Constructive Decision Theory: Short Summary

In the analytical hierarchy process (AHP), it needs the decision maker to establish a pairwise comparison matrix requires n(n–1)/2 judgments for a level with n criteria (or alternatives). In some instances, the decision maker may have to deal with the problems in which only partial information and uncertain preference relation is available. Consequently, the decision maker may provide interval fuzzy preference relation with incomplete information. In this paper, we focus our attention on the investigation of incomplete interval fuzzy preference relation. We first extend a characterization to the interval fuzzy preference relation which is based on the additive transitivity property. Using the characterization, we propose a method to construct interval additive consistent fuzzy preference relations from a set of n–1 preference data. The study reveals that the proposed method can not only alleviate the comparisons, but also ensure interval preference relations with the additive consistent property. We also develop a novel procedure to deal with the analytic hierarchy problem for group decision making with incomplete interval fuzzy preference relations. Finally, a numerical example is illustrated and a supplier selection case in supply chain management is investigated using the proposed method.

Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.

Linguistic preference relations are widely used by decision makers to elicit their preferences over alternatives in the Group Decision Making (GDM) process. Recent studies have shown that self-confidence, as an important human psychological behavior, has an important influence on decision-making results. However, multiple self-confidence levels of decision makers are seldom considered in the linguistic preference relation. Meanwhile many real-word decision-making problems are analyzed in a hierarchical structure, in which a complicated problem can be divided into several easier comprehended sub-problems. Hence, this paper aims at designing a linguistic hierarchy model with self-confidence preference relation (LHM-SCPR) to discuss complex GDM problems in a hierarchical structure. In the SC-LPR, each element contains two components, the first one is the preference value between pairs of alternatives, and the second one that is defined on a linguistic term set represents decision maker’s self-confidence level associated to the first component. Meanwhile, a nonlinear programming model is proposed to derive individual preference vector from SC-LPR. Then, we apply LHM-SCPR in co-regulation of food safety to present the validity of this method, and find that improving the participation skills regarding co-regulation of food safety is the most pressing task. Finally, detailed comparative analysis and discussion are presented to verify the validity of the proposal.

If a decision problem is said to be difficult, one usually assumes that there is a very complicated relationship between the decision and the corresponding outcome. The problem is considered as solved when this relationship has been sorted out and described. This means that the probelm of selecting the best outcome from a set of possible outcomes, is taken as trivial. The main, or only difficulty is to find the decision which will lead to the best of the possible outcomes. The author argues that the real difficulty may often be to specify a preference ordering over the set of outcomes. He illustrates the point with examples from economics, and discusses some investment problems, in which the outcome of a decision naturally can be considered as a stochastic process.

On the existence of weak subgame perfect equilibria

In multiple-attribute decision making, fuzzy theory is very helpful for dealing with the fuzziness widely existing human judgments. Usually, decision makers obtain their subjective opinions by comparing each pair of decision alternatives and then constructing a rational (consistent) judgment matrix, known as a preference relation (PR) (Saaty, 1980; Xu, 1988) to deal with the ranking of alternatives X = {x 1, x 2 ,..., x n } .

The cost of obtaining good information regarding the various probability distributions needed for the solution of most stochastic decision problems is considerable. It is important to consider questions such as: (1) what minimal amounts of information are sufficient to determine optimal decision rules; (2) what is the value of obtaining knowledge of the actual realization of the random vectors; and (3) what is the value of obtaining some partial information regarding the actual realization of the random vectors. This paper is primarily concerned with questions two and three when the decision maker has an a priori knowledge of the joint distribution function of the random variables. Some remarks are made regarding results along the lines of question one. Mention is made of assumptions sufficient so that knowledge of means, or of means, variances, co-variances and n-moments are sufficient for the calculation of optimal decision rules. The analysis of the second question leads to the development of bounds on the value of perfect information. For multiperiod problems it is important to consider when the perfect information is available. Jensen's inequality is the key tool of the analysis. The calculation of the bounds requires the solution of nonlinear programs and the numerical evaluation of certain functions. Generally speaking, tighter bounds may be obtained only at the expense of additional information and computational complexity. Hence, one may wish to compute some simple bounds to decide upon the advisability of obtaining more information. For the analysis of the value of partial information it is convenient to introduce the notion of a signal. Each signal represents the receipt of certain information, and these signals are drawn from a given probability distribution. When a signal is received, it alters the decision maker's perception of the probability distributions inherent in his decision problem. The choice between different information structures must then take into account these probability distributions as well as the decision maker's preference function. A hierarchy of bounds may be determined for partial information evaluation utilizing the tools of the multiperiod perfect information case. However, the calculation of these bounds is generally considerably more dicult than the calculation of similar boulids in the perfect information case. Most of the analysis is directed towards problems in which the decision maker has a linear utility function over profits, costs or some other numerical variable. However, some of the bounds generalize to the case when the utility function is strictly increasing and concave.

