A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.     

A vague set based decision support approach for evaluating research funding programs

Scientific Research Assessment (SRA) is receiving increasing attention in both academic and industry. More and more organizations are recognizing the importance of SRA for the optimal use of scarce resources. In this paper, a vague set theory based decision support approach is proposed for SRA. Specifically, a family of parameterized S-OWA operator is developed for the aggregation of vague assessments. The proposed approach is introduced to evaluate the research funding programs of the National Natural Science Foundation of China (NSFC). It provides a soft and expansive way to help the decision maker in NSFC to make his decisions. The proposed approach can also be used for some other agencies to make similar assessment.     

Application of fuzzy soft set in decision making problems based on grey theory

There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems.     

Application of fuzzy soft set in decision making problems based on grey theory

There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems.     

Level set evolution for boundary extraction based on a p-Laplace equation

This paper presents a new approach to boundary extraction. We represent the object boundary by a level set model that is embedded in several scalar functions. The motion of the dynamic interface is governed by a p-Laplace equation. Such level set models are flexible in handling complex topological changes and are concise in extracting object boundaries despite of deep depression. Furthermore, a relatively smooth evolution can be maintained without re-initialization. The cost of this method is moderate. The accuracy and efficiency of the proposed algorithm are illustrated by several numerical examples.     

Developing a straightforward approach for group decision making based on determining weights of decision makers

Group decision making is an active area of research within multiple attribute decision making. This paper assumes that all the decision makers (DMs) are not equally qualified to contribute equitably to the decision process. The aim of this paper is to develop an approach to determine weights of DMs, in which the decision information on alternatives with respect to attributes, provided by each DM, is represented in the form of interval data. We define the average of all individual decisions as the positive ideal decision (PID), and the maximum separation from PID as the negative ideal decision, which are characterized by a matrix, respectively. The weight of each DM is determined according to the Euclidean distances between the individual decision and ideal decisions. By using the obtained weights of DMs, all individual decisions are aggregated into a collective decision. Then the alternatives is ranked based on the collective decision. Meanwhile, this paper also gives a humanized decision method by using an optimistic coefficient, which is used in adjusting the relative importance between profit and risk. Finally, we give an example to illustrate the developed approach.     

Behavioural decision theory for multi-criteria decision analysis: a guided tour

Multi-criteria decision analysis (MCDA) involves asking decision makers difficult questions, and can leave them thinking that their judgements are not as coherent as they might have thought. This experience can be distressing and may even lead to rejection of the analysis. The psychology of preference sheds light both on how people naturally make choices without decision analytic assistance, and on how people think about the MCDA elicitation questions. As such, it can help the analyst to respond helpfully to difficulties which decision makers may face. In this paper, we review research from Behavioural Decision Theory relevant to MCDA. Our review follows the MCDA process, discussing research relevant to the structuring, value elicitation, and weighting phases of the analysis, outlining relevant and important findings, and open questions for research and practice.     

Asymptotic distribution theory of statistical functionals: The compact derivative approach for robust estimators

Summary Derivatives of statistical functionals have been used to derive the asymptotic distributions ofL-,M- andR-estimators. This approach is often heuristic because the types of derivatives chosen have serious limitations. The Gateaux derivative is too weak and the Fréchet derivative is too strong. In between lies the compact derivative. This paper obtains strong results in a rigorous manner using the compact derivative onC ₀(R). This choice of space allows results for a broader class of functionals than previous choices, and the fact that is often tight provides the compact set required. A major result is the derivation of the compact derivative of the inverse c.d.f. when the range space is endowed with the uniform norm. It has applications to the asymptotic theory ofL-,M- andR-estimators. We illustrate the power of this result by applications toL-estimators in settings including the one sample problem, data grouped by quantiles, and censored survival time data.     

