Group decision making procedure considering preference strength under incomplete information

This article deals with the multiple criteria decision making problem with incomplete information when multiple decision makers (Multiple Criteria Group Decision Making: MCGDM) are involved. Usually decision makers (DMs) are willing or able to provide only incomplete information, because of time pressure, lack of knowledge or data, and their limited expertise related to the problem domain. There have only been a few studies considering incomplete information in group settings. We also consider the case where importance weights are given incompletely. This article suggests the possibility that individually optimized results can be used to build group consensus. Individual optimization results by pairwise dominance, contain useful information in forming consensus, such as, ordinal rankings or preference intensity of an alternative over the others. Rather than using ordinal rankings for aggregation which do not consider preference strength, we suggest a procedure that takes account of individual DMs' preference strength.     

A data envelopment analysis approach to multicriteria decision problems with incomplete information

As a decision aid for discrete multicriteria decision problems, this paper proposes a multilevel graph of alternatives to represent the ranking, to the extent that this is possible when incomplete information on weights is available under the assumption of the additive value function. To construct it, the nested decomposition of the set of alternatives is established along the lines of data envelopment analysis (DEA). A numerical example is given to illustrate a multilevel graph based on the nested decomposition and compare it with the hierarchical dominance graph based on dominance relations proposed by Park and Kim.     

On a decision procedure for quantified linear programs

Quantified linear programming is the problem of checking whether a polyhedron specified by a linear system of inequalities is non-empty, with respect to a specified quantifier string. Quantified linear programming subsumes traditional linear programming, since in traditional linear programming, all the program variables are existentially quantified (implicitly), whereas, in quantified linear programming, a program variable may be existentially quantified or universally quantified over a continuous range. In this paper, the term linear programming is used to describe the problem of checking whether a system of linear inequalities has a feasible solution. On account of the alternation of quantifiers in the specification of a quantified linear program (QLP), this problem is non-trivial. QLPs represent a class of declarative constraint logic programs (CLPs) that are extremely rich in their expressive power. The complexity of quantified linear programming for arbitrary constraint matrices is unknown. In this paper, we show that polynomial time decision procedures exist for the case in which the constraint matrix satisfies certain structural properties. We also provide a taxonomy of quantified linear programs, based on the structure of the quantifier string and discuss the computational complexities of the constituent classes. This research has been supported in part by the Air Force Office of Scientific Research under contract FA9550-06-1-0050.     

A novel fuzzy multi-criteria decision framework for sustainable supplier selection with incomplete information

Both academic and corporate interest in sustainable supply chains has increased in recent years. Supplier selection process is one of the key operational tasks for sustainable supply chain management. This paper examines the problem of identifying an effective model based on sustainability principles for supplier selection operations in supply chains. Due to its multi-criteria nature, the sustainable supplier evaluation process requires an appropriate multi-criteria analysis and solution approach. The approach should also consider that decision makers might face situations such as time pressure, lack of expertise in related issue, etc., during the evaluation process. The paper develops a novel approach based on fuzzy analytic network process within multi-person decision-making schema under incomplete preference relations. The method not only makes sufficient evaluations using the provided preference information, but also maintains the consistency level of the evaluations. Finally, the paper analyzes the sustainability of a number of suppliers in a real-life problem to demonstrate the validity of the proposed evaluation model.     

Maximizing deviation method for neutrosophic multiple attribute decision making with incomplete weight information

This paper develops a method for solving the multiple attribute decision-making problems with the single-valued neutrosophic information or interval neutrosophic information. We first propose two discrimination functions referred to as score function and accuracy function for ranking the neutrosophic numbers. An optimization model to determine the attribute weights that are partly known is established based on the maximizing deviation method. For the special situations where the information about attribute weights is completely unknown, we propose another optimization model. A practical and useful formula which can be used to determine the attribute weights is obtained by solving a proposed nonlinear optimization problem. To aggregate the neutrosophic information corresponding to each alternative, we utilize the neutrosophic weighted averaging operators which are the single-valued neutrosophic weighted averaging operator and the interval neutrosophic weighted averaging operator. Thus, we can determine the order of alternatives and choose the most desirable one(s) based on the score function and accuracy function. Finally, some illustrative examples are presented to verify the proposed approach and to present its effectiveness and practicality.     

