This study addresses risk-averse distributed reinforcement learning in multi-agent systems, where agents collaboratively optimize their policies with a risk index in the objective function. Unlike conventional reinforcement learning, which maximizes the expected cumulative reward, the proposed risk-averse reinforcement learning incorporates Conditional Value at Risk (CVaR) to account for rare but significant adverse events. We propose a risk-averse distributed reinforcement learning algorithm based on the policy gradient method, which enables agents to collaboratively update their policies by sharing information through a communication network. Through a theoretical analysis, we show that the proposed algorithm ensures agreement among agents on their estimated policies. Moreover, we show that the consensus value converges in a neighborhood of a locally optimal solution, which ensures that each agent’s learned policy remains aligned with risk-aware optimization criteria.

This paper addresses decentralized event-triggered reinforcement learning with safety constraints. Each agent has an individual reward function and safety constraints that depend on the joint actions of agents. The objective is to maximize the team’s long-term return while satisfying the safety constraints. We formulate the reinforcement learning problem as a nonconvex-concave min-max optimization problem and propose a decentralized policy gradient algorithm. Each agent has estimations for the optimal primal and dual solutions of the min-max optimization problem. Different from the existing decentralized reinforcement learning, the agents share these estimates only when the error exceeds a predefined threshold. We show that the estimates of agents converge to a neighborhood of a locally optimal solution while effectively reducing the communication overhead.

We consider Byzantine-resilient distributed optimization with event-triggered communication. The proposed algorithm is designed to handle non-convex optimization problems in a network of agents where some agents may exhibit Byzantine behavior. Each normal agent has an estimate of a critical point of the global cost function and transmits the estimate to neighbors when the difference between the current and previously communicated values exceeds a predefined threshold. Normal agents then update their estimates by averaging the received values from a trusted set that is determined through the Iterative Outlier Scissor (IOS) procedure. By combining the event-triggered communication and the IOS filtering procedure, the proposed approach ensures resilience to Byzantine behavior and guarantees convergence even in adversarial settings.

When some coefficients of the constraints are uncertain with only their possible ranges being given, a conventional linear programming (LP) problem can be generalised to the one with set-inclusive constraints. We consider the case where the possible ranges are given by fuzzy sets in this paper. The set-inclusive constraints with fuzzy coefficients have been treated by a necessity measure. However, the usual necessity measure cannot express well the decision-maker’s requirement about the trade-off between the robustness level and the satisfaction level of the constraints. We extend the necessity measure to incorporate the trade-off between the robustness level and the satisfaction level of the constraints. We apply the extended necessity measure to LP problems with fuzzy coefficients. After the problem is formulated and reduced to the conventional programming problem, we propose a solution algorithm. Numerical examples are given to illustrate the proposed approach.

The analytic hierarchy process (AHP) provides a systematic approach to the evaluation of alternatives based on pairwise comparison matrices (PCMs) under multiple criteria. As human evaluation is not always accurate and precise, each component of a PCM showing relative importance has been expressed by an interval or a fuzzy number. In this paper, we treat a PCM whose components are represented by twofold intervals. The twofold intervals are composed of inner and outer intervals showing the range of surely acceptable values and the complement of the range of surely unacceptable values for relative importance, respectively. One may apply a fuzzy AHP approach by building a trapezoidal fuzzy number from the inner and outer intervals. However, this approach does not always fit the given information. Because the twofold interval information ambiguously specifies the range of acceptable values for the relative importance. Then we appropriately translate this information into a set of intervals including the inner interval and included in the outer interval, assuming that the decision-maker evaluates the priority weights implicitly as intervals. We investigate the decision analysis based on the twofold interval PCM. Three conflict resolution methods are proposed for treating the inconsistency in the twofold interval PCM. Parametric methods for visualizing possible alternative orderings are proposed. Numerical examples are given to demonstrate the differences between the proposed approach and the previous approaches.

