A New Ranking Approach for Interval Valued Intuitionistic Fuzzy Sets and its Application in Decision Making

2019 ◽  
Vol 8 (2) ◽  
pp. 110-125 ◽  
Author(s):  
Pranjal Talukdar ◽  
Palash Dutta

Ranking of interval valued intuitionistic fuzzy sets (IVIFSs) plays an important role because of its attraction and applicability to model uncertainty in real life problems. In this article, an attempt has been made to devise a new method for ranking of IVIFSs based on exponential function. The significance of the method is illustrated with the help of some numerical examples and the results are compared with other existing methods. Furthermore, a multi criteria decision making method is presented here to evaluate the final ranking of the alternatives using the proposed ranking method and discussed the consistency of so obtained results.

2016 ◽  
Vol 5 (4) ◽  
pp. 192-210 ◽  
Author(s):  
Bhagawati Prasad Joshi

Due to the huge applications of fuzzy set theory, many generalizations were available in literature. Atanassov (1983) and Atanassov and Gargov (1989) introduced the notions of intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) respectively. It is observed that IFSs and IVIFSs are more suitable tools for dealing with imprecise information and very powerful in modeling real life problems. However, many researchers made efforts to rank IVIFSs due to its importance in fusion of information. In this paper, a new ranking method is introduced and studied for IVIFSs. The proposed method is compared and illustrated with other existing methods by numerical examples. Then, it is utilized to identify the best alternative in multiple criteria decision-making problems in which criterion values for alternatives are IVIFSs. On the basis of the developed approach, it would provide a powerful way to the decision-makers to make his or her decision under IVIFSs. The validity and applicability of the proposed method are illustrated with practical examples.


2021 ◽  
Vol 21 (1) ◽  
pp. 3-18
Author(s):  
Melda Kokoç ◽  
Süleyman Ersöz

Abstract Many authors agree that the Interval-Valued Intuitionistic Fuzzy Set (IVIFS) theory generates as realistic as possible evaluation of real-life problems. One of the real-life problems where IVIFSs are often preferred is the Multi-Criteria Decision-Making (MCDM) problem. For this problem, the ranking of values obtained by fuzzing the opinions corresponding to alternatives is an important step, as a failure in ranking may lead to the selection of the wrong alternative. Therefore, the method used for ranking must have high performance. In this article, a new score function SKE and a new accuracy function HKE are developed to overcome the disadvantages of existing ranking functions for IVIFSs. Then, two illustrative examples of MCDM problems are presented to show the application of the proposed functions and to evaluate their effectiveness. Results show that the functions proposed have high performance and they are the eligibility for the MCDM problem.


2020 ◽  
Vol 33 (6) ◽  
pp. 1647-1668
Author(s):  
Basar Oztaysi ◽  
Sezi Cevik Onar ◽  
Cengiz Kahraman ◽  
Muharrem Gok

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.


Information ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 369 ◽  
Author(s):  
Peide Liu ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Kifayat Ullah

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples.


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