Bargaining with incomplete information

This paper analyses the process and outcomes of competitive bilateral negotiation for a model based on negotiation decision functions. Each agent has time constraints in the form of a deadline and a discounting factor. The importance of information possessed by participants is highlighted by exploring all possible incomplete information scenarios – both symmetric and asymmetric. In particular, we examine a range of negotiation scenarios in which the amount of information that agents have about their opponent’s parameters is systematically varied. For each scenario, we determine the equilibrium solution and study its properties. The main results of our study are as follows. Firstly, in some scenarios agreement takes place at the earlier deadline, while in others it takes place near the beginning of negotiation. Secondly, in some scenarios the price surplus is split equally between the agents while in others the entire price surplus goes to a single agent. Thirdly, for each possible scenario, the equilibrium outcome possesses the properties of uniqueness and symmetry – although it is not always Pareto optimal. Finally, we also show the relative impacts of the opponent’s parameters on the bargaining outcome.     

On the stability of price-adjusting oligopolies with incomplete information

A general linear price-adjusting scheme is examined in non-linear Bertrand oligopolies that contains the models of Negishi and Jin as special cases among others. The existence of a unique equilibrium of the dynamic process is first proved, and then under realistic conditions, the global asymptotic stability of the equilibrium is verified. Particular cases illustrate the general results.     

A method for multiple attribute decision making with incomplete weight information in linguistic setting

The aim of this paper is to investigate the multiple attribute decision making problems with linguistic information, in which the information about attribute weights is incompletely known, and the attribute values take the form of linguistic variables. We first introduce some approaches to obtaining the weight information of attributes, and then establish an optimization model based on the ideal point of attribute values, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the numerical weighting linguistic average (NWLA) operator to aggregate the linguistic variables corresponding to each alternative, and then rank the alternatives by means of the aggregated linguistic information. Finally, the developed method is applied to the ranking and selection of propulsion/manoeuvring system of a double-ended passenger ferry.     

Modeling a Markovian decision process by neural network

One of the difficulties in generating an optimal policy for systems planning and control by the Markov decision process is that the state transition probabilities must be known a priori. A usual approach to estimate the state transition probabilities is by using historical data. However, if the process is not completely stationary, it may be more convenient to obtain estimates of the transition probabilities by using another approach, namely, parameter adaptation by neural networks.

A significant advantage of neural network modeling of the Markovian decision problem is that the temporal nonstationary state transition probabilities can be revised by a parameter learning paradigm. The objective of this paper is to present this approach and demonstrate its applicability by modeling a finite-stage decision problem.     

GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting

The aim of this paper is to investigate the multiple attribute decision-making problems with intuitionistic fuzzy information, in which the information about attribute weights is incompletely known, and the attribute values take the form of intuitionistic fuzzy numbers. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method, by which the attribute weights can be determined. Then, based on the traditional GRA method, calculation steps for solving intuitionistic fuzzy multiple attribute decision-making problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution are calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of grey relation to both the positive-ideal solution (PIS) and negative-ideal solution (NIS) simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Solving a decision problem with linguistic information

Artificial Intelligence (AI) is the science that focuses its study to achieve the understanding of intelligent entities. It is evident that computers that possess intelligence at a human level will have very important repercussions in our daily life. Inside the fields of AI it is necessary to highlight the decision-making, where AI supposes a great help. In this paper, we present a methodology in a decision-making problem where only linguistic information was available. The main purpose of this paper is to present a technique to obtain the weights and the utilities to resolve the multicriteria decision-making when the knowledge about it is linguistic. Thus we can have systems where the input of data in the computer can be of a determined type and the output can be of the same or a different type, making more intelligent computers. The aim of this paper is to present an evaluation model based on a multicriteria decision analysis that offers the “assembly workshop manager” the possibility of expressing its knowledge in a linguistic framework. In this paper the linguistic decision analysis is interpreted in a multicriteria decision-making context.     

