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2021
The paper is devoted to the problem of multi criteria decision making under linguistic uncertainty. Information of different approaches for modeling linguistic uncertainty have been analyzed. The concept of z-numbers proposed by L. Zadeh have been presented. Z-number is presented as cortege of two fuzzy number A and B, where A is analyzed factor, B is reliability of A assessment. The method of conversion z-numbers into generalized fuzzy numbers have been applied. As test have been used server selection problem. As decision making model have been used weighted average method. All calculations and results are presented.
Hesitant fuzzy linguistic term set (HFLTS), as a °exible tool to represent people's uncertain cognition, has attracted lots of scholars' research interests, and a series of methodologies have been proposed to deal with a variety of decision-making problems. In this paper, we develop a hesitant fuzzy linguistic possibility degree-based linear assignment (HFL-PDLA) method to tackle the multiple criteria decision-making (MCDM) problems under hesitant fuzzy linguistic environment. Firstly, we de¯ne the possibility degree of hesitant fuzzy linguistic element (HFLE). Additionally, some relevant concepts related to the HFL-PDLA method are proposed, such as the relative di®erence matrix, the rank contribution matrix, the optimal permutation matrix, etc. Furthermore, the algorithm of the HFL-PDLA method is given to deal with hesitant fuzzy linguistic MCDM problems. Moreover, we apply the HFL-PDLA method to deal with a practical case which is to select the optimal treatment technology for disposing the outspent or old medical apparatuses and instruments in West China Hospital (WCH). Finally, we show the advantages of the HFL-PDLA method by making some comparative analyses with the TOPSIS method, the VIKOR method the PROMETHEE method and the LINMAP method.
Mathematics and Statistics, 2021
Dual hesitant fuzzy set (DHFS) consists of two parts: membership hesitant function and non-membership hesitant function. This set supports more exemplary and flexible access to set degrees for each element in the domain and can address two types of hesitant in this situation. It can be considered a powerful tool for expressing uncertain information in the decision-making process. The function of z-score, namely z-arithmetic mean, z-geometric mean, and z-harmonic mean, has been proposed with five important bases, these bases are hesitant degree for dual hesitant fuzzy element (DHFE), DHFE deviation degree, parameter , (the importance of the hesitant degree), parameter , (the importance of the deviation degree) and parameter , (the importance of membership (positive view) or non-membership (negative view). A comparison of the z-score with the existing score function was made to show some of their drawbacks. Next, the z-score function is then applied to solve multi-criteria decision making (MCDM) problems. To illustrate the proposed method's effectiveness, an example of MCDM specifically in pattern recognition has been shown.
Mathematics and Statistics, 2021
The hesitant fuzzy set (HFS) concept as an extension of fuzzy set (FS) in which the membership degree of a given element, called the hesitant fuzzy element (HFE), is defined as a set of possible values. A large number of studies are concentrating on HFE and HFS measurements. It is not just because of their crucial importance in theoretical studies, but also because they are required for almost any application field. The score function of HFE is a useful method for converting data into a single value. Moreover, the scoring function provides a much easier way to determine each alternative's ranking order for multi-criteria decision-making (MCDM). This study introduces a new hesitant degree of HFE and the z-score function of HFE, which consists of z-arithmetic mean, z-geometric mean, and z-harmonic mean. The z-score function is developed with four main bases: a hesitant degree of HFE, deviation value of HFE, the importance of the hesitant degree of HFE, , and importance of the deviation value of HFE, . These three proposed scores are compared with the existing scores functions to identify the proposed z-score function's flexibility. An algorithm based on the z-score function was developed to create an algorithm solution to MCDM. Example of secondary data on supplier selection for automated companies is used to prove the algorithms’ capability in ranking order for MCDM.