There are typical learning methods for fuzzy inference models such as the steepest descent method, genetic algorithm, etc. It is generally impossible to apply the steepest descent method to fuzzy inference models with consequent fuzzy sets, such as Mamdani’s fuzzy inference models that use min and max operations. Therefore, genetic algorithm will be useful for the above model. However, the computational complexity of genetic algorithm is much larger than the steepest descent method. Also, since all input items are set to the antecedent parts in typical fuzzy inference model, the number of rules increases exponentially. Moreover, considering the computational complexity of genetic algorithm, it will not be necessarily suitable. On the other hand, Single Input Connected (SIC) fuzzy inference model sets the fuzzy rule of 1 input 1 output, so the number of rules can be reduced drastically. The consequent parts of the conventional SIC model were real number although linguistic interpretation is possible and easy to understand if the consequent parts are fuzzy sets. Therefore, we propose a new SIC model which extends real number of the consequent parts to fuzzy sets, and the fuzzy rules are derived by using genetic algorithm. In addition, it is applied to a medical diagnosis and compared with the conventional fuzzy inference models.

Since Mamdani adapted concept of fuzzy inference to control of steam engine experimental equipment, it has been applied in various fields. In the simplified fuzzy inference model, which is one of the conventional fuzzy inference models, a learning method by using teach data and a method for automatically adjusting fuzzy rules has been proposed. In Mamdani's fuzzy inference model, the fuzzy rules were often set by expert on hand. In the fuzzy inference model, the calculations of min and max operations are used in the output derivation process. Therefore, it is difficult to differentiate, and applying it to steepest descent method is generally impossible. On the other hand, fuzzy rules of Mamdani are easier to interpret linguistically than simplified reasoning models, so they are applied in many fields. However, knowledge of fuzzy rules to be used is not necessarily obtained from experts, and development of the method for automatic adjustment in Mamdani type fuzzy inference model is desired. Focusing on the equivalence which is one of the properties of fuzzy inference, inference results are derived using the centroid and area of the consequent fuzzy set, replace the operation of min and max with algebraic product, addition, subtraction. This shows that the fuzzy inference model of Mamdani can be expressed in a form that can be differentiated and learned using the steepest descent method. Although a learning algorithm for a fuzzy inference model using max operation has been proposed, it has not been applied to real systems. In this paper, we apply it to the construction of a medical diagnosis system as one of the applications of real system, and compare the accuracy. Moreover it shows that the learning method can obtain knowledge.

In this paper we focus on generalizations of the classical rough set approach to fuzzy environments. There are two aspects of rough set approaches: classification and approximation. In the classification aspect, by rough set approaches we can classif

We propose a column generation algorithm for solving sequence dependent flowshop scheduling problems (SDST flowshop) to minimize the total weighted tardiness. The continuous relaxation of the set partitioning formulation of the Dantzig-Wolfe decomposition for SDST flowshop is solved by the column generation. The pricing subproblem for the column generation is decomposed into each job-level subproblem. In order to strengthen the lower bound, the additional constraints are imposed to the pricing problems in the proposed algorithm. The cut generation algorithm is developed for the column generation. Computational experiments show that the proposed method can derive the solutions with a smaller duality gap compared with those of the conventional algorithm of ordinary column generation and Lagrangian relaxation with cuts.

In order to analyze the distribution of individual opinions (decision rules) in a group, clustering of decision tables is proposed. An agglomerative hierarchical clustering (AHC) of decision tables has been examined. The result of AHC does not always optimize some criterion. We develop non-hierarchical clustering techniques for decision tables. In order to treat positive and negative evaluations to a common profile, we use a vector of rough membership values to represent individual opinion to a profile. Using rough membership values, we develop a K -means method as well as fuzzy c-means methods for clustering decision tables. We examined the proposed methods in clustering real world decision tables obtained by a questionnaire investigation.

In this paper, group decision making is discussed from the view of aggregating the members' opinions. At first, the individual preferences are obtained by Interval Analytic Hierarchy Process (Interval AHP), which can handle subjective judgments and reflect uncertainty of information. The interval priority weights of alternatives are induced from the pairwise comparison matrix given by a decision maker easily. They help decision makers to reveal the differences and similarities between their own opinions and others concretely, and encourage them to reduce their communication barriers. Then, the individually obtained preferences are aggregated so as to reach the final group decision. The aggregation models from two viewpoints, such as decision makers and alternatives, are proposed. The former model emphasizes the members' consensus by reducing their dissatisfaction for the aggregation. The latter model emphasizes estimating the plausible values of alternatives by taking the essential part of many decision makers' opinions on each alternative.

