A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making

As an extension of fuzzy set, a Pythagorean fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision‐making problems. The aim of this paper is to introduce a novel aggregation method for the Pythagorean fuzzy set and analyze possibilities for its application in solving multiple attribute decision‐making problems. More specifically, a new Pythagorean fuzzy aggregation operator called the Pythagorean fuzzy induced ordered weighted averaging‐weighted average (PFIOWAWA) operator is developed. This operator inherits main characteristics of both ordered weighted average operator and induced ordered weighted average to aggregate the Pythagorean fuzzy information. Some of main properties and particular cases of the PFIOWAWA operator are studied. A method based on the proposed operator for multiple attribute group decision making is developed. Finally, we present a numerical example of selection of research and development projects to illustrate applicability of the new approach in a multiple attribute group decision‐making problem.     

一种利用信息熵确定属性权重的模糊单因素评价方法

在多属性决策问题中,由于问题的复杂性,属性的权重一般是未知量或者只有部分信息权重,研究如何确定多属性决策问题中属性的权重,以便对已有的方案进行排序或评价,已经成为多属性决策研究的一个重点问题。截止目前,多属性权重确定方法主要包括主观权重确定法和客观权重确定法,主观权重确定法具有受决策主体主观偏好影响的缺点,而客观权重确定方法往往忽略决策主体的参与程度。因此,如何研究将主客观权重复制相结合,提高决策的准确性,具有实际的研究意义。本文总结了多属性决策问题中权重的确定方法,提出了一种主观赋值与客观确定相结合的改进熵值权重确定方法,并通过实例证明了该算法的有效性。     

Studying interval valued matrix games with fuzzy logic

Matrix games have been widely used in decision making systems. In practice, for the same strategies players take, the corresponding payoffs may be within certain ranges rather than exact values. To model such uncertainty in matrix games, we consider interval-valued game matrices in this paper; and extend the results of classical strictly determined matrix games to fuzzily determined interval matrix games. Finally, we give an initial investigation into mixed strategies for such games. This work is partially supported by the NSF grant CCF-0202042.     

Game‐Based Simulation for Cross‐Cultural Decision Making Training

Increasing globalization has had a major impact on manufacturing and service industries as well as on coalition operations conducted by the military. What is common to both the commercial and military sectors is the recent surge in interest in cross‐cultural decision making (CCDM) training. Existing CCDM training approaches tend to employ either some form of multi‐agent simulation or some variant of classical game theory. Despite their manifest benefits, these approaches have specific limitations that need to be overcome to create an effective cross‐cultural training system. Multi‐agent simulations typically lack theoretical underpinnings while classical game theory‐based approaches take a limited view of strategic decision making. Specifically, by adopting a Western view of rationality, game‐theoretic approaches fail to accommodate considerations such as fairness, altruism and reciprocity. Empirical research in strategic economic games has shown that humans respond to more than merely monetary incentives. In particular, research has shown that cultural norms play a central role in human decision making behavior, especially in non‐Western cultures. This paper presents an innovative approach to game‐based simulation that combines findings from behavioral game theory with classical game theory and multi‐agent simulation to exploit the strengths of each approach while making learning enjoyable, memorable, and fun. An illustrative game‐based simulation for CCDM training is also presented. The simulation framework is equally applicable to teaching other soft skills as well as skills that are too hazardous or too expensive to teach in the realworld through live exercises. © 2012 Wiley Periodicals, Inc.     

Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making

The q‐rung orthopair fuzzy sets (q‐ROFs) are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the membership degree and the qth power of the degrees of non‐membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the q‐rung orthopair fuzzy weighted averaging operator and the q‐rung orthopair fuzzy weighted geometric operator to deal with the decision information, and their some properties are well proved. Further, based on these operators, we presented two new methods to deal with the multi‐attribute decision making problems under the fuzzy environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.     