Decision Making: Applications in Management and Engineering, 2020
In the paper is presented a model for selecting a location for a brigade command post during combat operations. Considering that this is a very complex model, which can be approached from several aspects, this paper is limited only to the criteria related to the construction or arrangement of the command post, respectively, the engineering aspect. The selection process is conducted using hybrid FUCOM–Z-number–MABAC model. The FUCOM method is used to define the weight coefficients of criteria based on which the selection is made. The MABAC method, modified by applying Z-number, is used to rank alternatives. The end results indicate that the application of Z-number in decision making includes broader set of uncertainties than standard fuzzy numbers, which is very important for deciding in combat situations.
2014
Multiple Criteria Decision Making (MCDM) problems always involve uncertainty and vague values since human judgments are highly subjective. Fuzzy concept has been applied extensively in MCDM to cater for the vagueness involved. However, the reliability of information given by fuzzy numbers is questionable. Hence, Z-number was introduced to enhance the reliability of fuzzy numbers. Usage of Z-number is very limited due to its newly introduced concept. Thus, the effect of R (reliability component) on solving MCDM problems has not been thoroughly explored and clearly explained. This is due to several available techniques on how R (reliability component) could be integrated into A (restriction component). The main objective of this study is to analyze the impact of introducing the concept of reliability of Znumber into a hybrid Analytic Hierarchy Process-Fuzzy Data Envelopment Analysis (AHP-FDEA) for risk assessment purposes. The Z-number extension to MCDM problem has been implemented to...
International Transactions in Operational Research, 2002
In this paper a new methodology is given for ranking a ®nite number of alternatives being described simultaneously by a number of criteria. The criteria are of either bene®t or cost type. The criteria values and the relative weights of criteria are either numerical or linguistic expressions de®ned by fuzzy sets. The ranking philosophy is based on a fuzzy comparison procedure that takes into account both the worst-pessimistic and the best-optimistic criteria values. We describe a decision support system that assists in the ranking of alternatives for various degrees of pessimistic-optimistic index, from the lowest to the highest level of optimism. A real-world autoroad construction problem, which is described by quantitative and qualitative criteria whose relative importance is expressed by numerical or linguistic values, has been considered.
Fuzzy Logic is used in those type of problems in which the solution cannot be defined in rigid boundary either yes or no. In this environment the decision are not biased because the decisions are making on the basis of different criteria involved in that problem. Here membership functionis given to that criteria and using various fuzzy operation the calculation is done. In this thesis we have studied about fuzzy set and fuzzy logic and implement this in out ranking problem. We have also develop a code in C using DevC++ compiler by which out ranking can be done among any alternatives in different criteria.
Scientific Reports, 2023
Due to the increasing complexity of decision problems, many managers employ multiple experts to reach a good decision in a group decision making. Now, if there is ambiguity in the evaluation of experts, the use of fuzzy numbers can be useful for each expert. In these situations, the use of hesitant fuzzy numbers (HFNs) which consists of several fuzzy numbers with special conditions can be suggested. HFNs are as an extension of the fuzzy numbers to take a better determining the membership functions of the parameters by several experts. Because of simple and fast calculations, in this paper, we use triangular HFNs in the pairwise comparison matrix of analytic hierarchy process by opinions of a group of decision makers in a hesitant fuzzy environment. We define consistency of the hesitant fuzzy pairwise comparison matrix and use the arithmetic operations on the HFNs and a new method of comparing HFNs to get the hesitant fuzzy performance score. By using score function to hesitant fuzzy score we can get a final score for alternatives. Finally, a practical example is provided to show the the effectiveness of this study. The obtained results from this paper show that new method can get a better answer by keeping the experts' opinions in the process of solving the problem. It is difficult for an expert to be able to consider all aspects of a decision-making problem. Therefore, group decision-making would often be preferred and would generate more benefits than individual decision-making. The relationships among the decision makers are important factors that affect on group decision-making process 1 . Also, if they are like-minded, they are aligned in choosing their opinions, but they may have hesitance in choosing the membership function as a fuzzy number in different forms. In most research articles on group decisionmaking, the opinions of different decision makers are aggregated, which causes the loss of some information. In such a situation, using a new