Addition and removal of information for a knowledge base with incomplete information

A knowledge base containing incomplete information in the form of disjunctions and negative information shows difficulties regarding the update operators. In this paper simple and straightforward definitions are given for an ‘adding’ operator (‘+’) and a ‘removing’ operator (‘−’) using Hebrand models.     

On defect propagation in multi-machine stochastically deteriorating systems with incomplete information

In many manufacturing environments, costly job inspection provides information about the random deterioration of the machines. The resulting maintenance and inspection problem is extensively studied for a single machine system by using the framework of Partially Observable Markov Decision Processes (POMDPs). In this work, this concept is extended to multiple operations and multiple job types by considering two process flow topologies: (i) re-entrant flow, (ii) hybrid flow. The resulting (significantly large sized) POMDPs are solved using a point based method called PERSEUS, and the results are compared with those obtained by conventionally used periodic policies.     

Optimization in periodic Markovian decision processes

We consider a Markovian decision process with a nonhomogeneous transition function satisfying a periodicity condition. An optimization method is proposed which computes the optimal periodic strategy for an unbounded time interval.Translated from Kibernetika, No. 2, pp. 91–94, 99, March–April, 1991.     

Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information

To solve group decision-making problems we have to take in account different aspects. On the one hand, depending on the problem, we can deal with different types of information. In this way, most group decision-making problems based on linguistic approaches use symmetrically and uniformly distributed linguistic term sets to express experts’ opinions. However, there exist problems whose assessments need to be represented by means of unbalanced linguistic term sets, i.e., using term sets which are not uniformly and symmetrically distributed. On the other hand, there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem and, as a result, they may present incomplete information. The aim of this paper is to present a consensus model to help experts in all phases of the consensus reaching process in group decision-making problems in an unbalanced fuzzy linguistic context with incomplete information. As part of this consensus model, we propose an iterative procedure using consistency measures to estimate the incomplete information. In addition, the consistency measures are used together with consensus measures to guided the consensus model. The main novelty of this consensus model is that it supports the management of incomplete unbalanced fuzzy linguistic information and it allows to achieve consistent solutions with a great level of agreement.     

Grey relational analysis method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

With respect to 2-tuple linguistic multiple attribute group decision making problems with incomplete weight information, some basic concepts and operational laws of 2-tuple linguistic variables are introduced. An optimization model based on the maximizing deviation method, by which the attribute weights can be determined, is established. According to the traditional ideas of grey relational analysis (GRA), the optimal alternative(s) is determined by calculating the linguistic degree of grey relation of every alternative and 2-tuple linguistic positive ideal solution and 2-tuple linguistic negative ideal solution. It is based on the concept that the optimal alternative should have the largest degree of grey relation from positive ideal solution and the smallest degree of grey relation from the negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective and easy to calculate.     

Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information

With respect to linguistic multiple attribute group decision making problems with incomplete weight information, a new method is proposed. In the method, the 2-tuple linguistic representation developed in recent years is used to aggregate the linguistic assessment information. In order to get the weight vector of the attribute, we establish an optimization model based on the basic ideal of traditional technique for order performance by similarity to ideal solution, by which the attribute weights can be determined. Then, the optimal alternative(s) is determined by calculating the shortest distance from the 2-tuple linguistic positive ideal solution, and on the other side, the farthest distance of the 2-tuple linguistic negative ideal solution. The method has exact characteristic in linguistic information processing. It avoided information distortion and losing, which occur formerly in the linguistic information processing. Finally, a numerical example is used to illustrate the use of the proposed method. The result shows the approach is simple, effective, and easy to calculate.