Intuitionistic Preference Relations Research Articles

Dynamic Flow Algorithm with Intermediate Storage for Emergency Evacuation Allowing Lane Reversal based on Incomplete Intuitionistic Fuzzy Preference Relation

Background Evacuation in case of disasters is of the greatest importance because of significant occurrences of natural and artificial disasters worldwide, which is why a reliable evacuation plan is always needed. However, evacuation models are difficult to develop due to various uncertain aspects that need to be considered, multiple and often conflicting criteria for evaluation and as lack of expertise regarding a specific preference of alternatives. Objective This study aims to transport the maximum number of evacuees in a dynamic network with lane reversal by a safe pattern of transportation, i.e., allowing storage at intermediate nodes. The optimal order of shelters and intermediate nodes for a reliable evacuation plan will be defined by incomplete intuitionistic fuzzy preference relation. Methods The illustrated method incorporates multiple and often conflicting criteria into a process of emergency decision-making. When evaluating evacuation alternatives, a decision-maker may hesitate and be unsure which alternative is better or not have sufficient expertise to evaluate a pair of alternatives. To model uncertainty and hesitation, intuitionistic fuzzy values are used to describe alternatives in more detail. This study relies on flow models and graph theory to simulate the movement of evacuees to safe destinations. Furthermore, fuzzy methods and their recent modifications are applied to determine the effective priority order of shelters. A case study which simulates the evacuation of aggrieved to safe destinations is presented. Results A method of evaluating the shelters and intermediate nodes for evacuation based on incomplete intuitionistic fuzzy preference relation is proposed. The method allows the missed values of experts’ assessments to be filled in regarding the evacuation alternatives and deals with intuitionistic fuzzy values, which describe experts’ hesitation. The dynamic character of flow distribution enables transit arc capacities and time factors to be processed. The contraflow technique, which is a powerful tool to decrease traffic jams and congestion on roads by reversing the movement along the unused segments, is applied to maximize the number of survivors. Conclusion The results of the method were compared to those of existing methods, and their consistency was proved. In the future, we intend to apply interval-valued intuitionistic preference relations and iterative algorithms to improve the consistency of intuitionistic preference relations to the tasks of transporting the maximum possible number of aggrieved to safe locations.

A new group decision-making method with incomplete intuitionistic multiplicative preference relations

PurposeConsistency and consensus are two important research issues in group decision-making (GDM). Considering some drawbacks associated with these two issues in existing GDM methods with intuitionistic multiplicative preference relations (IMPRs), a new GDM method with complete IMPRs (CIMPRs) and incomplete IMPRs (ICIMPRs) is proposed in this paper.Design/methodology/approachA mathematically programming model is constructed to judge the consistency of CIMPRs. For the unacceptably consistent CIMPRs, a consistency-driven optimization model is constructed to improve the consistency level. Meanwhile, a consistency-driven optimization model is constructed to supplement the missing values and improve the consistency level of the ICIMPRs. As to GDM with CIMPRs, first, a mathematically programming model is built to obtain the experts' weights, after that a consensus-driven optimization model is constructed to improve the consensus level of CIMPRs, and finally, the group priority weights of alternatives are obtained by an intuitionistic fuzzy programming model.FindingsThe case analysis of the international exchange doctoral student selection problem shows the effectiveness and applicability of this GDM method with CIMPRs and ICIMPRs.Originality/valueFirst, a novel consistency definition of CIMPRs is presented. Then, a consistency-driven optimization model is constructed, which supplements the missing values and improves the consistency level of ICIMPRs simultaneously. Therefore, this model greatly improves the efficiency of consistency improving. Experts' weights determination method considering the subjective and objective information is proposed. The priority weights of alternatives are determined by an intuitionistic fuzzy (IF) programming model considering the risk preference of experts, so the method determining priority weights is more flexible and agile. Based on the above theoretical basis, a new GDM method with CIMPRs and ICIMPRs is proposed in this paper.