approach can be useful. In this article, we try to solve this problem by considering the extension of fuzzy numbers and using the existing arithmetic operations on them. In the theory of decision making, the analytic hierarchy process (AHP) is a structured technique for organizing and analyzing complex decisions. It was developed by Saaty 2 , which the experts usually provide crisp values for decisions over paired comparisons of alternatives with respect to a criterion. If the experts are uncertain on the decisions, this uncertainty can be measured by intervals 3 . In uncertain situations, the decisions can also be represented by fuzzy values. As a popular methodology for confronting with uncertainty, the fuzzy logic combined with AHP, more commonly known as fuzzy AHP (FAHP), has found more applications in recent years 4 . Laarhoven and Pedrycz 5 presented a fuzzy version of AHP method. Buckley used fuzzy priorities of comparison ratios in place of exact ratios 6 . Chang introduced a new approach for FAHP with using triangular fuzzy numbers in pairwise comparison scale 7 . Cheng presented a new approach for evaluating naval tactical missile systems depending by the FAHP 8 . Chan and Kumar used fuzzy extended AHP-based approach to global supplier development considering risk factors. Huang et al. presented a FAHP method and utilize crisp judgment matrix to evaluate subjective expert judgments made by the technical committee of the Industrial Technology Development Program in Taiwan 9 . Tang provided an efficient budget allocation method using FAHP for businesses 10 . Das et al. focused on performance evaluation and ranking of seven Indian institute of technology in respect to stakeholders' preference using an integrated model consisting of FAHP and compressed proportional assessment methods 11 . Deng applied a FAHP approach for tackling qualitative multi criteria analysis problems 12 . Cheng et al. considered attack helicopters based on linguistic variables by a FAHP method 13 . Leung and Cao proposed a fuzzy consistency of a tolerance deviation in the FAHP method 14 . Karczmarek et al. developed FAHP in a graphical approach.
2017
Motivated by the idea of single valued neutrosophic uncertain linguistic sets (SVNULSs) and hesitant fuzzy sets (HFSs), in this article we combine SVNULSs with HFSs to present the idea of hesitant single valued neutrosophic uncertain linguistic sets (HSVNULSs), hesitant single valued neutrosophic uncertain linguistic elements (HSVNULEs) and defined some basic operational laws of HSVNULEs. We also presented the score, accuracy and certainty functions for HSVUNLEs. Then, based on the operational laws for HSVNULEs we presented hesitant single valued neutrosophic uncertain linguistic weighted average (HSVNULWA) operator and hesitant single valued neutrosophic uncertain linguistic weighted geometric average (HSVNULWGA) operator to aggregate the hesitant single valued neutrosophic uncertain linguistic information. Furthermore, some necessary assets of the two operators are scrutinized. Based on HSVNULWA and HSVNULWGA operators we defined a multiple criteria decision-making method to switch multiple criteria decision making problems, in which the criterion values with respect to alternatives take the form of HSVNULEs, under a HSVNULs environment. Finally, a numerical example about investment alternatives is specified to show the efficiency of the developed method.
Different multi-criteria decision-making (MCDM) techniques require different levels of computational intensity and may produce different outputs, so selecting an appropriate technique largely determines the quality of the recommended decision and the effort required to obtain that decision. In most real environments , criteria and their constraints are not deterministic and cannot be specified precisely; therefore, those criteria are uncertain or fuzzy. To facilitate the selection of an appropriate MCDM method under a fuzzy environment, this study investigates and statistically compares the performances of ten commonly used MCDM techniques: simple additive weights (SAW), weighted product method (WPM), compromise programming (CP), technique for order preference by similarity to ideal solution (TOPSIS), four types of analytical hierarchy process (AHP), VIKOR (in Serbian: VIseKriterijumska Optimizacija I Kompromisno Re-senje), and ELECTRE (in French: ELimination Et Choix Traduisant la REalité). These techniques' performances were compared using fuzzy criteria and constraints, matching the conditions usually found in real applications. To conduct the comparisons, the 10 multi-criteria decision ranking methods were applied to 1250 simulated sets of decision matrices with fuzzy triangular values, and 12,500 sets of ranks were analyzed to compare the ranking methods. SAW and TOPSIS had statistically similar performances. ELECTRE was not preferable in providing full, sorted ranks among the alternatives. VIKOR considering its ranking process, for specific conditions, assigns identical ranks for several alternatives; when full, sorted ranks are required, VIKOR is unfavorable, although it is a powerful technique in introducing the closest alternative to the ideal condition. Types 1 and 3 of AHP and types 2 and 4 of AHP had close performances. Notably, no ranking method was significantly sensitive to uncertainty levels when uncertainty changed symmetrically.
