuzzy set over the set of functions. All ST functions have full memberships in this fuzzy set. For n variables, there are (2n+2) ST functions. A distance measure between a nonsymmetric threshold function and the set of all ST functions is defined and investigated. An explicit expression for the membership function of a fuzzy ST function is defined through the use of this distance measure. An algorithm for obtaining this distance measure is presented with illustrative examples. It is also shown that any function and its complement always have the same grade of membership in the class of fuzzy ST functions. Applications to concise function representation and simple function implementation are also presented with examples. In addition, most inseparable unsymmetric functions are defined and investigated. Fuzzy ST functions are relevant to the development of practical applications of fuzzy methods and might contribute to the state of the art in the implementations of fuzzy methods in the areas requiring utilization of ST functions.