The fuzzy decision problem: An approach to the point estimation problem with fuzzy information

This paper is devoted to the extension of the Bayesian method for the point estimation, when the available information is ‘vague’.In the nonfuzzy case, the parametric estimation can be approached as a particularization in the statistical decision problem. This motivates us to accomplish the mentioned extension by looking at the parametric estimation in the fuzzy case as a special situation in the fuzzy decision problem (defined by Tanaka, Okuda and Asia).In this way, concepts in the fuzzy decision problem are first ‘expressed’ in the estimation terminology. Then, on the basis of these concepts, we shall introduce some notions and state some interesting results. Finally, several illustrative examples will be exposed.     

Fuzzy群的半格

引入 Fuzzy群的半格的概念 ,并讨论它们的一些代数性质。同时利用 Fuzzy理想对 Fuzzy群的半格作了一些等价刻画。     

Possibilistic bottleneck combinatorial optimization problems with ill-known weights

In this paper a general bottleneck combinatorial optimization problem with uncertain element weights modeled by fuzzy intervals is considered. A possibilistic formalization of the problem and solution concepts in this setting, which lead to compute robust solutions under fuzzy weights, are given. Some algorithms for finding a solution according to the introduced concepts and evaluating optimality of solutions and elements are provided. These algorithms are polynomial for bottleneck combinatorial optimization problems with uncertain element weights, if their deterministic counterparts are polynomially solvable.     

A fuzzy closeness approach to fuzzy multi-attribute decision making

The aim of this paper is to develop a new fuzzy closeness (FC) methodology for multi-attribute decision making (MADM) in fuzzy environments, which is an important research field in decision science and operations research. The TOPSIS method based on an aggregating function representing “closeness to the ideal solution” is one of the well-known MADM methods. However, while the highest ranked alternative by the TOPSIS method is the best in terms of its ranking index, this does not mean that it is always the closest to the ideal solution. Furthermore, the TOPSIS method presumes crisp data while fuzziness is inherent in decision data and decision making processes, so that fuzzy ratings using linguistic variables are better suited for assessing decision alternatives. In this paper, a new FC method for MADM under fuzzy environments is developed by introducing a multi-attribute ranking index based on the particular measure of closeness to the ideal solution, which is developed from the fuzzy weighted Minkowski distance used as an aggregating function in a compromise programming method. The FC method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum individual regret for the “opponent”. A real example of a personnel selection problem is examined to demonstrate the implementation process of the method proposed in this paper.     

The Arrow paradox with fuzzy preferences

This note considers a new factorization of a fuzzy weak binary preference relation into its asymmetric and symmetric parts. Arrow’s General Possibility Theorem is then examined within the resulting framework of vague individual and social preferences. The outcome of this exercise is compared with some earlier results available in the literature on the Arrow paradox with fuzzy preferences.     

Convex fuzzy sets

This paper gathers some elementary known results about convex fuzzy sets and completes the theory, introducing the necessary concepts. Using a representation theorem for fuzzy subspaces it gives separation theorems for convex fuzzy sets in the proper setting.     

An identification algorithm in fuzzy relational systems

The paper presents an effective identification method in fuzzy relational systems. We propose an algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques. The usefulness of the method provided is demonstrated by means of two numerical examples. Also a possible way of generating a linguistic decision-making algorithm is discussed.     

模糊商群的推广

引入关于一个子群的正规模糊子集概念，研究正规模糊子集的一些性质，并在此基础上将模糊商群做了自然推广，最后建立群同态下正规模糊子集的对应定理。     

Fuzzy preference orderings in group decision making

In this paper, some use of fuzzy preference orderings in group decision making is discussed. First, fuzzy preference orderings are defined as fuzzy binary relations satisfying reciprocity and max-min transitivity. Then, particularly in the case where individual preferences are represented by utility functions (utility values), group fuzzy preference orderings of which fuzziness is caused by differences or diversity of individual opinions are defined. Those orderings might be useful for proceeding the group decision making process smoothly, in the same manner as the extended contributive rule method.     

关于具有Fuzzy约束的Fuzzy多目标规划非控解的存在性

本文对具有Fuzzy约束集的Fuzzy多目标规划引进Fuzzy非控点和Fuzzy非控解的概念,讨论了它们的一些基本性质和存在性。     

Fuzzy带算子环和Fuzzy带算理想

提出Fuzzy带算子环、Fuzzy带算理想和Fuzzy带算商环的定义，讨论它们的一些初等性质。     

An interactive fuzzy satisficing method for structured multiobjective linear fractional programs with fuzzy numbers

In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem formulation process, multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers are formulated. Using the a-level sets of fuzzy numbers, the corresponding nonfuzzy a-multiobjective linear fractional programming problem is introduced. The fuzzy goals of the decision maker for the objective functions are quantified by eliciting the corresponding membership functions including nonlinear ones. Through the introduction of extended Pareto optimality concepts, if the decision maker specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method and Ritter's partitioning procedure are applicable. Then a linear programming-based interactive fuzzy satisficing method with decomposition procedures for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.     

含有模糊决策的线性分布式多目标规划

针对实际问题中决策变量通常是模糊的情况,讨论具有块角结构的含有模糊决策的线性分式多目标规划模型。使用α－水平集,建立了对应的α－多目标规划模型。为解决这类问题,设计了基于模糊模拟的遗传算法。数值例子表明,遗传算法很好地解决了这个问题。     

Fuzzy qualitative trigonometry

This paper presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing & control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalized fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyze general trigonometry-related physical systems from an artificial intelligence perspective.Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the paper to demonstrate the characteristics of fuzzy qualitative trigonometry. One of the examples focuses on robot kinematics and also explains how contributions could be made by fuzzy qualitative trigonometry to the intelligent connection of low-level sensing & control tasks to high-level cognitive tasks.     

Group decisions I. In arbitrary spaces of fuzzy binary relations

This article solves the problem of finding a set of group decisions that satisfy the classical Pareto unanimity principle for the case of initial data represented as fuzzy relations of individual preference. The solution proceeds from results obtained in studying the structure of convex (in the sense defined here) sets and their convex hulls. In the first part that study is carried out for spaces of arbitrary fuzzy binary relations.     

模糊子群直积的若干性质

在Ray的论文[Onproduct of fuzzy subgroups105（1999）181—183]中，作者给出了模糊子群直积在min下的一些性质。在本文中我们将给出更多关于模糊子群直积的性质，并推广到模糊子环上；最后讨论了模糊子群的直积在t-模下的一些性质。     

Fuzzy invariant subgroups and fuzzy ideals

The purpose of this paper is to introduce some basic concepts of fuzzy algebra, as fuzzy invariant subgroups, fuzzy ideals, and to prove some fundamental properties. In particular, it will give a characteristic of a field by a fuzzy ideal.     

Application of fuzzy differential transform method for solving fuzzy Volterra integral equations

This paper deals with the solutions of fuzzy Volterra integral equations with separable kernel by using fuzzy differential transform method (FDTM). If the equation considered has a solution in terms of the series expansion of known functions, this powerful method catches the exact solution. To this end, we have obtained several new results to solve mentioned problem when FDTM has been applied. In order to show this capability and robustness, some fuzzy Volterra integral equations are solved in detail as numerical examples.