Soft Computing, 2016
Decision-making about server selection is one of the multi-criteria decision-making (MCDM) processes where interactions among criteria should be considered. The paper introduces and develops some solutions for considering interactions among criteria in the MCDM problems. In the frame procedure for MCDM by using the group of methods, based on assigning weights, special attention is given to the synthesis of the local alternatives' values into the aggregate values where the mutual preferential independence between two criteria is not assumed. Firstly, we delineate how to complete the additive model into the multiplicative one with synergic and redundancy elements in the case that criteria are structured in one level and in two levels. Furthermore, we adapted the concept of the fuzzy Choquet integral to the multiattribute value theory. Studying and comparing the results of the example case of the server selection obtained by both aggregation approaches, the paper highlights the advantages of the first one since it does not require from decision makers to determine the weights of all possible combinations of the criteria and it enables the further use of the most preferred MCDM methods.
Fuzzy multi-criteria decision-making follows aggregation of different basic attributes through hierarchy structure. This aggregation is performed through combination of fuzzy assessment and priority matrices. When available data is imprecise, the assessment and priority matrices for different hierarchy level attributes are developed from expert judgments in the relevant fields. In fuzzy aggregation, the uncertainties in the assessment matrix are captured with fuzzy membership functions. The priority matrix is developed through pairwise comparison, in which the relative importance of the attributes are represented by the experts in crisp values; thus uncertainties associated with priority assignment are not incorporated in fuzzy aggregation. In this paper, a methodology to incorporate fuzziness in developing priority matrix has been presented. Fuzzy α-cut technique for different confidence intervals has been incorporated. The gradient eigenvector method has been followed to obtain consistency in constructing the priority matrix for different hierarchy level attributes. The max-min paired elimination method for hierarchical aggregation has been used to obtain the final fuzzy set. A case study for drinking water treatment technology evaluation is performed to present the potential environmental application of this approach, leading to the identification of the best treatment technology.
Information Sciences, 2017
Hesitant fuzzy linguistic term set (HFLTS) is a useful tool for describing people's subjective cognitions in the process of decision making. Multiple criteria decision making (MCDM) involves two important steps: (1) determining the criteria weights; (2) obtaining a suitable ranking of alternatives. In this paper, we propose some hesitant fuzzy linguistic entropy and cross-entropy measures, and then establish a model for determining the criteria weights, which considers both the individual effect of each hesitant fuzzy linguistic element (HFLE) and the interactive effect between any two HFLEs with respect to each criterion. Additionally, we give a hesitant fuzzy linguistic alternative queuing method (HFL-AQM) to deal with the MCDM problems. The directed graph and the precedence relationship matrix make the calculation processes and the final results much more intuitive. Finally, a case study concerning the tertiary hospital management is made to verify the weight-determining method and the HFL-AQM.
Application of Decision Science in Business and Management [Working Title]
Multi-criteria decision-making (MCDM) is a crucial process in many business and management applications. The final decision is based upon the relative weights to the decision-making team. The analytic hierarchy process (AHP) has found to be one of the most successful approaches for evaluations of the weights and the importance of the criteria. However, most of the evaluated values are not so precise due to the fuzziness of the evaluating environment. This chapter surveys essentially the basic analytic hierarchy process and the fuzzy analytic hierarchy process (FAHP). It depicts through an example the steps for using the original analytic hierarchy process for two levels of criteria. Then, it uses the same example to explain the fuzzy approach in the evaluation. Finally, it compares both approaches.
