Triangular Fuzzy Preference Relations Research Articles

Ranking factors critical to the adoption ofmHealth devices in clinical use among Indian healthcare providers using consistent triangular fuzzy preference relations (TFPR)

Ranking factors critical to the adoption ofmHealth devices in clinical use among Indian healthcare providers using consistent triangular fuzzy preference relations (TFPR)

Additive consistent triangular fuzzy preference relation and likelihood comparison algorithm based group decision making

Additive consistent triangular fuzzy preference relation and likelihood comparison algorithm based group decision making

A group decision making method with intuitionistic triangular fuzzy preference relations and its application

This paper aims to offer an intuitionistic triangular fuzzy group decision making method by preference relations. For this purpose, the concept of intuitionistic triangular fuzzy preference relations (ITFPRs) is first offered. Then, an additive consistency concept for ITFPRs is introduced. Meanwhile, a programming model is built to check the consistency of ITFPRs. Considering the case where incomplete ITFPRs are obtained, two programming models are constructed, which aim at maximizing the consistency and minimizing the uncertainty of missing information. To achieve the goals of the minimum total adjustment and the smallest number of adjusted elements, two programming models are established to repair inconsistent ITFPRs. In addition, the weights of decision makers are considered, and the consensus levels of individual ITFPRs are studied to ensure the representativeness of decision results. When individual ITFPRs do not meet the consensus requirement, a programming model to reach the consensus threshold is constructed, which permits different intuitionistic triangular fuzzy variables (ITFVs) to have different adjustments and minimizes the total adjustment. Finally, a group decision making algorithm with ITFPRs is proposed, and its feasibility and efficiency are demonstrated through an example of evaluating the intelligent traditional Chinese medicine decocting centers.

A nonlinear programming approach to solve MADM problem with triangular fuzzy preference and non-preference information

In this paper, we present a new approach to solve multi-attribute decision making (MADM) problems considering subjective preferences and non-preferences of the decision maker in the form of triangular fuzzy preference relations and triangular fuzzy non-preference relations, respectively. Some important characteristics of these relations are used to form non-linear programming problems corresponding to lower, middle, and upper limits of the triangular fuzzy numbers. The optimization problems corresponding to lower and upper limits are solved to obtain corresponding limits of basic triangular fuzzy multiplicative preference weights (TFMPWs) and basic triangular fuzzy multiplicative non-preference weights (TFMNPWs). The obtained optimal weight values are used to find the modal values of TFMPWs and TFMNPWs that helps in the ranking of the alternatives. The working of the proposed approach is demonstrated by solving a MADM problem from the literature. Furthermore, to validate the superiority of the proposed approach, a comparative analysis with similar existing approaches has been provided. The obtained results reveal the applicability and usefulness of the proposed approach.

A New Model for Deriving the Priority Weights from Hesitant Triangular Fuzzy Preference Relations

Fuzzy preference relation is a common tool to express the uncertain preference information of decision maker in the process of decision making. However, the traditional fuzzy preference relation will fail under hesitant fuzzy environment as the membership has a single value. In addition, it is very difficult to obtain the precise membership values. Therefore, a new model of fuzzy preference relation is proposed in this paper. Firstly, the concept of hesitant triangular fuzzy preference relation is defined and its properties are investigated based on the concepts of hesitant fuzzy set, hesitant triangular fuzzy set, fuzzy preference relation, and hesitant fuzzy preference relation. Then, the steps of applying this novel model are offered for the case of determining the weights of failure modes. Finally, an example is used to illustrate the proposed model.

A Goal-Programming-Based Heuristic Approach to Deriving Fuzzy Weights in Analytic Form from Triangular Fuzzy Preference Relations

Triangular fuzzy preference relations (TFPRs) have long been viewed as an effective framework to express subjective preferences with ambiguity in fuzzy multicriteria decision-making systems. This paper focuses on solving two important and challenging issues: First, how to judge the quality of nondiagonal preferences in a TFPR; and second, how to find an analytic solution of optimal fuzzy weights for consistent TFPRs and an analytic solution of heuristic fuzzy weights for inconsistent TFPRs. This paper analyzes two existing normalization models of triangular fuzzy weights and illustrates their deficiency. Notions of normalized triangular fuzzy multiplicative weights (TFMWs) and basic TFMWs are then introduced and used to characterize a group of triangular fuzzy weight vectors with equivalency. This paper proposes transformation models among triangular fuzzy weights, normalized TFMWs and basic TFMWs, and employs basic TFMWs to define consistent TFPRs. Some important properties are presented for the fuzziness of a consistent TFPR and its corresponding basic TFMWs. These properties are subsequently used to develop a two-step approach consisting of three-goal programming (GP) models to find basic TFMWs of consistent TFPRs. By using the Lagrangian multiplier method, this paper finds analytic solutions of the three GP models and obtains optimized basic TFMWs denoted by three computation formulas for consistent TFPRs. By changing the constraints of the three GP models and using heuristics, three concise and visualized formulas are devised, respectively, to obtain the lower and upper support bounds and the modal values of heuristic-based TFMWs for any TFPR. A numerical example comprising of a consistent TFPR and two inconsistent TFPRs is supplied and a comparative study is conducted to show that the two challenging issues are reasonably solved, and a hierarchical fuzzy multicriteria decision-making example is offered to illustrate the applicability of the proposed fuzzy priority model.

