Symmetric Triangular Interval Type-2 Intuitionistic Fuzzy Sets with Their Applications in Multi Criteria Decision Making

An improved CLVA method for evaluating the endurance quality level of young male basketball players with 2-tuple linguistic neutrosophic information

For a long time, the level of endurance quality of our male basketball athletes is not high, and there is a gap with the strongest countries in Europe and America. The former head coach of Chinese men’s basketball team diagnosed the biggest problem of Chinese men’s basketball team and Chinese youth men’s basketball team is the poor quality of endurance. It is especially important to strengthen the endurance training of our basketball players and improve their endurance level. However, from the current situation, the teams in the training due to the lack of standards for endurance quality training has led to a great blindness in endurance quality training. The endurance quality level evaluation of young male basketball players is a classic multiple attribute group decision making (MAGDM) issue with vague, inconsistent, and indeterminate information. The 2-tuple linguistic neutrosophic sets (2TLNSs) is an appropriate form to express the indeterminate decision-making information in the endurance quality level evaluation of young male basketball players. Therefore, in this paper, the 2-tuple linguistic neutrosophic numbers CLVA (2TLNN-CLVA) is built based on traditional close value (CLVA) method and applies it to evaluate the endurance quality level of young male basketball players. Finally, a numerical example for evaluating the endurance quality level of young male basketball players has been given and some decision comparisons are also conducted to further illustrate the advantages of the 2TLNN-CLVA method.

Applications to biogas-plant implementation problem based on type-2 picture fuzzy matrix game under new minkowski type measures

To manage ambiguity and uncertainty information in real life problems, certain intellectuals have initiated numerous modifications of fuzzy sets. But, in certain situations, the decision-makers have been neglected to take a feasible decision. For instance, when an intellectual provides information in the form of a two-dimension or type-1 fuzzy set, then the prevailing theories have been neglected. For this, in this study, we elaborated the new idea of type-2 picture fuzzy sets (T2-PFS) and their algebraic laws have been given. Moreover, by using the T2-PFS, Hamacher aggregation operators are proposed and discussed their important properties. The Minkowski sorts of measures under the T2-PFS are also initiated. In the current study, we aim to utilize the matrix game in a type-2 picture fuzzy environment. By using the proposed operators and measures based on the Hausdorff metric. The elaborated idea has been defined with the biogas-plant implementation dilemma to verify the pertinence and authenticity. Lastly, to discuss the sensitivity analysis and geometrical shown of the initiated works, certain examples are illustrated to determine the supremacy and consistency of the proposed approaches.

Interaction hamy mean operators for complex pythagorean fuzzy information and their applications to security threats in computers

Complex Pythagorean fuzzy set (CPFS) is a massive influential principle for managing ambiguity and inconsistent information in genuine life dilemmas. To determine the relationship among any number of attributes, the Hamy mean (HM) operators based on interaction operational laws are very dominant and massive flexible to manage awkward and problematic information. This study aims to combine the complex Pythagorean fuzzy (CPF) information with interaction HM operators to initiate the CPF interaction HM (CPFIHM) operator, CPF interaction weighted HM (CPFIWHM) operator, CPF interaction dual HM (CPFIDHM) operator, CPF interaction weighted dual HM (CPFIWDHM) operator and their powerful properties. Additionally, a decision-making strategy for determining the security threats in the computer is elaborated under the interaction of HM operators based on the CPF setting. Numerous examples are illustrated with the help of presented operators to determine the consistency and flexibility of the investigated operators. Finally, with the help of sensitivity analysis, advantages, and geometrical representation, the supremacy, and efficiency of the presented works are also elaborated.

Modeling pricing decision problem based on interval type-2 fuzzy theory

In practical decision-making problems, decision makers are often affected by uncertain parameters because the exact distributions of uncertain parameters are usually difficult to determine. In order to deal with this issue, the major contribution in this paper is to propose a new type of type-2 fuzzy variable called level interval type-2 fuzzy variable from the perspective of level-sets, which is a useful tool in modeling distribution uncertainty. With our level interval type-2 fuzzy variable, we give a method for constructing a parametric level interval (PLI) type-2 fuzzy variable from a nominal possibility distribution by introducing the horizontal perturbation parameters. The proposed horizontal perturbation around the nominal distribution is different from the vertical perturbation discussed in the literature. In order to facilitate the modeling in practical decision-making problems, for a level interval type-2 fuzzy variable, we define its selection variable whose distribution can be determined via its level-sets. The numerical characteristics like expected value and second order moments are important indices in practical optimization and decision-making problems. With this consideration, we establish the analytical expressions about the expected values and second order moments of the selection variables of PLI type-2 trapezoidal, normal and log-normal fuzzy variables. Furthermore, in order to derive the analytical expressions about the numerical characteristics of the selection variable for the sums of the common PLI type-2 fuzzy variables, we discuss the arithmetic about the sums of common PLI type-2 fuzzy variables. Finally, we apply the proposed optimization method to a pricing decision problem to demonstrate the efficiency of our new method. The computational results show that even a small perturbation of the nominal possibility distribution can affect the quality of solutions.