Novel intuitionistic fuzzy decision making models in the framework of decision field theory

The intuitionistic fuzzy decision making problems have gained great popularity recently. Most of the current methods depend on various aggregation operators that provide collective intuitionistic fuzzy values of alternatives to be ranked. Such collective information only depicts the overall characteristics of the alternatives but ignores the detailed contrasts among them. Most important of all, the current decision making procedure is not in accordance with the way that the decision makers (DMs) think about the decision making problems. In this paper, we develop a novel intuitionistic fuzzy decision making model in the framework of decision field theory. The decision making model emphasizes the contrasts among alternatives with respect to each attribute that competes and influences each other, and thus, the preferences for alternatives can dynamically evolve and provide the final optimal result. After that, we develop an intuitionistic fuzzy group decision making model based on decision field theory, and then make a practical case study on the application of the developed models to the “one belt, one road” investment decision making problems. Finally, we point out the characteristics and the limitations of our models in detail.     

Solving scalarized multi‐objective network flow problems using an interior point method

In this paper, we present a primal‐dual interior‐point algorithm to solve a class of multi‐objective network flow problems. More precisely, our algorithm is an extension of the single‐objective primal infeasible dual feasible inexact interior point method for multi‐objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on bi‐objective instances are reported. The multi‐objective instances are converted into single objective problems with the aid of an achievement function, which is particularly adequate for interactive decision‐making methods.     

基于云模型的不确定性大群体多属性决策方法

针对传统不确定性大群体多属性决策方法中只考虑决策信息的模糊性,没有考虑信息的随机性这一问题,提出了一种基于云模型的多属性决策方法,从而用于解决由多个小群体组成的不确定性大群体决策问题。首先将不确定语言评价值转化为一维正态云;其次采用决策者主观确定和一致性分析相结合的方法确定针对不同决策对象的小群体权重,进而生成综合云;然后提出了一种改进的云相似度算法作为云模型距离的度量,通过比较各方案综合云与最优云的相似度对方案排序。最后通过实例验证了所提方法的可行性和有效性。     

A normal wiggly hesitant fuzzy MABAC method based on CCSD and prospect theory for multiple attribute decision making

Normal wiggly hesitant fuzzy set (NWHFS) is a new fuzzy information form to help decision makers (DMs) express their evaluations, which can further dig the potential uncertain information hidden in the original data given by the DMs. Firstly, we define a new distance measure and new operational laws of NWHFSs. Then, for the situation where attribute weights are completely unknown, we propose an extended CCSD method to produce them objectively, which comprehensively uses standard deviation (SD) and correlation coefficient (CC). What's more, we introduce the MABAC (multiattributive border approximation area comparison) method, which takes the distance between alternatives and the border approximation area (BAA) into consideration for handling the complex and uncertain decision‐making problems. Meanwhile, we combine the MABAC method with prospect theory (PT), which considers DMs' psychological behavior, and propose a new NWHF‐CCSD‐PT‐MABAC method to cope with the multi‐attribute decision making problems under normal wiggly hesitant fuzzy environment. Lastly, we illustrate the validity and advantages of the proposed method through an example of college book supplier selection.     

A hybrid fuzzy logic/constraint satisfaction problem approach to automatic decision making in simulation game models

Possible techniques for representing automatic decision-making behavior approximating human experts in complex simulation model experiments are of interest. Here, fuzzy logic (FL) and constraint satisfaction problem (CSP) methods are applied in a hybrid design of automatic decision making in simulation game models. The decision processes of a military headquarters are used as a model for the FL/CSP decision agents choice of variables and rulebases. The hybrid decision agent design is applied in two different types of simulation games to test the general applicability of the design. The first application is a two-sided zero-sum sequential resource allocation game with imperfect information interpreted as an air campaign game. The second example is a network flow stochastic board game designed to capture important aspects of land manoeuvre operations. The proposed design is shown to perform well also in this complex game with a very large (billionsize) action set. Training of the automatic FL/CSP decision agents against selected performance measures is also shown and results are presented together with directions for future research.     