Fuzzy Group Consensus Decision Making and Its Use in Selecting Energy-Saving and Low-carbon Technology Schemes in Star Hotels.

Energy-saving and low-carbon technologies play important roles in reducing environmental risk and developing green tourism. An energy-saving and low-carbon technology scheme selection may often involve multiple criteria and sub-criteria as well as multiple stakeholders or decision makers, and thus can be structured as a hierarchical multi-criteria group decision making problem. This paper proposes a framework to solve group consensus decision making problems, where decision makers’ preferences between the alternatives considered with respective to each criterion are elicited by the paired comparison method, and expressed as triangular fuzzy preference relations (TFPRs). The paper first simplifies the existing computation formulas used to determine triangular fuzzy weights of TFPRs. A consistency index is then devised to measure the inconsistency degree of a TFPR and is used to check acceptable consistency of TFPRs. By introducing a possibility degree formula of comparing any two triangular fuzzy weights, an index is defined to measure the consensus level between an individual ranking order and the group ranking order for all alternatives. A consensus model is developed in detail for solving group decision making problems with TFPRs. A case study of selecting energy-saving and low-carbon technology schemes in star hotels is provided to illustrate how to apply the proposed group decision making consensus model in practice.

A New Method for Triangular Fuzzy Compare Wise Judgment Matrix Process Based on Consistency Analysis

To cope with the uncertainty in the process of decision making, fuzzy preference relations are proposed and commonly applied in many fields. In practical decision-making problems, the decision maker may use triangular fuzzy preference relations to express his/her uncertainty. Based on the row weighted arithmetic mean method, this paper develops an approach for deriving the fuzzy priority vector from triangular fuzzy compare wise judgment matrices. To do this, this paper first analyzes the upper and lower bounds of the triangular fuzzy priority weight of each alternative, which indicates the decision maker’s optimistic and pessimistic attitudes. Based on (acceptably) consistent multiplicative preference relations, the triangular fuzzy priority vector is obtained. Meanwhile, a consistency concept of triangular fuzzy compare wise judgment matrices is defined, and the consistent relationship between triangular fuzzy and crisp preference relations is studied. Different to the existing methods, the new approach calculates the triangular fuzzy priority weights separately. Furthermore, the fuzzy priority vector from trapezoidal fuzzy reciprocal preference relations is considered. Finally, the application of the new method to new product development (NDP) project screening is tested, and comparative analyses are also offered.

Consistency analysis and priority derivation of triangular fuzzy preference relations based on modal value and geometric mean

Triangular fuzzy preference relation (TFPR) is an effective framework to model pairwise estimations with imprecision and vagueness. In order to obtain a reliable and rational decision result, it is important to investigate consistency and priority derivation of TFPRs. The paper analyzes existing definitions and properties of consistent TFPRs, and illustrates that they have no invariance with respect to permutations of decision alternatives. A new triangular fuzzy arithmetic based transitivity equation is introduced to define consistent TFPRs. The new transitivity equation reflects multiplicative consistency of modal values and multiplicative consistency of geometric means of triangular fuzzy estimations. Some properties are presented for consistent TFPRs, and a notion of acceptable consistency is put forward for TFPRs. Geometric mean and uncertainty ratio based transformation formulae are devised to convert normalized triangular fuzzy multiplicative weights into consistent TFPRs. A logarithmic least square model is further established for deriving a normalized triangular fuzzy multiplicative weight vector from a TFPR with acceptable consistency. A geometric mean based method is developed to compare and rank triangular fuzzy multiplicative weights. Three numerical examples including a group decision making problem are examined to demonstrate validity and advantages of the proposed models.

Optimal Weight Determination and Consensus Formation under Fuzzy Linguistic Environment

This paper deals with the consensus problem from the linguistic preference relations. The linguistic variables are transformed into triangular fuzzy numbers. Then an optimal consensus model is proposed to derive weights for fuzzy triangular fuzzy preference relations. An iterative algorithm is presented to describe the consensus reaching process. By changing the weights and modifying a pair of individual's comparison judgments which have largest deviation value to the group judgments, the consensus reaching process can terminate while both individual consensus index (ICI) and group consensus index (GCI) are controlled with predefined thresholds. The algorithm aims to preserve the decision-makers’ original information as much as possible. Finally, an example is given to show the effectiveness of the proposed method.