Dynamic choice in a complex world

Multi criteria decision making (MCDM) and group decision making (GDM) are two well practiced approaches to solve decision making problems. Group decision making combines opinions from Decision makers (DMs) into a coherent group decision. The aim of this paper is to develop a new fuzzy group decision making algorithm and apply it to a real-world groundwater development problem to select the most preferred alternative. Five decision makers (DMs) are selected to express their judgments about relative importance of 3 criteria (water pumped, cost, and risk) and have given their preferences as ordinal preferences, utility values, fuzzy preference relations and multiplicative preference relations. Decision makers' opinions are aggregated based on a fuzzy group decision making. Ordered weighted averaging (OWA) operator has been used to aggregate decision makers' opinions. Consensus measure is also defined to evaluate convergence between group and individual opinions. The outcomes of the proposed algorithm show that proposed fuzzy group decision making process is a relevant approach to aggregate the individual expert's opinion and is a desirable tool to reach consensus among DMs.

Introduce the basic ideas, principle and modeling approach of the analytic hierarchy process and take examples of post selection and decision of graduates, making specific demonstration about the utilization of AHP to prove the scientificity and practicability of AHP for multi-attribute decision-making problems. There may be several kinds of natural conditions facing the people, and meanwhile there are also several kinds of action plans alternative for people when they are dealing with problems. Decision maker is required to make the decision based on the known information in such case, i.e. select the optimal action plan, and such problems are classified into decision-making problems (1-3). The several natural conditions faced by people are also known as natural state or abbreviated to state that is existed objectively and uncontrollable factor. The alternative action plans are collectively referred to as decision that is controlled factor. The decision maker is responsible for selecting the plan. As a major constituent part of the decision-making analytical problems, the multi- attribute decision-making is widely existed in the real life. For example, buy a house. It is necessary to comprehensively consider the price, area, floor, position, surrounding environment and other various factors of the house. Although the multi- attribute decision-making problems lie in different backgrounds, they usually have some common features: ①It is always mutual conflicting between attributes (with different dimensions); ②There may be qualitative attribute and quantitative attribute in an attribute set at the same time; ③Attribute normally constitute a hierarchical structure; ④Sometimes the decision information is not complete, and the decision maker can only provide the incomplete information of decision parameters; Based on the link where the decision maker provides information and its sufficient degree, the multi-attribute decision-making can be classified into 3 categories. They are decision without preference information, decision with attribute preference information and decision with preference information among the alternative plans. In decisions with attribute preference information, such decisions with the known attribute weight base information are applied most widely to create linear distribution method, simple weighting method, AHP and other classical decision-making methods. Mechanisms of various multi-attribute decision-making methods are also varied and have different application scopes in practice. By contrast, AHP is more useful

Study on Assessment Level of Experts based on Difference Preference Information

A group decision making method for sustainable design using intuitionistic fuzzy preference relations in the conceptual design stage

Some issues on consistency of fuzzy preference relations

Users’ preferences show up in different formats: quantitative vs. qualitative, conditional vs. unconditional, prioritized vs. flat, etc. In fact, depending on the reason, it could be more natural to express preferences in one a format or another. Thus, it became a challenge for researchers to adequately capture many varieties of preference forms. To this end, artificial intelligence has seen a number of compact languages for preference representation (cf. Chapter 3). However, each language has not been conceived to explicitly and naturally capture all forms of preferences. Instead, it focuses on a particular specification of preferences. It induces a preference relation over the set of outcomes which is a partial or total (pre)order.

In order to solve Group Decision Making (GDM) problems where the preference relations are provided by decision makers with incomplete linguistic labels, this paper develops a GDM approach on the basis of multiple objective optimization and goal programming methods. The proposed approach first analyzes the incomplete linguistic preference relation and then builds the corresponding optimization model. Subsequently, a programming model is developed to minimize the inconsistency among the decision makers' opinions. By solving the programming model, the ranking of alternatives or selection of the most desirable alternative can be obtained according to the optimization result. A numerical example with incomplete linguistic preference relations is examined to illustrate and show the applicability of the proposed approach.