A VIKOR-based method for hesitant fuzzy multi-criteria decision making

doi:10.1007/S10700-013-9162-0

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A VIKOR-based method for hesitant fuzzy multi-criteria decision making

Journal Article•DOI•

A VIKOR-based method for hesitant fuzzy multi-criteria decision making

Huchang Liao¹, Zeshui Xu¹•Institutions (1)

Shanghai Jiao Tong University¹

01 Dec 2013-Fuzzy Optimization and Decision Making (Springer US)-Vol. 12, Iss: 4, pp 373-392

TL;DR: The classical VIKOR method is extended to accommodate hesitant fuzzy circumstances, and a practical example is provided to show that the method is very effective in solving multi-criteria decision making problems with hesitant preference information.

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Abstract: Since it was firstly introduced by Torra and Narukawa (The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 2009, pp. 1378---1382), the hesitant fuzzy set has attracted more and more attention due to its powerfulness and efficiency in representing uncertainty and vagueness. This paper extends the classical VIKOR (vlsekriterijumska optimizacija i kompromisno resenje in serbian) method to accommodate hesitant fuzzy circumstances. Motivated by the hesitant normalized Manhattan distance, we develop the hesitant normalized Manhattan $$L_p$$ --metric, the hesitant fuzzy group utility measure, the hesitant fuzzy individual regret measure, and the hesitant fuzzy compromise measure. Based on these new measures, we propose a hesitant fuzzy VIKOR method, and a practical example is provided to show that our method is very effective in solving multi-criteria decision making problems with hesitant preference information.

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Journal Article•DOI•

Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

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Xiaolu Zhang¹, Zeshui Xu²•Institutions (2)

Southeast University¹, Sichuan University²

01 Dec 2014-Journal of intelligent systems

TL;DR: Some novel operational laws of PFSs are defined and an extended technique for order preference by similarity to ideal solution method is proposed to deal effectively with them for the multicriteria decision‐making problems with PFS.

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Abstract: Recently, a new model based on Pythagorean fuzzy set PFS has been presented to manage the uncertainty in real-world decision-making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision-making problems with PFSs, we propose an extended technique for order preference by similarity to ideal solution method to deal effectively with them. In this approach, we first propose a score function based comparison method to identify the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. Then, we define a distance measure to calculate the distances between each alternative and the Pythagorean fuzzy positive ideal solution as well as the Pythagorean fuzzy negative ideal solution, respectively. Afterward, a revised closeness is introduced to identify the optimal alternative. At length, a practical example is given to illustrate the developed method and to make a comparative analysis.

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1,084 citations

Journal Article•DOI•

Fuzzy multiple criteria decision-making techniques and applications - Two decades review from 1994 to 2014

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Abbas Mardani¹, Ahmad Jusoh¹, Edmundas Kazimieras Zavadskas²•Institutions (2)

Universiti Teknologi Malaysia¹, Vilnius Gediminas Technical University²

15 May 2015-Expert Systems With Applications

TL;DR: This study reviewed a total of 403 papers published from 1994 to 2014 in more than 150 peer reviewed journals and indicated that, in 2013, scholars have published papers more than other years.

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Abstract: Two decades was systematically reviewed on fuzzy MCDM techniques from 1994 to 2014.The database for review was 403 papers from more than 150 high-ranking journals.403 scholarly papers were grouped in four different main fields.Papers were classified based on utilizing, developing and proposing research papers. MCDM is considered as a complex decision-making tool involving both quantitative and qualitative factors. In recent years, several fuzzy FMCDM tools have been suggested to choosing the optimal probably options. The purpose of this paper is to review systematically the applications and methodologies of the fuzzy multi decision-making (FMCDM) techniques. This study reviewed a total of 403 papers published from 1994 to 2014 in more than 150 peer reviewed journals (extracted from online databases such as ScienceDirect, Springer, Emerald, Wiley, ProQuest, and Taylor & Francis). According to experts' opinions, these papers were grouped into four main fields: engineering, management and business, science, and technology. Furthermore, these papers were categorized based on authors, publication date, country of origin, methods, tools, and type of research (FMCDM utilizing research, FMCDM developing research, and FMCDM proposing research). The results of this study indicated that, in 2013, scholars have published papers more than other years. In addition, hybrid fuzzy MCDM in the integrated method and fuzzy AHP in the individual section were ranked as the first and second methods in use. Additionally, Taiwan was ranked as the first country that contributed to this survey, and engineering was ranked as the first field that has applied fuzzy DM tools and techniques.