Group decision making based on consistency and consensus analysis of dual multiplicative linguistic preference relations

This paper proposes a new group decision making (GDM) method based on the consistency and the consensus analysis of dual multiplicative linguistic preference relations (DMLPRs). A new type of linguistic variables , called dual multiplicative linguistic variables (DMLVs), is presented, which is defined on the multiplicative linguistic scale. DMLVs are used to represent asymmetrical qualitative hesitancy judgments of decision makers (DMs). A maximum-consistency-based interactive algorithm to derive multiplicative linguistic intuitionistic preference relations (MLIPRs) is presented, by which the consistency concept for DMLPRs is obtained. Then, we define the concept of inconsistent DMLPRs and propose an optimal-model-based method for deriving consistent DMLPRs. Furthermore, incomplete DMLPRs also can be dealt with by the proposed maximum-consistency-based interactive algorithm. For GDM, the weights of DMs are determined by the cosine-based correlation coefficient between individual DMLPRs. Moreover, we propose a consensus measure to calculate the agreement degree of DMLPRs and build an optimal model to increase the consensus level of individual DMLPRs. Finally, a new GDM method (call Algorithm III ) is offered and an application example is used to illustrate the proposed GDM method. The proposed GDM method outperforms the former GDM methods for GDM in the environments of DMLPRs.

A novel method to derive the intuitionistic multiplicative priority vector for the intuitionistic multiplicative preference relation

A novel method to derive the intuitionistic multiplicative priority vector for the intuitionistic multiplicative preference relation

Call center performance measurement using intuitionistic fuzzy sets

PurposeThe companies are struggling to collect invoices due to the decrease in the economic growth. This global trend does not only affect undeveloped countries, but it also has a strong impact on the developed countries. Improving the debt collection process become a significant element to maintain financial stability. The institutions that are specialized on collecting payments, debt collection agencies and their call centers, with their expertise in the field can improve the payment process. Yet, managing evaluating the performance of debt collection agencies is a very hard process that involves uncertainty and imprecision. Performance measurement (PM) is a combination of numerically expressed characteristics which give insight about the success or degree of accomplishment of an activity. PM can be handled in various levels such as individual, team, department or company. The aim of this study is to present a systematic and objective PM method for call centers.Design/methodology/approachIn this study, first an exploratory approach is used to understand the call center measurement problem. Several meetings are done with the representatives of both call center firms and the parent firms that outsource debt collection process. Simultaneously, a broad literature review is conducted. An iterative approach is selected to reach deeper knowledge on the process. New meetings are planned and scope of the literature review has changed based on this iterative approach. After these steps, the problem has been considered as the multi-criteria decision-making problem since more than one criteria should be considered for evaluating the performances of call centers. The result of the literature review and the meetings with experts show that defining the weights for the criteria is very crucial for evaluating the performances accurately. Collecting human judgment for defining the weights of call center criteria necessitates dealing with vagueness and uncertainty. The intuitionistic fuzzy sets excellent tools for representing uncertainty. Interval valued intuitionistic fuzzy sets can easily represent the human judgments. Thus, in this study, an intuitionistic fuzzy multi-criteria decision making approach is used to design the proposed methodology. Incomplete interval-valued intuitionistic preference relations are used to determine the weights of the indicators aggregating linguistic evaluations of the decision makers.FindingsThe proposed approach provides an objective calculation of performance measurement. In order to provide objectivity, indicator performance functions are proposed for the first time in this study. Nine different functions and related parameters are defined to objectively measure indicator performances.Originality/valueThe paper proposes an objective and easy-to-modify approach for call-center PM, which can be used by call center managers. It presents a new fuzzy multi-criteria decision-making (MCDM) method for call center performance evaluation, which can consider the multi-experts' judgments under vagueness and impreciseness, which may be conflicting and incomplete interval-valued intuitionistic fuzzy preference relations. Also nine new functions are defined for indicator performance.

