Interval-valued Intuitionistic Fuzzy Set Theory Research Articles

Modelling attack and defense games in infrastructure networks with interval-valued intuitionistic fuzzy set payoffs

Infrastructure networks are critical components of contemporary society, and numerous approaches have been suggested for the selection of strategies to protect these networks. However, for uncertain environments, research on attack and defense game models for infrastructure networks is limited. Therefore, after reviewing the existing approaches, a method based on interval-valued intuitionistic fuzzy set (IVIFS) theory is proposed for attack and defense games in critical infrastructure networks. First, we present the process of constructing the game model proposed in this paper, which mainly includes the formulation of the cost model, the strategies, and the method of generating IVIFS payoffs. Next, the Nash equilibria of the game are identified by a pair of nonlinear programming models based on IVIFS theory. Finally, experiments are conducted on a target scale-free network, and an investigation into the variation patterns of the Nash equilibria under different circumstances is also conducted. We provide explanations for these variation patterns by considering payoffs from the perspective of mathematical programming models. Furthermore, we find that compared to the existing attack and defense game model with crisp payoffs, the model proposed in this paper leads to superior Nash equilibria. Our work is a preliminary attempt to analyse attack and defense games for infrastructure networks based on IVIFS theory, providing a method for assessing payoffs in uncertain environments for the attacker and defender. This topic deserves further study.

Interval-Valued Intuitionistic Fuzzy Synthetic Measure (I-VIFSM) Based on Hellwig’s Approach in the Analysis of Survey Data

Several complex phenomena are measured with the use of tools in the form of a questionnaire where the values of criteria are assessed by the respondents using ordinal scales. Therefore, a special method of construction of synthetic measure is needed which takes into account the fact that such measurement scale allows only to determine the relationship between the states of objects: diversity, equality, minority, and majority. The main goal of this study is to propose a synthetic measure based on Hellwig’s approach and the interval-valued intuitionistic fuzzy set theory which allows to measure complex social phenomena under uncertainty, including data from questionnaire surveys. First, the method of converting ordinal data from questionnaires to interval-valued intuitionistic fuzzy sets (I-VIFS) is proposed. Next, the method of constructing a synthetic measure for I-VIFS is presented. Finally, through this synthetic measure, the optimism coefficient is defined, which allows to set the limits of the intervals for I-VIFS parameters. The usefulness of the proposed approach is showed using the results of a questionnaire survey of the subjective quality of life of inhabitants of selected communes in Poland. Results indicate that the synthetic measure is suitable and effective to evaluate complex phenomena based on ordinal data from questionnaire surveys under the conditions of measurement uncertainty. Moreover, the use of the concept of the optimism coefficient increases the flexibility of its application.

Project Delivery System Selection with Interval-Valued Intuitionistic Fuzzy Set Group Decision-Making Method

A project delivery system (PDS) is the relationship and contractual structure between the owner and the contractors of a construction project; this system defines the roles and responsibilities of the participates involved in the project. Selecting a suitable PDS is one of the keys to achieve a construction project’s goals. PDS selection is a typical multi-attribute decision making problem that can be effectively solved by group decision making. Interval-valued intuitionistic fuzzy set (IVIFS) is used to solve complex decision making problems, especially multi-attribute group decision making problems, under uncertain circumstances. In this paper, a group decision making model for PDS selection is proposed using IVIFS theory as basis. In order to improve the reliability of decision making, a new decision maker weight determination method is introduced based on information utility level. Finally, the validity of the method is verified through a case study. This method can aid project owners in PDS selection.

Target priority determination methods by interval-valued intuitionistic fuzzy sets with unknown attribute weights

The paper aims at the problem of multi-targets threat degree being hard to be evaluated accurately in complex air defense battlefield environments. Combined with multi-sensors information fusion and interval-valued intuitionistic fuzzy sets (IVIFS) theories, the target priority determination is studied. The score and accuracy functions of IVIFS are improved with thinking about the hesitating information in order to increase the rationality. Then, the influence factors of target priority and the nonlinear relationship between the influence factors and target priority are analyzed. Next, the algorithms for calculating the factor weights and sensor weights are given. Based on the theory of IVIFS and technique for order preference by similarity to an ideal solution (TOPSIS), two methods of target priority determination based on the IVIFS and TOPSIS are proposed. At last, an application example verifies the effectiveness and flexibility of the proposed algorithms.

