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1.
S.E. Rodabaugh 《Fuzzy Sets and Systems》1982,8(1):39-52
Under the hypothesis L is a chain, we construct a binary operation ⊕ on the L-fuzzy real line (L) which reduces to the usual addition on if ⊕ is restricted to the embedded image of in (L), which yields a partially ordered, abelian cancellation semigroup with identity, and which is jointly fuzzy continuous on (L). We show ⊕ is unique, i.e. it is the only extension of addition to (L) which is consistent. We study the relationship between ⊕ and other fuzzy continuous extensions of the usual addition. We also show that fuzzy translation is a weak fuzzy homeomorphism and, under certain conditions, a fuzzy homeomorphism. 相似文献
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In this study, by the use of Yuan and Lee’s definition of the fuzzy group based on fuzzy binary operation we give a new kind
of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical
study their basic properties analogous to those of ordinary rings.
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Michael Smithson 《Fuzzy Sets and Systems》1984,14(1):1-3
Linear programming problems with fuzzy parameters are formulated by fuzzy functions. The ambiguity considered here is not randomness, but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership. Parameters on constraint and objective functions are given by fuzzy numbers. In this paper, our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters. This fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential. 相似文献
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定义了n维模糊向量的模糊距离、n维模糊度量空间及其完备性的概念,实现了用R上的模糊数度量模糊向量间距离的目的,不仅使得模糊距离的度量更加合理、更加贴切,也创立一套独立于实数的模糊数学分析理论打下了基础。 相似文献
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Fuzzy logic adds to bivalent logic an important capability—a capability to reason precisely with imperfect information. Imperfect information is information which in one or more respects is imprecise, uncertain, incomplete, unreliable, vague or partially true. In fuzzy logic, results of reasoning are expected to be provably valid, or p-valid for short. Extended fuzzy logic adds an equally important capability—a capability to reason imprecisely with imperfect information. This capability comes into play when precise reasoning is infeasible, excessively costly or unneeded. In extended fuzzy logic, p-validity of results is desirable but not required. What is admissible is a mode of reasoning which is fuzzily valid, or f-valid for short. Actually, much of everyday human reasoning is f-valid reasoning.f-Valid reasoning falls within the province of what may be called unprecisiated fuzzy logic, FLu. FLu is the logic which underlies what is referred to as f-geometry. In f-geometry, geometric figures are drawn by hand with a spray pen—a miniaturized spray can. In Euclidean geometry, a crisp concept, C, corresponds to a fuzzy concept, f-C, in f-geometry. f-C is referred to as an f-transform of C, with C serving as the prototype of f-C. f-C may be interpreted as the result of execution of the instructions: Draw C by hand with a spray pen. Thus, in f-geometry we have f-points, f-lines, f-triangles, f-circles, etc. In addition, we have f-transforms of higher-level concepts: f-parallel, f-similar, f-axiom, f-definition, f-theorem, etc. In f-geometry, p-valid reasoning does not apply. Basically, f-geometry may be viewed as an f-transform of Euclidean geometry.What is important to note is that f-valid reasoning based on a realistic model may be more useful than p-valid reasoning based on an unrealistic model. 相似文献
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A.A.Salama 《模糊系统与数学》2010,24(2)
Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have been introduced to fuzzy topological spaces in the last twenty years but not have been studied using fuzzy ideals so,the main aim of our work in this paper is to define and study some new various types of fuzzy compactness with respect to fuzzy ideals namely fuzzy L-compact and L*-compact spaces. Also fuzzy compactness with respect to ideal is useful as unification and generalization of several others widely studied concepts. Possible application to superstrings and E∞ space-time are touched upon. 相似文献
8.
Walenty Ostasiewicz 《Fuzzy Sets and Systems》1982,7(2):139-152
A fuzzy program is defined in the usual way as a sequence of statements (instruction) which are considered as functions (possibly fuzzy functions) and fuzzy predicates defined on the given input domain. The essential difference in the approach presented in this paper is the new interpretation of the execution of fuzzy programs, and a new method of evaluating fuzzy predicates. The result of the fuzzy program execution is an appropriate fuzzy subset in the output domain. 相似文献
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A bi-matrix game with fuzzy goal is shown to be equivalent to a (crisp) non-linear programming problem in which the objective as well as all constraint functions are linear except two constraint functions, which are quadratic. This equivalence is further extended to bi-matrix games with fuzzy pay-offs, as well as to bi-matrix games with fuzzy goals and fuzzy payoffs, whose equilibrium strategies are conceptualized by employing a suitable ranking (defuzzification) function. 相似文献
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I.M. Hanafy 《Fuzzy Sets and Systems》1997,90(3):365-353
The aim of this paper is devoted to make use of operations on IX of a fuzzy topological space X to unify and generalize classes of strong forms of fuzzy complete continuity. Furthermore, we add more types of strong forms of fuzzy completely continuous functions by choosing special operations. A comparison between these types of functions is of interest. Preservations of some fuzzy aspects under these functions are studied. 相似文献
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Our main objective is to study properties of a fuzzy ideals(fuzzy dual ideals).A study of special types of fuzzy ideals(fuzzy dual ideals) is also furnished.Some properties of a fuzzy ideals(fuzzy dual ideals) are furnished.Properties of a fuzzy lattice homomorphism are discussed.Fuzzy ideal lattice of a fuzzy lattice is defined and discussed.Some results in fuzzy distributive lattice are proved. 相似文献
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本文指出了以往的一些错误,同时给出了一个新定理,从而得到了严格的理论依据;构造了一种较新的直接聚类法。 相似文献
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Gunther Jäger 《Fuzzy Sets and Systems》1997,90(3):737-348
Lowen and Lowen [Applications of category theory to fuzzy subsets (Kluwer, 1992) p. 153] and Lowen et al. [Fuzzy Sets and Systems 40 (1991) 347] recently introduced the category FCS of fuzzy convergence spaces, a topological quasitopos which is a supercategory of FTS, the category of fuzzy topological spaces. In this paper, compactness in FCS is examined. Doing so we found that to define compactness as an absolute property we had to generalize the definition of fuzzy convergence space to fuzzy subsets. All basic theorems are proved including the Tychonoff product theorem. Based on the theory developed here, in a following publication, a Richardson compactification for fuzzy convergence spaces will be given. 相似文献
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给出模糊半群上的模糊同余的概念,并进一步研究它的一些基本代数性质。同时研究带有模糊半群上的模糊同余扩张性质(FCEPF)的半群类,得到一个半群有模糊半群上的模糊同余扩张性质、有模糊同余扩张性质(FCEP)、有同余扩张性质(CEP)三个条件是等价的。 相似文献