Intuitionistic Fuzzy Possibility Degree Measure for Ordering of IVIFNs with Its Application to MCDM

In this article, the concept of an intuitionistic fuzzy possibility degree (IFPD) for ordering several interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced. The IFPD ranks IVIFNs by distinguishing the comparable and non-comparable components of the joint intervals of membership and non-membership degrees. The incomparable cases of nested joint intervals can also rank respective IVIFNs through the proposed IFPD approach. An intuitionistic fuzzy possibility preference relation based on the proposed IFPD measure for IVIFNs is defined as a more effective tool for modelling uncertainty than existing intuitionistic preference relations. Further, an approach for solving multicriteria interval-valued intuitionistic fuzzy decision-making problems based on IFPD measure of IVIFNs is advanced also provides a possibility degree as supplementary information to the ranking of alternatives. The validity and effectiveness of the advanced approach are demonstrated through two illustrative examples.

PERSONEL SEÇİMİ İÇİN SEZGİSEL BULANIK SAYI TEMELLİ GRUP KARAR VERME YAKLAŞIMI

The most appropriate personnel selection is a very important issue for an organization’s success due to the increasing competition in global market. Traditionally, Saaty’s consistency method is used to check the consistency of the experts’ judgments in personnel selection problem and the inconsistency judgments can be sent to return to the experts for reevaluation, which is time consuming and sometimes undesired by experts, or can be extracted from decision making process. A perfect multiplicative consistent intuitionistic preference relation (IPR) will be repaired the inconsistent IPRs of the experts into a consistent one automatically. There is no paper about personnel selection using integrated intuitionistic fuzzy analytic hierarchy process method (IFAHP)-IFVIKOR (intuitionistic fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje) approach under group decision making with perfect multiplicative consistent IPR. This paper presents an integrated multi-criteria decision making method for personnel selection with perfect multiplicative consistent IPR under intuitionistic fuzzy environment. Priority value of criteria has been defined by utilizing IFAHP method and the most appropriate personnel among candidates has been found by utilizing intuitionistic fuzzy VIKOR. The application of personnel selection is conducted to illustrate the effectiveness of the proposed method in a logistic firm. The personel selection is realized according to a questionnaire responded by three experts in human resources management area. Five criteria for personel selection are defined through literature review and the judgments of expert team. K1 (self-confidence) is defined as the most important criteria for personnel selection of the specified logistic firm by using IFAHP. Alt 3 is defined as the most suitable personnel for the specified logistic firm by using IFVIKOR.

A Multicriteria Decision-Making Approach Based on Fuzzy AHP with Intuitionistic 2-Tuple Linguistic Sets

In the modern literature related to linguistic decision-making, the 2-tuple linguistic representation model and its useful applications in various fields have been extensively studied and used during the last decade. Recently, some useful multicriteria decision-making (MCDM) methods have been introduced based on fuzzy analytic hierarchy process (AHP) for 2-tuple linguistic representation model. By keeping in mind the importance of this linguistic model, in this paper, we introduce a fuzzy AHP methodology for intuitionistic 2-tuple linguistic sets (I2TLSs) which is a useful extension of the 2-tuple linguistic representation model. This study is comprised of four stages. In the first stage, we define some operational laws for I2TL elements (I2TLEs) and prove some related important properties. In the second stage, intuitionistic 2-tuple linguistic preference relation (I2TLPR) and multiplicative I2TLPR are defined using I2TLSs. In the 3rd stage, a transformation mechanism is introduced which can transform an I2TLPR to a corresponding intuitionistic preference relation (IPR) and vice versa. In the fourth stage, an approach is proposed for checking the consistency of an I2TLPR and presented a method to repair the inconsistent one by using the proposed transformation mechanism. Finally, a numerical example is given and comparative analysis is carried out with the TOPSIS method to verify the validity of the proposed method.