Technology audit and production reserves, 2022
The object of research is decision-making support systems. Local wars and armed conflicts of recent decades are characterized by high dynamics of operations (combat operations) and a significant amount of diverse information circulating in information systems. These features determine the search for new approaches to increase the efficiency of decision-making support systems, given their reliability. This article solves the problem of developing a method of multicriteria evaluation in conditions of uncertainty. In the course of the research, the authors used the main provisions of the theory of artificial intelligence, automation theory, theory of complex technical systems and general scientific methods of cognition, namely analysis and synthesis. The proposed methodology was developed taking into account the practical experience of the authors of this work during the military conflicts of the last decade. The method of multicriteria evaluation is universal and can be used to assess...
Soft Computing, 2020
The decision-making under several uncertainties is a major concern to choose the best alternative among the several separate alternatives. This paper deals with the uncertainty of using a complete ranking classification of generalized trapezoidal fuzzy numbers (GTrFNs). In the view of that several measures such as mode, spread, midpoint the score, radius, left and right fuzziness score and linguistic expression are considered to compute the ranking order of GTrFN. Using the proposed complete ranking of GTrFN, this paper presents a method for solving fuzzy multi-criteria decision-making problems. The comparative analysis of existing methods with our proposed method is also described.
Journal of Computer Science Technology, 2014
Multi-Criteria Decision Analysis (MCDA) is a usual activity among organisations and decisions related to people's activities. Due to the complexity of considering multiple criteria, to select an alternative is a non-trivial task. From operative levels to managerial ones, MCDA is implemented by using several (formal and informal) techniques. Two useful techniques that help to make a decision are the Analytic Hierarchy Process (AHP) and MCDA models based on Linguistic Information (LI). This work describes a MCDA framework that combines the mentioned techniques in order to provide more confidence in the decision making process. To test the proposed model, framework was used to select the adequate network configuration to improve quality of service (QoS). Finally, the framework's outputs were compared to real experts' opinions obtaining satisfactory results.
IAES International Journal of Artificial Intelligence (IJ-AI)
In this article, the researchers main contribution is to investigate three factors which may correlate in implementation of Expert Judgment Z-Numbers as new Fuzzy Logic Ranking Indicator such as: expert relevance judgment or score, the expert confidence and the level of expertise. The Expert Judgment Z-Numbers then will be an input to the Hierarchical Fuzzy Logic System of Domain Specific Text Retrieval, along with other indicators such as Ontology BM25 Score, Fabrication Rate, Shia Rate and Positive Rate of hadith document. The results showed, the proposed system, with the additional new indicator of Expert Judgment Z-Numbers, may improve the original BM25 ranking function, by yielding better results on 26 queries, on all evaluation metrics that are measured in this research such as P@10, %no measures and MAP, and has achieved better results in 28 queries on P@10 alone, compared to the BM25 original score, that only yield better results in 2 queries on all evaluation metrics, and a...
PLOS ONE
Correlation is considered the most important factor in analyzing the data in statistics. It is used to measure the movement of two different variables linearly. The concept of correlation is well-known and used in different fields to measure the association between two variables. The hesitant 2-tuple fuzzy linguistic set (H2FLS) comes out to be valuable in addressing people’s reluctant subjective data. The purpose of this paper is to analyze new correlation measures between H2FLSs and apply them in the decision-making process. First and foremost, the ideas of mean and variance of hesitant 2-tuple fuzzy linguistic elements (H2FLEs) are introduced. Then, a new correlation coefficient between H2FLSs is established. In addition, considering that different H2FLEs may have different criteria weights, the weighted correlation coefficient and ordered weighted correlation coefficient are further investigated. A practical example concerning the detailed procedure of solving problems is exempl...
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