Hydrogen Production Technologies Evaluation Based on Interval-Valued Intuitionistic Fuzzy Multiattribute Decision Making Method

We establish a decision making model for evaluating hydrogen production technologies in China, based on interval-valued intuitionistic fuzzy set theory. First of all, we propose a series of interaction interval-valued intuitionistic fuzzy aggregation operators comparing them with some widely used and cited aggregation operators. In particular, we focus on the key issue of the relationships between the proposed operators and existing operators for clear understanding of the motivation for proposing these interaction operators. This research then studies a group decision making method for determining the best hydrogen production technologies using interval-valued intuitionistic fuzzy approach. The research results of this paper are more scientific for two reasons. First, the interval-valued intuitionistic fuzzy approach applied in this paper is more suitable than other approaches regarding the expression of the decision maker’s preference information. Second, the results are obtained by the interaction between the membership degree interval and the nonmembership degree interval. Additionally, we apply this approach to evaluate the hydrogen production technologies in China and compare it with other methods.

Induced interval-valued intuitionistic fuzzy Einstein ordered weighted geometric operator and their application to multiple attribute decision making

Interval-valued intuitionistic fuzzy information aggregation plays an important part in interval-valued intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on interval-valued intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop the induced interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (I-IVIFEOWG) operator. We also establish some desirable properties of this operator, such as commutativity, idempotency and monotonicity. Then, we apply the induced interval-valued intuitionistic fuzzy Einstein hybrid geometric (I-IVIFEHG) operator to deal with multiple attribute decision making under interval-valued intuitionistic fuzzy environments. Finally, an illustrative example for software quality evaluation is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Fuzzy multi-objective group decision making based on interval-valued intuitionistic fuzzy set

In order to improve the accuracy of data decision making,an optimization approach was proposed for the algorithm of multi-objectives group decision making.By the interval-valued intuitionistic fuzzy set theory,the optimization was approached by the method of iterative computation gradually in the situation that the part weight information was incomplete usually.Results of the simulation indicate that the algorithm has low time complexity,and can be implemented in the computer easily;moreover,it also shows the effectiveness and accuracy of the algorithm.

Interval-valued intuitionistic fuzzy soft sets and their properties

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the interval-valued intuitionistic fuzzy soft set theory is proposed. Our interval-valued intuitionistic fuzzy soft set theory is a combination of an interval-valued intuitionistic fuzzy set theory and a soft set theory. In other words, our interval-valued intuitionistic fuzzy soft set theory is an interval-valued fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension of the interval-valued fuzzy soft set theory. The complement, “and”, “or”, union, intersection, necessity and possibility operations are defined on the interval-valued intuitionistic fuzzy soft sets. The basic properties of the interval-valued intuitionistic fuzzy soft sets are also presented and discussed.

An interval-valued rough intuitionistic fuzzy set model

Rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. This paper presents an interval-valued rough intuitionistic fuzzy (IF) set model by means of integrating the classical Pawlak rough set theory with the interval-valued IF set theory. In this paper, we first introduce some concepts and properties of interval-valued IF set theory. Then, the rough approximations of an interval-valued IF set in the classical Pawlak approximation space and the generalised Pawlak approximation space are respectively defined, and some fundamental properties of the approximation operators are studied. Furthermore, by employing cut sets of interval-valued IF sets, classical representations of interval-valued rough IF approximation operators are presented, and the connections between special binary relations and interval-valued rough IF approximation operators are constructed. Finally, we discuss the knowledge reduction and knowledge discovery of the interval-valued IF information systems.

Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group

Szmidt and Kacprzyk (Lecture Notes in Artificial Intelligence 3070:388---393, 2004a) introduced a similarity measure, which takes into account not only a pure distance between intuitionistic fuzzy sets but also examines if the compared values are more similar or more dissimilar to each other. By analyzing this similarity measure, we find it somewhat inconvenient in some cases, and thus we develop a new similarity measure between intuitionistic fuzzy sets. Then we apply the developed similarity measure for consensus analysis in group decision making based on intuitionistic fuzzy preference relations, and finally further extend it to the interval-valued intuitionistic fuzzy set theory.

An Interval-Valued Intuitionistic Fuzzy Rough Set Model

Given a widespread interest in rough sets as being applied to various tasks of data analysis it is not surprising at all that we have witnessed a wave of further generalizations and algorithmic enhancements of this original concept. This paper proposes an interval-valued intuitionistic fuzzy rough model by means of integrating the classical Pawlak rough set theory with the interval-valued intuitionistic fuzzy set theory. Firstly, some concepts and properties of interval-valued intuitionistic fuzzy set and interval-valued intuitionistic fuzzy relation are introduced. Secondly, a pair of lower and upper interval-valued intuitionistic fuzzy rough approximation operators induced from an interval-valued intuitionistic fuzzy relation is defined, and some properties of approximation operators are investigated in detail. Furthermore, by introducing cut sets of interval-valued intuitionistic fuzzy sets, classical representations of interval-valued intuitionistic fuzzy rough approximation operators are presented. Finally, the connections between special interval-valued intuitionistic fuzzy relations and interval-valued intuitionistic fuzzy rough approximation operators are constructed, and the relationships of this model and the others rough set models are also examined.