A Novel Approach for Group Decision-Making from Intuitionistic Fuzzy Preference Relations and Intuitionistic Multiplicative Preference Relations

During the decision-making process, evaluation information may be given in different formats based on the decision makers’ research fields or personal customs. To address the situation that alternatives are evaluated by both intuitionistic fuzzy preference relations (IFPRs) and intuitionistic multiplicative preference relations (IMPRs), a new priority approach based on a net flow score function is proposed. First, the two preference relations above are transformed into the corresponding interval-valued fuzzy preference relations (IVFPRs) and interval-valued multiplicative preference relations (IVMPRs), respectively. Second, the net flow score functions of individual IFPRs and IMPRs are obtained. Third, according to information theory, a mean deviation maximization model is constructed to compute the weights of decision-makers objectively. Finally, the collective net flow score of each alternative is obtained to determine the ranking result. The proposed method is certified to be simple, valid, and practical with three examples.

Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings

The intuitionistic multiplicative preference relation (IMPR), which takes into account both the ratio degree to which an alternative is preferred to another and the ratio degree to which an alternative is non-preferred to another, is a useful tool for decision makers to elicit their preference information using Saaty’s 1–9 scale. In this paper, we focus on group decision making with IMPRs. First, we analyze the flaws of the consistency definition of an IMPR in previous work and then propose a new definition to overcome the flaws. On this basis, a linear programming-based algorithm is developed to check and improve the consistency of an IMPR. Second, we discuss the relationships between an IMPR and a normalized intuitionistic multiplicative weight vector and develop two approaches to group decision making based on complete and incomplete IMPRs, respectively. Based on the proposed algorithm and approaches, a general framework for group decision making with IMPRs is proposed. Finally, some numerical examples are provided to demonstrate the proposed approaches. The results show that the proposed approaches can deal with group decision-making problems with IMPRs effectively.

An Error Analysis Decision Making Method for Priority in Intuitionistic Preference Relation

This article describes how intuitionistic fuzzy sets theory, which is the generalisation of fuzzy sets theory, is a more suitable tool for dealing with imprecise information. The information provided by the decision maker is often imprecise in many situations. So, intuitionistic preference relation is a suitable tool for such cases. The estimation of the priority vector of the intuitionistic preference relation is an important part in decision making. In this article, an intuitionistic fuzzy Choquet integral is proposed and combined with the famous error propagation formula, and developed a method for the priority of an intuitionistic preference relation to estimate the ranking of the considered alternatives. Also, an experiment has been conducted to demonstrate and implementation of the proposed approach.

A Group Decision Making Approach Based on Newly Defined Additively Consistent Interval-Valued Intuitionistic Preference Relations

Because of the complexity of interval-valued intuitionistic fuzzy set, there are few literatures investigating the additive consistency of the interval-valued intuitionistic preference relation. This paper proposes a group decision making approach with interval-valued intuitionistic preference relations. Firstly, two additive reciprocal fuzzy preference relations and two fuzzy non-preferred relations are obtained by dividing an interval-valued intuitionistic preference relation in order to avoid the operations of interval-valued intuitionistic fuzzy numbers. Here, the fuzzy non-preferred relation is interpreted as the non-preferred intensity of one alternative over another one. Moreover, the rational concept of additive consistency of interval-valued intuitionistic preference relation is defined. Secondly, optimizing models to derive priority weight vector from interval-valued intuitionistic preference relation are constructed. In particular, the priority weight vector is in terms of interval-valued intuitionistic fuzzy numbers, which is rational under the interval-valued intuitionistic fuzzy environment. Thirdly, an extended approach to address group decision making (GDM) problems is proposed. Each individual expert’s consistency index is applied to measure his/her degree of importance. Finally, an illustrative example of supplier selection is provided to illustrate the proposed approach addressing GDM problems. The feasibility to derive priority weight vector in terms of interval-valued intuitionistic fuzzy numbers using the developed approach is verified. And the proposed approach is compared with the other conventional existing ones to show its advantages.