一类基于指数型模糊数的模糊多属性topsis决策

针对指数型模糊数上的模糊多属性决策问题,根据模糊理想点法的思想,给出两种多属性topsis决策方法。通过定义指数型模糊数的期望值,实现属性权重向量的解模糊化处理;定义指数型模糊数之间的距离测度,以计算各方案与理想方案之间的距离。基于期望值和距离测度的定义,从两种不同的角度出发,给出了两种模糊多属性topsis决策方法。实例验证两种方法的可行性和有效性,并对这两种方法进行比较和分析。     

Dynamics in network interaction games

We study the convergence times of dynamics in games involving graphical relationships of players. Our model of interaction games generalizes a variety of recently studied games in game theory and distributed computing. In a local interaction games each agent is a node embedded in a graph and plays the same 2-player game with each neighbor. He can choose his strategy only once and must apply his choice in each 2-player game he is involved in. This represents a fundamental model of decision making with local interaction and distributed control. Furthermore, we introduce a generalization called 2-type interaction games, in which one 2-player game is played on edges and possibly another game is played on non-edges. For the popular case with symmetric 2 ×?2 games, we show that several dynamics converge to a pure Nash equilibrium in polynomial time. This includes arbitrary sequential better-response dynamics, as well as concurrent dynamics resulting from a distributed protocol that does not rely on global knowledge. We supplement these results with an experimental comparison of sequential and concurrent dynamics.     

Project risk evaluation using a fuzzy analytic hierarchy process: An application to information technology projects

Projects are critical to the realization of performing organization's strategies. Each project contains some degree of risk and it is required to be aware of these risks and to develop the necessary responses to get the desired level of project success. Because projects' risks are multidimensional, they must be evaluated by using multi‐attribute decision‐making methods. The aim of this article is to provide an analytic tool to evaluate the project risks under incomplete and vague information. The fuzzy analytic hierarchy process (AHP) as a suitable and practical way of evaluating project risks based on the heuristic knowledge of experts is used to evaluate the riskiness of an information technology (IT) project of a Turkish firm. The means of the triangular fuzzy numbers produced by the IT experts for each comparison are successfully used in the pairwise comparison matrices. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 559–584, 2006.     

Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q‐rung orthopair fuzzy environment

A Q‐rung orthopair fuzzy set (q‐ROFS) originally proposed by Yager (2017) is a new generalization of orthopair fuzzy sets, which has a larger representation space of acceptable membership grades and gives decision makers more flexibility to express their real preferences. In this paper, for multiple attribute decision‐making problems with q‐rung orthopair fuzzy information, we propose a new method for dealing with heterogeneous relationship among attributes and unknown attribute weight information. First, we present two novel q‐rung orthopair fuzzy extended Bonferroni mean (q‐ROFEBM) operator and its weighted form (q‐ROFEWEBM). A comparative example is provided to illustrate the advantages of the new operators, that is, they can effectively model the heterogeneous relationship among attributes. We prove that some existing known intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are special cases of the proposed q‐ROFEBM and q‐ROFEWEBM operators. Meanwhile, several desirable properties are also investigated. Then, a new knowledge‐based entropy measure for q‐ROFSs is also proposed to obtain the attribute weights. Based on the proposed q‐ROFWEBM and the new entropy measure, a new method is developed to solve multiple attribute decision making problems with q‐ROFSs. Finally, an illustrative example is given to demonstrate the application process of the proposed method, and a comparison analysis with other existing representative methods is also conducted to show its validity and superiority.     