In this paper, we propose a general decomposition method for transition firing sequence problems for first order hybrid Petri nets. The optimal transition firing sequence problem for first-order hybrid Petri nets is formulated as a mixed integer programming problem. We propose a Lagrangian relaxation method for solving optimal transition firing sequence problems. The hybrid Petri net is decomposed into several subnets in which the optimal firing sequence for each subnet is easily solved. The optimality of solution can be evaluated by duality gap derived by Lagrangian relaxation method. The proposed method is applied to a small-scale example. Computational experiments demonstrate the validity of the proposed formulation.

In this paper, we address a new integration of column generation and Lagrangian relaxation for solving flowshop scheduling problems to minimize the total weighted tardiness. In the proposed method, initial columns are generated by using near-optimal dual solution using the Lagrange multipliers derived by Lagrangian relaxation method. After the generation of base columns, the column generation is executed. Computational results demonstrate that the integrated column generation and Lagrangian relaxation can drastically speed up the conventional column generation.

The Self-Organizing map (SOM) proposed by T. Kohonen is a method to produce a low-dimensional representation from high-dimensional input data automatically, where output units are restrictedly placed on grid points. We propose real-number SOM (RSOM), where output units are freely placed on the real-number coordinates plane and visualized as a Voronoi diagram. RSOM is a natural extension of the conventional SOM because Voronoi tessellation for the output units on the square grid generates square regions on the output plane, the same as the conventional SOM. We propose two methods of moving with preserving topology of the input data and several visualization method such as minimum spanning tree, variable boundary width and spherical RSOM. We illustrate moving methods decrease errors in results of simulation.

Each technique has its own drawback and advantage. There is no method that is powerful in any problems. Therefore, the hybridization of two or more different techniques is important to overcome the disadvantages of the individual techniques. In this paper, a data sequence having a linear tendency with upper/positive and lower/negative aberrances is analyzed. Based on the linear regression analysis, the data sequence is classified into three parts: upper/positive aberrant data, lower/negative aberrant data and normal data. Then introducing the grey disaster forecast analysis, we establish three models: a GM(1,1) disaster model based on upper aberrant data, a GM(1,1) disaster model based on lower aberrant data and a linear regression model based on the remaining normal data. Using the established models, we obtain aberrant forecasting values at oncoming aberrant time points by GM(1,1) from upper and lower aberrant data, and normal forecasting value obtained by the linear regression function. Applying it to the prediction of regional grain production, we demonstrate the good performance and effectiveness of the proposed hybrid method.

In this paper, we propose a decomposition and coordination method for timed automata for modeling and solution of scheduling problems. Parallel composition of timed automata makes it possible to describe concurrent dynamics for several submodels represented by timed automata. To reduce state space explosion for parallel composition of timed automata, a decomposition and coordination method is developed. In the proposed method, a feasible solution is derived by coordinating the solution of each decomposed subproblem. Computational experiments demonstrate the feasibility of the proposed method.

In this paper, attribute reduction in variable precision rough set model is discussed. Several kinds of reducts preserving some of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Relations among those kinds of reducts are investigated. As a basis for reduct computation, Boolean function representations of the preservation of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Throughout this paper, the great difference between the analysis using variable precision rough sets and the classical rough set analysis is emphasized.

In this paper, it is proposed to cluster decision classes before applying a rule induction method. The similarity between decision classes is defined and an agglomerative hierarchical clustering method is applied. At each branch of the obtained dendrogram, LEM2, one of frequently used rule induction algorithm, is applied to induce decision rules inferring clusters. In such a way, a set of decision rules classifying objects into decision classes is obtained. The performance of the proposed method is compared with the direct application of LEM2 to each decision class by a numerical experiment.

In conventional cooperative games, it is assumed that each player will choose whether he/she joins a coalition or not. In bicooperative games defined by Bilbao, each player is allowed to choose one among three alternatives such as to be a defender, to be a fence-sitter and to be a defeater. In this paper, we define a solution which is the probabilistic value of a player when coalitions not containing him/her are equally likely to arise for a bicooperative game. We call this solution the pseudo-Banzhaf value on the class of bicooperative games. Axiomatizations to show rationality of the solution are given. Further, we formulate a weighted majority game as a bicooperative game and give a numerical example.

