Shadowed Sets-Based Linguistic Term Modeling and Its Application in Multi-Attribute Decision-Making

For many multi-attribute decision-making (MADM) problems, linguistic variables are more convenient for people to express the attribute values. In this paper, a novel shadowed set-based method is proposed to deal with linguistic terms, where the linguistic term sets are symmetrical both in meaning and form. Firstly, to effectively express the linguistic variables, we develop a data-driven method to construct the shadowed set model for the linguistic terms. Secondly, the Pythagorean shadowed set is defined, and some theorems are subsequently explored. Thirdly, we propose the score function of the Pythagorean shadowed number and develop a new MADM method on the basis of the Pythagorean shadowed set. Finally, a case study of the supplier selection problem is provided to illustrate the effectiveness of the proposed method, and the superiority of our method is demonstrated by comparison analysis.

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Fuzzy Analytic Hierarchy Process and Its Application to E-Marketplace Selection

Enterprise Business Modeling, Optimization Techniques, and Flexible Information Systems ◽

10.4018/978-1-4666-3946-1.ch003 ◽

2013 ◽

pp. 26-44 ◽

Cited By ~ 2

Author(s):

Beyza Ahlatcioglu Ozkok ◽

Elisa Pappalardo

Keyword(s):

Decision Making ◽

Analytic Hierarchy Process ◽

Fuzzy Ahp ◽

Multi Criteria Decision Making ◽

Linguistic Variables ◽

Analytic Hierarchy ◽

Multi Attribute Decision Making ◽

Electronic Parts ◽

Hierarchy Process

Making decisions is a part of daily life. The nature of decision-making includes multiple and usually conflicting criteria. Multi Criteria Decision-Making (MCDM) problems are handled under two main headings: Multi Attribute Decision Making (MADM) and Multi Objective Decision Making (MODM). Analytic Hierarchy Process (AHP) is a widely used multi-criteria decision making approach and has successfully been applied to many practical problems. Traditional AHP requires exact or crisp judgments (numbers). However, due to the complexity and uncertainty involved in real world decision problems, decision makers might be more reluctant to provide crisp judgments than fuzzy ones. Furthermore, even when people use the same words, individual judgments of events are invariably subjective, and the interpretations that they attach to the same words may differ. This is why fuzzy numbers and fuzzy sets have been introduced to characterize linguistic variables. Here, the authors overview the most known fuzzy AHP approaches and their application, and they present a case study to select an e-marketplace for a firm, which produces and sells electronic parts of computers in Turkey.

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Induced Unbalanced Linguistic Ordered Weighted Average and Its Application in Multiperson Decision Making

The Scientific World JOURNAL ◽

10.1155/2014/642165 ◽

2014 ◽

Vol 2014 ◽

pp. 1-19 ◽

Cited By ~ 5

Author(s):

Lucas Marin ◽

Aida Valls ◽

David Isern ◽

Antonio Moreno ◽

José M. Merigó

Keyword(s):

Decision Making ◽

Weighted Average ◽

Multicriteria Decision Making ◽

Aggregation Operators ◽

New Order ◽

Linguistic Variables ◽

Linguistic Terms ◽

Ordered Weighted Average ◽

Decision Making Model

Linguistic variables are very useful to evaluate alternatives in decision making problems because they provide a vocabulary in natural language rather than numbers. Some aggregation operators for linguistic variables force the use of a symmetric and uniformly distributed set of terms. The need to relax these conditions has recently been posited. This paper presents the induced unbalanced linguistic ordered weighted average (IULOWA) operator. This operator can deal with a set of unbalanced linguistic terms that are represented using fuzzy sets. We propose a new order-inducing criterion based on the specificity and fuzziness of the linguistic terms. Different relevancies are given to the fuzzy values according to their uncertainty degree. To illustrate the behaviour of the precision-based IULOWA operator, we present an environmental assessment case study in which a multiperson multicriteria decision making model is applied.