Fuzzy differential games for nonlinear stochastic systems:suboptimal approach

A fuzzy differential game theory is proposed to solve the n-person (or n-player) nonlinear differential noncooperative game and cooperative game (team) problems, which are not easily tackled by the conventional methods. In the paper, both noncooperative and cooperative quadratic differential games are considered. First, the nonlinear stochastic system is approximated by a fuzzy model. Based on the fuzzy model, a fuzzy controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or with the cooperative game in the sense of Pareto-optimal strategies. Using a suboptimal approach, the outcomes of the fuzzy differential games for both the noncooperative and the cooperative cases are parameterized in terms of an eigenvalue problem. Since the state variables are usually unavailable, a suboptimal fuzzy observer is also proposed in this study to estimate the states for these differential game problems. Finally, simulation examples are given to illustrate the design procedures and to indicate the performance of the proposed methods     

Possibilistic programming approach for fuzzy multidimensional analysis of preference in group decision making

Multiple attribute decision making (MADM) problems are the most encountered problems in decision making. Fuzziness is inherent in decision making process and linguistic variables are well suited to assessing an alternative on qualitative attributes using fuzzy rating. A few techniques in MADM assess the weights of attributes based on preference information on alternatives. But they are not practical any more when the set of all paired comparison judgments from decision makers (DMs) on attributes are not crisp and also we have to deal with fuzzy decision matrix. This paper investigates the generation of a possibilistic model for multidimensional analysis of preference (LINMAP). The model assesses the fuzzy weights as well as locating the ideal solution with fuzzy decision making preference on attributes and fuzzy decision matrix. All of the information is assumed as triangular fuzzy numbers (TFNs). This method is developed in group decision making environments and formulates the problem as a possibilistic programming with multiple objectives.     

N-person credibilistic strategic game

This paper enlarges the scope of fuzzy-payoff game to n-person form from the previous two-person form. Based on credibility theory, three credibilistic approaches are introduced to model the behaviors of players in different decision situations. Accordingly, three new definitions of Nash equilibrium are proposed for n-person credibilistic strategic game. Moreover, existence theorems are proved for further research into credibilistic equilibrium strategies. Finally, two numerical examples are given to illustrate the significance of credibilistic equilibria in practical strategic games.     

Pythagorean Fuzzy Multigranulation Rough Set over Two Universes and Its Applications in Merger and Acquisition

Pythagorean fuzzy set, an extension form of intuitionistic fuzzy set, which owns many advantages for dealing with uncertainties, and it has been developed to deal with various complex decision‐making problems. Furthermore, based on lower and upper approximations induced by multiple binary relations, the multigranulation rough set has become one of the most promising directions in rough set theory. To combine the two ideas and explore the practical decision‐making problems, we develop a new multigranulation rough set model, called Pythagorean fuzzy multigranulation rough set over two universes. In the framework of our study, we introduce the models of Pythagorean fuzzy rough set over two universes and Pythagorean fuzzy multigranulation rough set over two universes, respectively. Both the definition and basic properties are explored. Finally, we give a general algorithm, which is applied to a decision‐making problem in merger and acquisition, and the effectiveness of the algorithm is demonstrated by a numerical example.     

Application of reinforcement learning to the game of Othello

Operations research and management science are often confronted with sequential decision making problems with large state spaces. Standard methods that are used for solving such complex problems are associated with some difficulties. As we discuss in this article, these methods are plagued by the so-called curse of dimensionality and the curse of modelling. In this article, we discuss reinforcement learning, a machine learning technique for solving sequential decision making problems with large state spaces. We describe how reinforcement learning can be combined with a function approximation method to avoid both the curse of dimensionality and the curse of modelling. To illustrate the usefulness of this approach, we apply it to a problem with a huge state space—learning to play the game of Othello. We describe experiments in which reinforcement learning agents learn to play the game of Othello without the use of any knowledge provided by human experts. It turns out that the reinforcement learning agents learn to play the game of Othello better than players that use basic strategies.     

An approach of the criteria importance theory to decision making problems with hierarchical criterial structures

A new hierarchical model of decision making under multiple criteria that form a multilevel system is proposed. With this model, one can use approaches and methods of the criteria importance theory to collect information about the importance of criteria and use it to analyze practical multicriterial decision making problems in a correct way.