Generalization and ranking of fuzzy numbers by relative preference relation

We define $$2n+1$$ 2 n + 1 and 2n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$ 2 n + 1 and 2n fuzzy numbers. When the data is representable in terms of $$2n+1$$ 2 n + 1 fuzzy number, we generalize the FMCDM (fuzzy multi-criteria decision making) model constructed with TOPSIS and relative preference relation. Lastly, we give an example from telecommunications to present the proposed FMCDM model and validate the results obtained.

Consumption Smoothing and Discounting in Infinite-Horizon, Discrete-Choice Problems

Suppose the consumption space is discrete. Our first contribution is a technical result showing that any continuous utility function of any stationary preference relation over infinite consumption streams has convex range, provided that the agent is sufficiently patient. Putting the result to use, we consider a model of endogenous discounting (a generalization of the standard model with geometric discounting) and show the uniqueness of the consumption-dependent discount factor as well as the cardinal uniqueness of utility. Comparative statics are then provided to substantiate the uniqueness. For instance, we show that, as in the more familiar case of an infinitely divisible good, the cardinal uniqueness of utility captures an agent’s desire to smooth consumption over time.

A Fuzzy Evaluation Approach for Scientific Research Projects with 2-Tuple Linguistic Preference Relations

Science and technology project evaluation is an important means of science and technology management. Whether the evaluation of science and technology projects is fair or not directly affects the development of national economy and the allocation of science and technology resources. Due to the complexity of the project and the fuzziness of human thinking, the expert information is often difficult to quantify in the process of project evaluation. Generally, the better choice is to express it in qualitative language. In this paper, the 2-tuple linguistic preference relation is proposed to evaluate scientific research projects. The reasonableness of the concept of complete consistency for the 2-tuple linguistic preference relation is discussed. Priority of 2-tuple linguistic preference relation is set up based on the 2-tuple weighted geometric averaging operator. Finally, combined with Science and technology project evaluation problem, the effectiveness and feasibility of the method are verified.

A novel group decision making method for interval-valued pythagorean fuzzy preference relations

Interval-valued Pythagorean fuzzy preference relation (IVPFPR) plays an important role in representing the complex and uncertain information. The application of IVPFPRs gives better solutions in group decision making (GDM). In this paper, we investigate a new method to solve GDM problems with IVPFPRs. Firstly, novel multiplicative consistency and consensus measures are proposed. Subsequently, the procedure for improving consistency and consensus levels are put forward to ensure that every individual IVPFPR is of acceptable multiplicative consistency and consensus simultaneously. In the context of minimizing the deviations between the individual and collective IVPFPRs, the objective experts’ weights are decided according to the optimization model and the aggregated IVPFPR is derived. Afterwards, a programming model is built to derive the normalized Pythagorean fuzzy priority weights, then the priority weights of alternatives are identified as well. An algorithm for GDM method with IVPFPRs is completed. Finally, an example is cited and comparative analyses with previous approaches are conducted to illustrate the applicability and effectiveness of the proposed method.

Scalarization and convergence in unified set optimization

This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterizations for a unified preference relation and the corresponding unified minimal solution in terms of a generalized oriented distance function of the sup-inf type. We establish continuity of a function associated with the generalized oriented distance function and provide an existence result for the unified minimal solution. We establish Painlevé-Kuratowski convergence of minimal solutions of a family of scalar problems to the minimal solutions of the unified set optimization problem.

On Rational Choice and the Representation of Decision Problems

In economic theory, an agent chooses from available alternatives—modeled as a set. In decisions in the field or in the lab, however, agents do not have access to the set of alternatives at once. Instead, alternatives are represented by the outside world in a structured way. Online search results are lists of items, wine menus are often lists of lists (grouped by type or country), and online shopping often involves filtering items which can be viewed as navigating a tree. Representations constrain how an agent can choose. At the same time, an agent can also leverage representations when choosing, simplifying their choice process. For instance, in the case of a list he or she can use the order in which alternatives are represented to make their choice. In this paper, we model representations and decision procedures operating on them. We show that choice procedures are related to classical choice functions by a canonical mapping. Using this mapping, we can ask whether properties of choice functions can be lifted onto the choice procedures which induce them. We focus on the obvious benchmark: rational choice. We fully characterize choice procedures which can be rationalized by a strict preference relation for general representations including lists, list of lists, trees and others. Our framework can thereby be used as the basis for new tests of rational behavior. Classical choice theory operates on very limited information, typically budgets or menus and final choices. This is in stark contrast to the vast amount of data that specifically web companies collect about their users’ choice process. Our framework offers a way to integrate such data into economic choice models.