2-tuple linguistic intuitionistic preference relation and its application in sustainable location planning voting system

2-tuple linguistic intuitionistic preference relation and its application in sustainable location planning voting system

Evaluation and Classification of Overseas Talents in China Based on the BWM for Intuitionistic Relations

Efficient utilization of human resources is an important force for the sustainable development of society and the economy. Against the backdrop of the development of economic globalization, the Chinese Government is presently implementing the strategy of “Strengthening the Nation with Talent” to assist the exploitation and management of human resources. Overseas talents have recently become an important resource. How to scientifically evaluate and classify overseas talents has become an important research topic, and it is necessary to seek a systematic decision aid. This paper introduces a novel methodology to evaluate and classify overseas talents in China under the intuitionistic relations environment. Firstly, we determine the weighted values of decision makers and criteria through defining geometry consistency. Secondly, we construct a non-linear Best-Worst-Method (BWM) model with intuitionistic preference relations. A highlight of this BWM model for intuitionistic relations is taking both positive and negative aspects into consideration, which is different from the original BWM. Finally, the proposed methodology is applied to an illustrative example of overseas talent evaluation, indicating the simultaneous efficiency and practicability of the method.

A Group Decision Framework with Intuitionistic Preference Relations and Its Application to Low Carbon Supplier Selection.

This article develops a group decision framework with intuitionistic preference relations. An approach is first devised to rectify an inconsistent intuitionistic preference relation to derive an additive consistent one. A new aggregation operator, the so-called induced intuitionistic ordered weighted averaging (IIOWA) operator, is proposed to aggregate individual intuitionistic fuzzy judgments. By using the mean absolute deviation between the original and rectified intuitionistic preference relations as an order inducing variable, the rectified consistent intuitionistic preference relations are aggregated into a collective preference relation. This treatment is presumably able to assign different weights to different decision-makers’ judgments based on the quality of their inputs (in terms of consistency of their original judgments). A solution procedure is then developed for tackling group decision problems with intuitionistic preference relations. A low carbon supplier selection case study is developed to illustrate how to apply the proposed decision model in practice.

Medical Waste Disposal Method Selection Based on a Hierarchical Decision Model with Intuitionistic Fuzzy Relations.

Although medical waste usually accounts for a small fraction of urban municipal waste, its proper disposal has been a challenging issue as it often contains infectious, radioactive, or hazardous waste. This article proposes a two-level hierarchical multicriteria decision model to address medical waste disposal method selection (MWDMS), where disposal methods are assessed against different criteria as intuitionistic fuzzy preference relations and criteria weights are furnished as real values. This paper first introduces new operations for a special class of intuitionistic fuzzy values, whose membership and non-membership information is cross ratio based ]0, 1[-values. New score and accuracy functions are defined in order to develop a comparison approach for ]0, 1[-valued intuitionistic fuzzy numbers. A weighted geometric operator is then put forward to aggregate a collection of ]0, 1[-valued intuitionistic fuzzy values. Similar to Saaty’s 1–9 scale, this paper proposes a cross-ratio-based bipolar 0.1–0.9 scale to characterize pairwise comparison results. Subsequently, a two-level hierarchical structure is formulated to handle multicriteria decision problems with intuitionistic preference relations. Finally, the proposed decision framework is applied to MWDMS to illustrate its feasibility and effectiveness.