Modified Vogel’s approximation method for transportation problem under uncertain environment

The fuzzy transportation problem is a very popular, well-known optimization problem in the area of fuzzy set and system. In most of the cases, researchers use type 1 fuzzy set as the cost of the transportation problem. Type 1 fuzzy number is unable to handle the uncertainty due to the description of human perception. Interval type 2 fuzzy set is an extended version of type 1 fuzzy set which can handle this ambiguity. In this paper, the interval type 2 fuzzy set is used in a fuzzy transportation problem to represent the transportation cost, demand, and supply. We define this transportation problem as interval type 2 fuzzy transportation problems. The utility of this type of fuzzy set as costs in transportation problem and its application in different real-world scenarios are described in this paper. Here, we have modified the classical Vogel’s approximation method for solved this fuzzy transportation problem. To the best of our information, there exists no algorithm based on Vogel’s approximation method in the literature for fuzzy transportation problem with interval type 2 fuzzy set as transportation cost, demand, and supply. We have used two Numerical examples to describe the efficiency of the proposed algorithm.

Resolving Indeterminacy Approach to Solve Multi-Criteria Zero-Sum Matrix Games with Intuitionistic Fuzzy Goals

The intuitionistic fuzzy set (IFS) is applied in various decision-making problems to express vagueness and showed great success in realizing the day-to-day problems. The principal aim of this article is to develop an approach for solving multi-criteria matrix game with intuitionistic fuzzy (I-fuzzy) goals. The proposed approach introduces the indeterminacy resolving functions of I-fuzzy numbers and discusses the I-fuzzy inequalities concept. Then, an effective algorithm based on the indeterminacy resolving algorithm is developed to obtain Pareto optimal security strategies for both players through solving a pair of multi-objective linear programming problems constructed from two auxiliary I-fuzzy programming problems. It is shown that this multi-criteria matrix game with I-fuzzy goals is an extension of the multi-criteria matrix game with fuzzy goals. Moreover, two numerical simulations are conducted to demonstrate the applicability and implementation process of the proposed algorithm. Finally, the achieved numerical results are compared with the existing algorithms to show the advantages of our algorithm.

Intuitionistic Type-2 Fuzzy Set and Its Properties

Decision making under uncertainty describes situations that consider a profound lack of knowledge, where the functional form is completely unknown, and often, the relevant input and output variables are unknown as well. Data, being the vital input of decision making, contain a dissimilar level of imprecision that necessitates different approaches for making a proper and legitimate decision. In this article, we propose the concept of the intuitionistic type-2 fuzzy set (IT2FS). Several arithmetic operations on IT2FS such as union, intersection, complement, containment, etc., are defined, and the related algebraic properties of IT2FS are also studied. Subsequently, we define two new operators, namely the necessity operator and the possibility operator, to convert an IT2FS into an ordinary T2FS, and then discuss some of their basic properties. Moreover, in this study, two distance measures, the Hamming distance and Euclidian distance of IT2FS, are proposed, and their applications are illustrated with an example.

Grey Regulatory Focus Theory Weighting Method for the Multi-Criteria Decision-Making Problem in Evaluating University Reputation

Evaluating the reputation of higher institutions is important as a benchmark for the continuous development of universities. In multi-criteria decision-making (MCDM), the estimation of the criteria weight is significant in improving the accuracy of the evaluation results. However, criteria weights assigned by decision makers (DMs) can be inaccurate when not measured from the orientations from which the DMs pursue their decision goals. This paper combines the grey system theory (GST) and regulatory focus theory (RFT) in estimating the weights of criteria by measuring the promotional and prevention focus orientations of the DMs and representing it as grey numbers. In this paper, we showed not all weight measurements from the DMs are symmetrical. In essence, to improve the accuracy of the MCDM weights, the grey regulatory focus theory (GRFT) weighting method is proposed to estimate the weights of an MCDM problem as well as aggregating the weights of the group DMs, thereby overcoming the limitation of a single orientation measurement. Furthermore, the GRFT weighting method is applied in ranking four universities in Xi’an city of China from a sample data from 1,200 students. The most reputable university is consistent with the other ranking indexes in the literature.

Some Interval-Valued Intuitionistic Fuzzy Dombi Hamy Mean Operators and Their Application for Evaluating the Elderly Tourism Service Quality in Tourism Destination

In this paper, we expand the Hamy mean (HM) operator and Dombi operations with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval-valued intuitionistic fuzzy Dombi Hamy mean (IVIFDHM) operator, interval-valued intuitionistic fuzzy weighted Dombi Hamy mean (IVIFWDHM) operator, interval-valued intuitionistic fuzzy dual Dombi Hamy mean (IVIFDDHM) operator, and interval-valued intuitionistic fuzzy weighted dual Dombi Hamy mean (IVIFWDDHM) operator. Then the MADM models are designed with IVIFWDHM and IVIFWDDHM operators. Finally, we gave an example for evaluating the elderly tourism service quality in tourism destination to show the proposed models.

Prioritized Linguistic Interval-Valued Aggregation Operators and Their Applications in Group Decision-Making Problems

The linguistic interval-valued intuitionistic fuzzy (LIVIF) set is an efficient tool to represent data in the form of interval membership degrees in a qualitative rather than a quantitative manner. The LIVIF set combines the features of interval-valued intuitionistic fuzzy sets (IFSs) and the linguistic variables (LV) and hence provides more freedom to decision-makers. Under this environment, the main objective of this manuscript is to propose some new aggregation operators by capturing the prioritized relationship between the objects. For this, different weighted averaging and geometric aggregation operators are proposed in which preferences related to each object are expressed in terms of LIVIF numbers. Desirable properties of the proposed operators are studied. Further, a group decision-making (DM) approach is presented to solve the multi-attribute DM problems, and its efficiency has been verified with an illustrative example.