Fuzzy值Fuzzy测度的和与乘积的零可加与自连续性

本文讨论了Ｆｕｚｚｙδ－代数上的Ｆｕｚｚｙ值Ｆｕｚｚｙ测度的和与乘积的零可加、自连续性。     

Toward extended fuzzy logic—A first step

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.     

Associative monotonic operations in fuzzy set theory

The properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets, on fuzzy numbers and on fuzzy probabilistic sets.     

Some formal relationships among soft sets,fuzzy sets,and their extensions

We prove that every hesitant fuzzy set on a set E can be considered either a soft set over the universe $[0,1]$ or a soft set over the universe E. Concerning converse relationships, for denumerable universes we prove that any soft set can be considered even a fuzzy set. Relatedly, we demonstrate that every hesitant fuzzy soft set can be identified with a soft set, thus a formal coincidence of both notions is brought to light. Coupled with known relationships, our results prove that interval type-2 fuzzy sets and interval-valued fuzzy sets can be considered as soft sets over the universe $[0,1]$. Altogether we contribute to a more complete understanding of the relationships among various theories that capture vagueness and imprecision.     

Towards fuzzy differential calculus part 2: Integration on fuzzy intervals

The problem of integrating mappings over fuzzy domains has already received some attention in the literature. However, there is not a unique approach, but several definitions have been proposed, each carrying its own meaning. This paper tries to emphasize the relationships and the differences between the various points of view.     

A note on the article “Fuzzy alpha-sets and alpha-continuous maps”

In this note we show that some results which appeared in the article by M.K. Singal and N. Rajvanshi [Fuzzy Sets and Systems 48 (1992) 383–390] are incorrect.     

Fuzzy sets-the approximation of semisets

This paper deals with alternative set theory which substantially departs from classical set theory. The main notion of it -a semiset-is proposed to model the same intuitive notion as fuzzy set but it is more general. The reasonable tool for ‘grasping’ semisets could be provided by fuzzy sets whose applicability is beyond discussion. In the paper reasons for such an approximation are given and two ways how to provide it are proposed. The fact that the membership function is modeled within the theory should be stressed. At the end, some problems and an indication for further investigation are discussed.     

Development of an energy-emission model using fuzzy sets

In searching for cost-efficient strategies to reduce emissions from energy conversion, most western countries use energy-emission models. In these models, the whole energy conversion chain and possible future options for energy supply and emission reduction are mapped into a network of energy flows. Total discounted cost of energy supply and emission reduction is minimized under the restriction of maximum allowed emissions of SO₂, NO _x , or CO₂. The present paper extends one of these models to allow for fuzzy parameters. Such an extension appears to be useful when the data situation is weak. In this paper, a fuzzy linear program is developed, which has been applied to an energy-emission model of Lithuania.     

基于模糊集值映射的粗糙近似算子

给出基于模糊集值映射F的模糊集的下(上)近似等概念,研究F-下(上)近似算子aprF(aprF)的性质,探讨求它们的方法,得到若干结果.     

Perturbation of fuzzy sets and fuzzy reasoning based on normalized Minkowski distances

In this paper, we extend the concept of the perturbation of fuzzy sets based on normalized Minkowski distances and present some new conclusions on perturbation raised by various operations of fuzzy sets. These operations are induced by triangular norms and conorms. Furthermore, we discuss the perturbation of fuzzy reasoning.     

Convex-cone-based comparisons of and difference evaluations for fuzzy sets

Abstract

This paper focuses on how to compare two fuzzy sets and, from the viewpoint of set optimization, proposes eight types of fuzzy-set relations based on a convex cone as new comparison criteria of fuzzy sets. Then, difference evaluation functions for fuzzy sets are introduced. Under suitable assumptions of certain compactness and stability of fuzzy sets, we show that these functions correspond well to the fuzzy-set relations. In addition, through transforming these functions stepwise, we deal with numerical calculation methods of them in particular cases. Consequently, we can judge whether each fuzzy-set relation holds or not for given two fuzzy sets with the aid of computers.     

Fuzzy local ω-systems

The natural language computing today demands for the study of ω-languages. Therefore in this respect it is convenient to consider fuzzy ω-languages. In this paper, the concept of fuzzy local ω-language, Büchi fuzzy local ω-language, and some closure properties of fuzzy local ω-languages are presented. We introduce deterministic fuzzy finite automaton with different acceptance mode on fuzzy ω-languages and establish the relationship between these various classes of fuzzy ω-languages. We have defined deterministic fuzzy local automaton and also establish relationships between deterministic fuzzy local automaton, fuzzy local ω-language and Büchi fuzzy local ω-language. Further we show that every fuzzy regular ω-language is a projection of a Büchi fuzzy local ω-language.     

Maximum flow in a network with fuzzy arc capacities

Our main concern is the maximum flow in a network in which an excess over the beforehand fixed quota of arc capacity is admissible. The problem is represented as a partially fuzzy linear programming task. A theorem equivalent to the Ford and Fulkerson one concerning the classic task of maximum flow is proved in the paper. An algorithm for searching maximum flow assuming integer values of flows on network arcs is presented.     

Fuzzy importance in fault tree analysis

In fault tree analysis, system success or failure can be described by the state of the top event, which is usually defined by a so-called structure function. In this paper, we attempt to simplify the calculation process of the structure function and to newly define the state of the top event by the membership function, using fuzzy sets theory. Furthermore, it is shown that the importance of each basic event can be evaluated through fuzzy operations. The method proposed herein is demonstrated by some examples with respect to the failure analysis of structures.     

Fuzzy Closure Spaces vs. Fuzzy Rough Sets

This paper investigates the relationship among fuzzy rough sets, fuzzy closure spaces and fuzzy topology. It is shown that there exists a bijective correspondence between the set of all fuzzy reflexive approximation spaces and the set of all quasi-discrete fuzzy closure spaces satisfying a certain extra condition. Similar correspondence is also obtained between the set of all fuzzy tolerance approximation spaces and the set of all symmetric quasi-discrete fuzzy closure spaces satisfying a certain extra condition.     

The aggregation operations for decision making in probabilistic fuzzy environment

This paper deals with some important classes of aggregation operations on various kinds of sets applied to decision making problems.These operations are mainly based on general concepts such as triangular norms (t- and s-norms). In this paper we focus particularly on operations on probabilistic sets and their distribution function representation. The considerations are illustrated by means of numerical examples.