We discuss a special kind of rough inclusions and its relation to fuzzy inclusions. One of four conditions of rough inclusions is detailed and a rough inclusion which satisfies the detailed condition as well as an additional condition is called a 'meticulous rough inclusion'. We show that a meticulous rough inclusion is closed with respect to upper and lower closure operators defined for a rough inclusion. We discuss conditions for a rough inclusion to be a meticulous rough inclusion. Moreover, the relations between meticulous rough inclusions and fuzzy inclusions are investigated. Sufficient conditions for a fuzzy inclusion defined by an implication function to be a meticulous rough inclusion are given. Examples of fuzzy inclusions which are meticulous rough inclusions are presented.

We treat possibilistic linear programming problems whose uncertain parameters are globally interactive. We assume that the possible range of globally interactive uncertain parameters can be expressed by a fuzzy set whose h-level sets are polytopes. We consider three models, i.e., fractile optimization, modality optimization and symmetric models using a necessity measure. To those models, we discuss solution algorithms. We show that the fractile optimization model is reduced to a semi-infinite linear programming problem and solved by a relaxation procedure developed for semi-infinite linear programming problems. Moreover, we show that the other models are reduced to semi-infinite programming problems and solved by a relaxation procedure together with a bisection method. As a result, the three models are solved by iterative use of linear programming techniques.

A necessity measure N is defined by an implication function. However, specification of an implication function is difficult. Necessity measures are closely related to inclusion relations. In this paper, we propose an approach to necessity measure specification by giving a parametric inclusion relation between fuzzy sets A and B which is equivalent to N A (B) ≥ h. It is shown that, in such a way, we can specify a necessity measure, i.e., an implication function. Moreover, when a necessity measure or equivalently, an implication function is given, then the derivation of an associated parametric inclusion relation is discussed. The associated parametric inclusion relation cannot be obtained for any implication function but only for implication functions which satisfy certain conditions. Applying our results to necessity measures defined by S-, R- and reciprocal R-implications with continuous Archimedean t-norms, associated parametric inclusion relations are shown.

In this paper, a kind of ranking system, called agent-clients evaluation system, is proposed and investigated where there is no such authority with the right to predetermine weights of attributes of the entities evaluated by multiple evaluators for obtaining an aggregated evaluation result from the given fuzzy multiattribute values of these entities. Three models are proposed to evaluate the entities in such a system based on fuzzy inequality relation, possibility, and necessity measures, respectively. In these models, firstly the weights of attributes are automatically sought by fuzzy linear programming (FLP) problems based on the concept of data envelopment analysis (DEA) to make a summing-up assessment from each evaluator. Secondly, the weights for representing each evaluator's credibility are obtained by FLP to make an integrated evaluation of entities from the viewpoints of all evaluators. Lastly, a partially ordered set on a one-dimensional space is obtained so that all entities can be ranked easily. Because the weights of attributes and evaluators are obtained by DEA-based FLP problems, the proposed ranking models can be regarded as fair-competition and self-organizing ones so that the inherent feature of evaluation data can be reflected objectively.

In this paper, we focus on solving problems modeled after a real-world high school timetable problem. It includes multiple objectives and a variety of constraints. It mainly involves producing an optimal schedule for each teacher and for each class. The conventional integer programming approach seems to have some difficulties with solving such problems. The versatility of our proposed heuristic based on a modification of the threshold accepting method is exemplified through our problem solving. For comparison sake, simulated annealing was also used to solve the same problems.

In this paper, a possibilistic linear program is formulated when a measurable multiattribute value function is given. The possibilistic linear program in this paper is an unconstrained linear program with several objective functions whose coefficients are represented by possibility distributions. A possibility measure and a necessity measure are derived from a possibility distribution. Using fuzzy integrals of the measurable multiattribute value function with respect to the possibility measure and the necessity measure, the possible value and the necessary value are defined respectively. In an analogy of the expected utility, the principles of maximizing the possible value and the necessary value are considered as decision procedures under a possibility distribution. The possibilistic linear program is formulated based on these decision procedures and reduced to a nonlinear program. A solution method using linear programming technique is proposed. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.