Optimal weighting models based on linear uncertain constraints in intuitionistic fuzzy preference relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Although the classic exponential-smoothing models and grey prediction models have been widely used in time series forecasting, this paper shows that they are susceptible to fluctu- ations in samples. A new fractional bidirectional weakening buffer operator for time series prediction is proposed in this paper. This new operator can effectively reduce the negative impact of unavoidable sample fluctuations. It overcomes limitations of existing weakening buffer operators, and permits better control of fluctuations from the entire sample period. Due to its good performance in improving stability of the series smoothness, the new op- erator can better capture the real developing trend in raw data and improve forecast accu- racy. The paper then proposes a novel methodology that combines the new bidirectional weakening buffer operator and the classic grey prediction model. Through a number of case studies, this method is compared with several classic models, such as the exponential smoothing model and the autoregressive integrated moving average model, etc. Values of three error measures show that the new method outperforms other methods, especially when there are data fluctuations near the forecasting horizon. The relative advantages of the new method on small sample predictions are further investigated. Results demonstrate that model based on the proposed fractional bidirectional weakening buffer operator has higher forecasting accuracy

Minimum Cost Consensus Models based on Random Opinions

In some complex group decision making cases, the opinions of decision makers (DMs) present random characteristic. However, it is difficult to determine the range of opinions by knowing only their probability distributions. In this paper, we construct cost consensus models with random opinions. The objective function is obtaining the minimum consensus budget under a certain confidence level. Nonetheless, the constraints restrict the upper limit of the consensus cost, the lower limit of DMs' compensations, and the opinions deviation between DMs and the moderator. As such, probabilistic planning based on a genetic algorithm is designed to resolve the minimum cost consensus models based on China's urban demolition negotiation, which can better simulate the consensus decision-making process and obtain a satisfactory solution for the random optimization consensus models. The proposed models generalize both Ben-Arieh's minimum cost consensus model and Gong's consensus model with uncertain opinions. Considering that the opinions of DMs and the moderator obey various distributions, the models simulate the opinion characteristics more effectively. In the case analysis, a sensitivity analysis method is adopted to obtain the minimum budget, and probabilistic planning based on genetic algorithm to obtain a satisfactory solution that is closer to reality

The Optimization Ordering Model for Intuitionistic Fuzzy Preference Relations with Utility Functions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Intuitionistic fuzzy sets describe information from the three aspects of membership degree, non-membership degree and hesitation degree, which has more practical significance when uncertainty pervades qualitative decision problems. In this paper, we investigate the problem of ranking intuitionistic fuzzy preference relations (IFPRs) based on various non-linear utility functions. First, we transform IFPRs into their isomorphic interval-value fuzzy preference relations (IVFPRs), and utilise non-linear utility functions, such as parabolic, S-shaped, and hyperbolic absolute risk aversion, to fit the true value of a decision-maker's judgement. Ultimately, the optimization ordering models for the membership and non-membership of IVFPRs based on utility function are constructed, with objective function aiming at minimizing the distance deviation between the multiplicative consistency ideal judgment and the actual judgment, represented by utility function, subject to the decision-maker's utility constraints. The proposed models ensure that more factual and optimal ranking of alternative is acquired, avoiding information distortion caused by the operations of intervals. Second, by introducing a non-Archimedean infinitesimal, we establish the optimization ordering model for IFPRs with the priority of utility or deviation, which realises the goal of prioritising solutions under multi-objective programming. Subsequently, we verify that a close connection exists between the ranking for membership and non-membership degree IVFPRs. Comparison analyses with existing approaches are summarized to demonstrate that the proposed models have advantage in dealing with group decision making problems with IFPRs

Consensus measure with multi-stage fluctuation utility based on China’s urban demolition negotiation

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Utility functions are often used to reflect decision makers' (DMs') preferences. They have the following two merits: one refers to the representation of the DM's utility (satisfaction) level, the other one to the measuring of the consensus level in a negotiation process. Taking the background of China's urban house demolition, a new kind of consensus model is established by using di erent types of multi-stage fluctuation utility functions, such as concave, convex, S-shaped, reversed S-shaped, reversed U-shaped as well as their combinations, to reveal negotiators' dynamic physiological preferences and consensus level. Moreover, the eff ects of budget and the individual compensation tolerance on the consensus level are also discussed with previous research, the proposed model takes both the negotiation cost and DM's consideration, and most importantly, it is computational less complex

Consensus modeling with probability and cost constraints under uncertainty opinions

Goal programming is often applied into uncertain group decision making to achieve the optimal solution. Exiting models focus on either the minimum cost (guaranteeing negotiation budget) or the maximum utility (improving satisfaction level). This paper constructs a stochastic optimization cost consensus group decision making model adopting the minimum budget and the maximum utility as objective function simultaneously to study the negotiation consensus with decision makers' opinions expressed in the forms of multiple uncertain preferences such as utility function and normal distribution. Thus, the proposed model is a generalization of the existing cost consensus model and utility consensus model, respectively. Furthermore in this model, utility priority coefficients cause acceptable budget range and chance constraint shows the probability of reaching consensus. Differing from previous optimization models, the proposed model designs a Monte Carlo simulation combined with Genetic Algorithm to reach an optimal solution, which makes it more applicable to real-world decision making

Properties of a firm’s factor demands, optimal production correspondence, and an economy‘s aggregated supply/demand

Many theoretically beautiful conclusions of the producer theory were derived on the common assumption that every firm attempts to maximize its profit and minimize its cost, while all firms employ the same methodology in their optimization efforts. By losing up these two behavioral assumptions and by introducing the concept of value-belief systems for individual firms, this paper reestablishes a few well-known results of the producer theory for the general case of not specifying what criteria of priority a firm holds. At the same time, this paper shows by using counterexamples, among others, that generally, (i) except for a specific scenario, the optimal production correspondence does not satisfy the homogeneity of degree zero, and (ii) even when individuals act in their own best self-interests, they may not collectively produce unintended greater social benefits and public goods. In the end, several topics of expected significance are suggested for future research

The spherical distance for intuitionistic fuzzy sets and its application in decision analysis

Different from traditional distances between Intuitionistic Fuzzy Sets (IFS), the spherical distance between two IFSs relies not only on their relative differences but also their absolute values. In this paper, we generalize the properties of spherical distance measures between IFSs, and investigate the applications of spherical distance measures in group decision making, pattern recognition and medical diagnosis. We develop an optimization spherical distance model with IFS preference in group decision making, and demonstrate that this model is feasible and practical with an evaluation model of drought risk. By using comparative analysis method, we show that this new spherical distance can also be applied in other fields such as pattern recognition and medical diagnosis

On Consistency Test Method of Expert Opinion in Ecological Security Assessment

To reflect the initiative design and initiative of human security management and safety warning, ecological safety assessment is of great value. In the comprehensive evaluation of regional ecological security with the participation of experts, the expert’s individual judgment level, ability and the consistency of the expert’s overall opinion will have a very important influence on the evaluation result. This paper studies the consistency measure and consensus measure based on the multiplicative and additive consistency property of fuzzy preference relation (FPR). We firstly propose the optimization methods to obtain the optimal multiplicative consistent and additively consistent FPRs of individual and group judgments, respectively. Then, we put forward a consistency measure by computing the distance between the original individual judgment and the optimal individual estimation, along with a consensus measure by computing the distance between the original collective judgment and the optimal collective estimation. In the end, we make a case study on ecological security for five cities. Result shows that the optimal FPRs are helpful in measuring the consistency degree of individual judgment and the consensus degree of collective judgment