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An Extended VIKOR Method Based on q-Rung Orthopair Shadowed Set and Its Application to Multi-Attribute Decision Making

Symmetry ◽

10.3390/sym12091508 ◽

2020 ◽

Vol 12 (9) ◽

pp. 1508

Author(s):

Huidong Wang ◽

Yao Zhang ◽

Jinli Yao

Keyword(s):

Decision Making ◽

Normal Distribution ◽

Distance Measures ◽

Basic Operation ◽

Interval Numbers ◽

Location Selection ◽

Operation Rules ◽

Shadowed Set ◽

Multi Attribute Decision Making ◽

Shadowed Sets

In the multi-attribute decision making (MADM) process, the attribute values are sometimes provided by experts or the public in the form of words. To model the linguistic evaluation more accurately, this paper proposes the q-rung orthopair shadowed set (q-ROSS) to represent attribute values and extends the VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) method to solve MADM problems in the q-ROSS context. First, we propose the q-ROSS to express evaluation information. Some basic operation rules and distance measures are investigated accordingly. When the amount of data is large, the left and right endpoints of the collected interval numbers will obey symmetric normal distribution. Secondly, based on the normal distribution assumption, the collected data intervals are mapped to shadowed sets through a data processing approach. Furthermore, we extend the VIKOR model to tackle the MADM problem where the evaluation values are expressed by q-rung orthopair shadowed numbers. A location selection problem verifies the practicability of our method, and the effectiveness and superiority of the presented approach are reflected through comparative analysis.

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The application of probabilistic linguistic CODAS method based on new score function in multi-criteria decision-making

Computational and Applied Mathematics ◽

10.1007/s40314-021-01568-6 ◽

2021 ◽

Vol 41 (1) ◽

Author(s):

Liuxin Chen ◽

Xiaoling Gou

Keyword(s):

Decision Making ◽

Score Function ◽

Multi Criteria Decision Making ◽

Topsis Method ◽

Linguistic Terms ◽

Complete Representation ◽

Linguistic Term ◽

Probabilistic Linguistic Term Sets ◽

Todim Method

AbstractProbabilistic linguistic term sets (PLTSs) play an important role in multi-criteria decision-making(MCDM) problems because it can not only describe objects with several possible linguistic terms, but also represent the proportion of each linguistic term, which can effectively avoid the distortion of decision information to a greater extent and ensure the credibility of decision results. First, to compare PLTS more simply and reasonably, we define a new score function that takes into account partial deviations. Then considering the superiority of the classic combinative distance-based assessment (CODAS) method in the complete representation of information, it is extended to the probabilistic linguistic environment. Subsequently, we improved the classic CODAS method and proposed the PL-CODAS method. Finally, we apply the PL-CODAS method to a cases of venture investors choosing emerging companies, and we compare the proposed method with PL-TOPSIS method, PL-TODIM method and PL-MABAC method to verify its applicability and effectiveness.

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Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

Mathematics ◽

10.3390/math9212730 ◽

2021 ◽

Vol 9 (21) ◽

pp. 2730

Author(s):

Zeeshan Ali ◽

Tahir Mahmood ◽

Gustavo Santos-García

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Weighted Averaging ◽

Linguistic Variables ◽

Linguistic Terms ◽

Operational Laws ◽

Multi Attribute Decision Making ◽

Complex Linear ◽

Reference Parameters

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.

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Supplier selection in Telecom supply chain management: a Fuzzy-Rasch based COPRAS-G method

Technological and Economic Development of Economy ◽

10.3846/20294913.2017.1295289 ◽

2018 ◽

Vol 24 (2) ◽

pp. 765-791 ◽

Cited By ~ 13

Author(s):

Kajal CHATTERJEE ◽

Samarjit KAR

Keyword(s):