Prioritization and Aggregation of Intuitionistic Preference Relations: A Multiplicative-Transitivity-Based Transformation from Intuitionistic Judgment Data to Priority Weights

This article proposes a goal programming framework for deriving intuitionistic fuzzy weights from intuitionistic preference relations (IPRs). A new multiplicative transitivity is put forward to define consistent IPRs. By analyzing the relationship between intuitionistic fuzzy weights and multiplicative consistency, a transformation formula is introduced to convert normalized intuitionistic fuzzy weights into multiplicative consistent IPRs. By minimizing the absolute deviation between the original judgment and the converted multiplicative consistent IPR, two linear goal programming models are developed to obtain intuitionistic fuzzy weights from IPRs for both individual and group decisions. In the context of multicriteria decision making with a hierarchical structure, a linear program is established to obtain a unified criterion weight vector, which is then used to aggregate local intuitionistic fuzzy weights into global priority weights for final alternative ranking. Two numerical examples are furnished to show the validity and applicability of the proposed models.

Group decision making with incomplete intuitionistic preference relations based on quadratic programming models

This paper presents a quadratic-program-based framework for group decision making with incomplete intuitionistic preference relations (IPRs). The framework starts with introducing a notion of additive consistency for incomplete IPRs, followed by a two-stage quadratic program model for estimating missing values in an incomplete IPR. The first stage aims to minimize inconsistency of the completed IPR and control hesitation margins of the estimated judgments within an acceptable threshold. The second stage is to find the most suitable estimates without changing the inconsistency level. Subsequently, a parameterized formula is proposed to transform normalized interval fuzzy weights into additively consistent IPRs. Two quadratic programs are developed to generate interval fuzzy weights from a complete IPR. The first model obtains interval fuzzy weight vectors by minimizing the squared deviation between the two sides of the transformation formula. By optimizing the parameter value, the second model finds the best weight vector based on the optimal solutions of the first model. A procedure is then developed to solve group decision problems with incomplete IPRs. A numerical example and a group selection problem for enterprise resource planning software products are provided to demonstrate the proposed models.

Confidence-consistency driven group decision making approach with incomplete reciprocal intuitionistic preference relations

Intuitionistic preference relations constitute a flexible and simple representation format of experts’ preference on a set of alternative options, while at the same time allowing to accommodate degrees of hesitation inherent to all decision making processes. In comparison with fuzzy preference relations, the use of intuitionistic fuzzy preference relations in decision making is limited, which is mainly due to the computational complexity associated to using membership degree, non-membership degree and hesitation degree to model experts’ subjective preferences. In this paper, the set of reciprocal intuitionistic fuzzy preference relations and the set of asymmetric fuzzy preference relations are proved to be mathematically isomorphic. This result can be exploited to use methodologies developed for fuzzy preference relations to the case of intuitionistic fuzzy preference relations and, ultimately, to overcome the computation complexity mentioned above and to extend the use of reciprocal intuitionistic fuzzy preference relations in decision making. In particular, in this paper, this isomorphic equivalence is used to address the presence of incomplete reciprocal intuitionistic fuzzy preference relations in decision making by developing a consistency driven estimation procedure via the corresponding equivalent incomplete asymmetric fuzzy preference relation procedure. Additionally, the hesitancy degree of the reciprocal intuitionistic fuzzy preference relation is used to introduce the concept of expert’s confidence from which a group decision making procedure, based on a new aggregation operator that takes into account not only the experts’ consistency but also their confidence degree towards the opinion provided, is proposed.

An Acceptable Consistency-Based Framework for Group Decision Making with Intuitionistic Preference Relations

This article studies acceptable consistency of intuitionistic preference relations (IPRs) and examines how to aggregate individual IPRs into a collective judgment in a group decision making (GDM) context. A consistency index is first introduced to measure the consistency level, thereby defining acceptable consistency for IPRs. If a decision-maker is unwilling or unavailable to revise his/her judgment for an IPR with unacceptable consistency, an automated approach is developed to improve its consistency to an acceptable level. The acceptably consistent IPRs are subsequently aggregated into a group opinion by using an induced ordered weighted averaging operator. A procedure is then proposed to solve GDM problems with IPRs. An illustrative example is presented to demonstrate the effectiveness and applicability of the proposed approach.