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In this paper, considering the traditional geometric operation laws and Pythagorean fuzzy information, a varies of new distance measures of Pythagorean fuzzy set are proposed, such as generalized Pythagorean fuzzy ordered geometric distance (GPFOWGD) measures and generalized Pythagorean fuzzy hybrid weighted geometric distance (GPFHWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, a decision-making model is built and illustrated by a mathematical calculation example to evaluate the service quality of sports clubs using Pythagorean fuzzy information. The results display that the approach is uncomplicated, valid and simple to compute. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiple attribute decision making. [ABSTRACT FROM AUTHOR]

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Quality function deployment (QFD) is an useful tool to solve Multi-criteria decision making, which can translate customer requirements (CRs) into the technical attributes (TAs) of a product and helps maintain a correct focus on true requirements and minimizes misinterpreting customer needs. In applying quality function deployment, rating technical attributes from input variables is a crucial step in fuzzy environments. In this paper, a new approach is developed, which rates technical attributes by objective penalty function and fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) based on weighted Hamming distance under the case of uncertain preference characteristics of decision makers in fuzzy quality function deployment. A pair of nonlinear programming models with constraints and a relevant pair of nonlinear programming models with unconstraints called objective penalty function models are proposed to gain the fuzzy important numbers of technical attributes. Then, this paper compares the fuzzy numbers by fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) method based on weighted Hamming distance in consideration of the uncertain preference characteristics of decision makers. To end with, the developed method is examined with the numerical examples. [ABSTRACT FROM AUTHOR]

The multiple attribute decision making (MADM) with interval grey uncertain linguistic (IGUL) is a topic of current interest, and various methods have been developed. However, few approaches taking the behavioral characteristics of the decision maker into account. In this paper, an extension of TODIM (i.e., an acronym in Portuguese of interactive and multiple attribute decision making) method, in which three behavioral characteristics of the decision maker (i.e., risk aversion, reference dependence and loss aversion) are considered, is proposed. First, the δ-Hamming distance is defined to deal with the interval grey uncertain linguistic variables by considering the level of the decision maker's risk aversion, and its distinguish ability is validated by compared to the classical Hamming distance. Then, the details of the TODIM· SIR method is demonstrated: (i) considering the reference dependence behaviour of the decision maker, the positive-ideal alternative (i.e., PIA) and the negative-ideal alternative (i.e., NIA) are defined, and the gain and loss degrees of each alternative relative to NIA and PIA are computed based on the δ-Hamming distance; (ii) taking the loss aversion behaviour of the decision maker into account, the perceived dominance degree of the decision maker for the gain and the loss is calculated; (iii) according to the idea of the Superiority and Inferiority Ranking method (i.e., SIR, an outranking method), the Gain-flow and the Loss-flow are defined, and the partial ranking orders and the complete ranking order are obtained. Finally, two numerical examples are given to illustrate the robustness and validity of the method, and a comparative analysis is also conducted to compare the TODIM· SIR method with both the classical TODIM method and the classical SIR method. [ABSTRACT FROM AUTHOR]

Neutrosphic sets define the uncertainty with three parameters, namely truthiness, indeterminacy and falsity. COmbinative Distance-based ASsessment (CODAS) method computes the Euclidean as the primary measure and Hamming distances as the secondary measure to assess alternatives based on predetermined criteria. In this paper, CODAS method is extended to its interval-valued neutrosophic CODAS version for handling the vagueness and impreciseness in human thoughts. A fuzzy inference system can be used as a decision making process of mapping from a given input to an output using fuzzy logic. The inputs of the used ordinary fuzzy Mamdani type inference system are crisp while the rules are fuzzy. The applicability of the proposed methodology is illustrated through the assessment of livability index of urban districts. Sensitivity analysis demonstrates the robustness of the decision-making methodology. [ABSTRACT FROM AUTHOR]

In this paper, a new version of distance measure for hesitant fuzzy linguistic term sets is developed. The new version of distance measure provides an objective way to handle the diverse dimensions of two HFLTSs, i.e., without shortening the HFLTS to be a linguistic interval or extending the shorter one by adding linguistic terms. The Hamming distance, the Euclidean distance and the corresponding forms are put forward. By the relationship between the distance measure and the similarity measure, some parallel similarity measures are also investigated. As applications of the proposed measures, the issues of pattern recognition, clustering analysis and multi-criteria decision making are considered. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new method for intuitionistic fuzzy decision making problems with induced aggregation operators and distance measures. Firstly, we introduce the intuitionistic fuzzy induced ordered weighted averaging distance (IFIOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the distance measures and uncertain information represented by intuitionistic fuzzy numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision-maker by using order-inducing variables in the aggregation of the distance measures. We further generalize the IFIOWAD by using weighted average. The result is the intuitionistic fuzzy induced ordered weighted averaging weighted average distance (IFIOWAWAD) operator. Finally, a practical example about the selection of investments is provided to illustrate the developed intuitionistic fuzzy aggregation operators. [ABSTRACT FROM AUTHOR]

As generalize of the hesitant fuzzy sets, hesitant interval-valued fuzzy sets (HIVFSs), which permits the memberships of an element to a given set having a few different interval values in [0,1] rather than real numbers, can be considered as a powerful tool to express uncertain information in the human decision making process. Based on the traditional Hamming distance, Euclidean distance, Hausdorff distance, and generalized distance, in this paper, we propose a variety of distance measures for hesitant interval-valued fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant interval-valued ordered weighted distance measures and hesitant interval-valued ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Finally, we shall present a numerical example to show potential evaluation of emerging technology commercialization with hesitant interval-valued fuzzy information in order to illustrate the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new fuzzy decision making technique called the fuzzy induced heavy ordered weighted averaging distance (FIHOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the Hamming distance, the heavy OWA (HOWA) and uncertain information represented as fuzzy numbers. A key feature of the FIHOWAD operator is that it generalizes a wide range of aggregation operators such as the fuzzy minimum distance, the fuzzy weighted Hamming distance (FWHD), the fuzzy OWA distance (FOWAD), the fuzzy IOWA distance (FIOWAD) and the fuzzy heavy OWA distance (FHOWAD) operators. We studied some of its main properties and different particular cases. Finally, we present a numerical example to illustrate the new approach in a financial decision making problem. [ABSTRACT FROM AUTHOR]