Decision Making ◽

Supply Chain ◽

Supplier Selection ◽

Telecommunication Sector ◽

Multi Attribute Decision Making ◽

The Stability ◽

Spearman’S Correlation ◽

Supplier Selection Problem

In the past decade, global competition are forcing firms to increase their level of outsourcing for raw or semi-finished products and building long term relationship with their supply chain partners. The objective is to present a wide-ranging decision making technique for ranking supplier alternatives in view of the effect of selected criteria. A proposed method is developed aiming the usage of Fuzzy-Rasch model applying five point Likert scale for criteria weight and Grey based COmplex PRoportional ASsessment (COPRAS-G) method for evaluating and ranking the potential alternatives, as per criteria. The applicability of the induced methodology for supplier selection problem in all environments is shown through a case study in telecommunication sector. A sensitivity analysis is performed based on changing weight patterns of criteria to show the stability in ranking result of the proposed approach. Further, a comparative analysis between the ranking results of proposed method done with existing grey multi-attribute decision-making methods viz. VIKOR-G, ARAS-G and TOPSIS-G using spearman’s correlation coefficient for checking the reliability of the ranking result.

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Multi-criteria decision-making algorithm based on aggregation operators under the complex interval-valued q-rung orthopair uncertain linguistic information

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-210442 ◽

2021 ◽

pp. 1-30

Author(s):

Harish Garg ◽

Zeeshan Ali ◽

Zaoli Yang ◽

Tahir Mahmood ◽

Sultan Aljahdali

Keyword(s):

Decision Making ◽

Brain Tumors ◽

Score Function ◽

Aggregation Operators ◽

Multi Criteria Decision Making ◽

Linguistic Features ◽

Interval Numbers ◽

Fundamental Properties ◽

Interval Valued

The paper aims to present a concept of a Complex interval-valued q-rung orthopair uncertain linguistic set (CIVQROULS) and investigated their properties. In the presented set, the membership grades are considered in terms of the interval numbers under the complex domain while the linguistic features are added to address the uncertainties in the data. To further discuss more, we have presented the operation laws and score function for CIVQROULS. In addition to them, we present some averaging and geometric operators to aggregate the different pairs of the CIVQROULS. Some fundamental properties of the proposed operators are stated. Afterward, an algorithm for solving the decision-making problems is addressed based on the proposed operator using the CIVQROULS features. The applicability of the algorithm is demonstrated through a case study related to brain tumors and their effectiveness is compared with the existing studies.

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A Multi-MOORA decision making method based on muirhead mean operators and complex spherical fuzzy uncertain linguistic setting

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211455 ◽

2021 ◽

pp. 1-26

Author(s):

Fen Wang ◽

Zeeshan Ali ◽

Tahir Mahmood ◽

Shouzhen Zeng

Keyword(s):

Decision Making ◽

General Structure ◽

Aggregation Operators ◽

Ratio Analysis ◽

Multi Objective Optimization ◽

Linguistic Terms ◽

Modifiable Factors ◽

Multi Attribute Decision Making ◽

Multiplicative Form ◽

Actual Life

The Muirhead mean (MM) operators offer a flexible arrangement with its modifiable factors because of Muirhead’s general structure. On the other hand, MM aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. In this manuscript, the complex spherical fuzzy uncertain linguistic set (CSFULS), covering the grade of truth, abstinence, falsity, and their uncertain linguistic terms is proposed to accomplish with awkward and intricate data in actual life dilemmas. Furthermore, by using the MM aggregation operators with the CSFULS, the complex spherical fuzzy uncertain linguistic MM (CSFULMM), complex spherical fuzzy uncertain linguistic weighted MM (CSFULWMM), complex spherical fuzzy uncertain linguistic dual MM (CSFULDMM), complex spherical fuzzy uncertain linguistic dual weighted MM (CSFULDWMM) operators, and their important results are also elaborated with the help of some remarkable cases. Additionally, multi-attribute decision-making (MADM) based on the Multi-MOORA (Multi-Objective Optimization Based on a Ratio Analysis plus full multiplicative form), and proposed operators are developed. To determine the rationality and reliability of the elaborated approach, some numerical examples are illustrated. Finally, the supremacy and comparative analysis of the elaborated approaches with the help of graphical expressions are also developed.

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