Resilient route selection of oversized cargo transport: the case of South Korea–Kazakhstan

PurposeResilient route selection for oversized cargoes, one of the general bulk cargoes, has not been adequately optimized in terms of using the Arctic route. This study solves the problem of selecting the optimal shipping routes for oversized cargoes from Busan (South Korea) to Balkhash (Kazakhstan).Design/methodology/approachThe study used the consistent fuzzy preference relation (CFPR) method, which is used to solve multi-criteria decision-making (MCDM) and uncertainty problems, to tackle the route selection. This method involves three procedures: first, the critical factors and alternative routes were obtained by the previous literature and an in-depth interview of experts of oversized cargo-handling with more than 20 years of working experience; second, the weightings for each critical factor were identified using the CFPR calculation process and third, alternative routes were evaluated using weighted critical factors.FindingsThe Northern Sea Route (NSR) combined with the inland waterways of Russia and Kazakhstan was first suggested for bulk carriers that handle oversized cargoes. The NSR could be a suitable route from Busan to Cape Kamenny of the Russian transshipment seaport, where oversized cargoes will be transferred to the river barge at Cape Kamenny, covering 4,913 km from the latter to Balkhash of Kazakhstan via the Ob/Irtysh River.Practical implicationsThis study equips stakeholders in route selection for cargoes with strategies and methods to improve transportation efficiently and enhance shipping routes between Asia and the Commonwealth of Independent States (CIS). In addition to oversized cargoes, coal and timber from Russia can be transported to Asia using inland waterways and the NSR, which can also be used to transport plant equipment for petroleum refineries among Asian countries.Originality/valueThis is the first study to evaluate the suitability of the Artic route for oversized cargoes from South Korea to Kazakhstan. It provides a comprehensive evaluation framework of multimodal shipping routes and offers references for decision-makers when dealing with similar problems.

Determination of Break-Even Point through Consumer Preference Relation

Social choice theory beliefs about how the consumers function to chose their interested goods and services. Preference relation with affine indifference curves that has a concave representation has a linear utility representation. This study asks how individual preference relations might be combined to give a single ordering which captures the overall wishes of the group of individuals. There are certain properties that one would like such a utility rule, utility have thus become a more abstract concept that is not necessarily solely based on the satisfaction or pleasure received. Concept of cardinal utility is studied in three different situations Debreu (1958) gave quite different approach. This study maintains link between mathematical theory and financial concept to determine break-even point through the consumers’ preference relation.

Two Different Approaches for Consistency of Intuitionistic Multiplicative Preference Relation using Directed Graph

Consistency is an important issue that causes wide public concern of decision-makers in the decision-making process. The lack of consistency in preference relations results in a vague solution. The main goal of this paper is to achieve the consistent intuitionistic multiplicative preference relation using a graphical approach. We have proposed two different characterizations of the consistency for intuitionistic multiplicative preference relation(IMPR). In the first approaches, we propose an algorithm to achieve the consistency of IMPR by using the cycles of various length in a directed graph. The second approach proves isomorphism between the set of IMPRs and the set of asymmetric multiplicative preference relations. That result is explored to use the methodologies developed for asymmetric multiplicative preference relations to the case of IMPRs and achieve the consistency of asymmetric multiplicative preference relation using a directed graph. Sometimes the decision maker may not be able to provide the complete relation. So the above-said method is applied for an incomplete IMPR also, here consistency plays an important role. The examples are provided to illustrate both the methods in all cases.