Orderings based on the banks set: Some new scoring methods for multicriteria decision making

This article introduces new methods for ranking alternatives in multicriteria decision making situations. Each is based on the normative position that the strength of an alternative is inversely related to the number of alternatives that could prevent it from being chosen. The scores discriminate among elements of the Banks set (Banks, Soc Choice Welfare, 1985, 1, 295–306). The new scoring methods are compared to traditional scoring methods and related to the amount of intransitivity (specifically, the size of the top‐cycle) of aggregated preference. The new scores are shown to measure important aspects of alternatives not captured by extant scoring methods and are illustrated in collective choice settings. © 2014 Wiley Periodicals, Inc. Complexity 20: 63–76, 2015     

Multi-attribute decision making based on a novel IF point operator

Intuitionistic fuzzy (IF) point operators transform an intuitionistic fuzzy set to a fuzzy set, or an intuitionistic fuzzy set with a smaller degree of hesitance. The purpose of which is to empower the operations of intuitionistic fuzzy sets with traditional fuzzy set methodologies. In the present paper, a new IF point operator is proposed. Different from the existing IF point operators, the new approach includes two parametric functions with respect to the number of iterations. It is proved that the newly proposed method could be degenerated to the traditional IF point operators. Meanwhile, the new IF point operator can extend our horizons in the exploration of the relationship between fuzzy sets and intuitionistic fuzzy sets. Specifically, a special case of the new IF point operator would be entitled as the memoryless multi-stage voting method, with which the decision makers are assumed to be affected only by the outcomes of the latest round of voting. It is proved that the memoryless multi-stage voting method converges to the limit produced by the infinite number of iterations much faster than the traditional voting method. Furthermore, a numerical example is employed to demonstrate the validity and performance of the memoryless multi-stage voting approach.     

Extension of VIKOR method for decision making problem based on hesitant fuzzy set

The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared.     

A methodology for analyzing decision networks, based on information theory

This paper assumes the organization as a distributed decision network. It proposes an approach based on application and extension of information theory concepts, in order to analyze informational complexity in a decision network, due to interdependence between decision centers.Based on this approach, new quantitative concepts and definitions are proposed in order to measure the information in a decision center, based on Shannon entropy and its complement in possibility theory, U uncertainty. This approach also measures the quantity of interdependence between decision centers and informational complexity of decision networks.The paper presents an agent-based model of organization as a graph composed of decision centers. The application of the proposed approach is in analyzing and assessing a measure to the organization structure efficiency, based on informational communication view. The structure improvement, analysis of information flow in organization and grouping algorithms are investigated in this paper. The results obtained from this model in different systems as distributed decision networks, clarifies the importance of structure and information distribution sources effect’s on network efficiency.     

Rough set theory fuzzy belief functions related to statistical confidence:application & evaluation for golf course closing

Rough set theory is developed in terms of fuzzy sets that will allow a decision maker to determine certain and possible rules. In the application presented these rules are determined for the decision to close a golf course when the number of rounds of golf to be played is anticipated to be low. Attributes having an effect on the number of rounds of golf to be played are statistically analyzed and those negative factors are selected for generating rules for closing. Furthermore, the degree of belief of the decision maker in these generated rules is determined to be directly related to statistical confidence intervals.     

Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

Within the multicriteria aggregation–disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM’s preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM’s preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach.     

A new methodology for sustainability measurement of banks based on rough set theory

Central European Journal of Operations Research - Sustainability measurement of banks is a complicated process, mainly dependent on the intuition of banking and sustainability experts. In this...     

The challenge of optimizing expensive black boxes: a scatter search/rough set theory approach

There is renewed interest in the development of effective and efficient methods for optimizing models of which the optimizer has no structural knowledge. This is what in the literature is referred to as optimization of black boxes. In particular, we address the challenge of optimizing expensive black boxes, that is, those that require a significant computational effort to be evaluated. We describe the use of rough set theory within a scatter search framework, with the goal of identifying high-quality solutions with a limited number of objective function evaluations. The rough set strategies that we developed take advantage of the information provided by the best and diverse solutions found during the search, in order to define areas of the solution space that are promising for search intensification. We test our procedure on a set of 92 nonlinear multimodal functions of varied complexity and size and compare the results with a state-of-the-art procedure based on particle swarm optimization.     

The semantics of realizability for the constructive set theory based on hyperarithmetical predicates

A semantics of realizability based on hyperarithmetical predicates of membership is introduced for formulas of the language of set theory. It is proved that the constructive set theory without the extensionality axiom is sound with this semantics.