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724 citations

Journal Article•DOI•

Cours d'economie politique

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Jean Marchal

01 Apr 1950-Population

601 citations

Journal Article•DOI•

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Huchang Liao¹, Huchang Liao², Zeshui Xu³, Xiao-Jun Zeng²•Institutions (3)

Shanghai Jiao Tong University¹, University of Manchester², Sichuan University³

01 Jul 2014-Information Sciences

TL;DR: Different types of distance and similarity measures for HFLTSs are investigated and developed and the satisfaction degrees for different alternatives are established and are then used to rank alternatives in multi-criteria decision making.

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509 citations

Cites background from "A VIKOR-based method for hesitant f..."

...Xu and Xia [46] proposed a variety of distance measures for HFSs, based on which the corresponding similarity measures were obtained....
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...Ordered weighted distance and similarity measures, first proposed by Xu and Chen [42], have also been investigated by many scholars and have been applied to fuzzy sets [40], linguistic fuzzy sets [40,41,45] and HFSs [46]....
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...The motivation for introducing HFSs was that it is sometimes difficult to determine the membership degree of an element to a set, and in some circumstances this difficulty is caused by a doubt between a few different values [30]....
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...Motivated by HFSs and linguistic fuzzy sets, Rodríguez et al. [26] proposed the concept of the hesitant fuzzy linguistic term set (HFLTS), which provides a different and more powerful form to represent decision makers’ preferences in the decision making process....
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...All these distance measures have been extended into fuzzy sets [23,35,39,40,42], intuitionistic fuzzy sets [2,7,11,17,28,29,38,43,47], interval-valued intuitionistic fuzzy sets [1,2,7,47], linguistic fuzzy sets [36,37,41,45] and HFSs [13,14,46]....
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Journal Article•DOI•

Hesitant Fuzzy Sets: State of the Art and Future Directions

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Rosa M. Rodríguez¹, Luis Martínez¹, Vicenç Torra, Zeshui Xu², Francisco Herrera³, Francisco Herrera⁴ - Show less +2 more•Institutions (4)

University of Jaén¹, Sichuan University², University of Granada³, King Abdulaziz University⁴

01 Jun 2014-Journal of intelligent systems

TL;DR: An overview on hesitant fuzzy sets is presented with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.

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Abstract: The necessity of dealing with uncertainty in real world problems has been a long-term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type-2 fuzzy sets, interval-valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so-called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets.

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405 citations

Cites background from "A VIKOR-based method for hesitant f..."

...[57] HFS 2012 Lee and Chen [20] HFLTS 2013 Liao and Xu [21] HFS 2013 Liu [23] HFS 2013 Xu and Zhang [53] HFS 2013 Zhang and Wei [64] HFS 2013 Liu and Rodŕıguez [22] HFLTS 2014 Wei et al....
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References

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Open Access

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Book•

Fuzzy sets

[...]

Lotfi A. Zadeh

01 Aug 1996

TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

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Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

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52,705 citations

Book Chapter•DOI•

The Analytic Hierarchy Process

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Thomas L. Saaty¹, Kevin P. Kearns•Institutions (1)

University of Pittsburgh¹

01 Jan 1985

TL;DR: Analytic Hierarchy Process (AHP) as mentioned in this paper is a systematic procedure for representing the elements of any problem hierarchically, which organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pairwise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy.

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Abstract: This chapter provides an overview of Analytic Hierarchy Process (AHP), which is a systematic procedure for representing the elements of any problem hierarchically. It organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pair-wise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy. These judgments are then translated to numbers. The AHP includes procedures and principles used to synthesize the many judgments to derive priorities among criteria and subsequently for alternative solutions. It is useful to note that the numbers thus obtained are ratio scale estimates and correspond to so-called hard numbers. Problem solving is a process of setting priorities in steps. One step decides on the most important elements of a problem, another on how best to repair, replace, test, and evaluate the elements, and another on how to implement the solution and measure performance.

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16,547 citations

Book•DOI•

Multiple Attribute Decision Making

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Ching-Lai Hwang, Kwangsun Yoon

01 Jan 1981

6,268 citations

Journal Article•DOI•

Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS

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Serafim Opricovic, Gwo-Hshiung Tzeng¹•Institutions (1)

National Chiao Tung University¹

16 Jul 2004-European Journal of Operational Research

TL;DR: A comparative analysis of the multiple criteria decision making methods VIKOR and TOPSIS is illustrated with a numerical example, showing their similarity and some differences.

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3,563 citations

"A VIKOR-based method for hesitant f..." refers background or methods in this paper

...…has been applied widely in many fields, such as mountain destination choosing (Opricovic and Tzeng 2004), alternative hydropower systems evaluating (Opricovic and Tzeng 2004), forestation and forest preservation (Kaya and Kahraman 2011), post-earthquake sustainable reconstruction (Opricovic 2002),…...
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...They sometimes can only depend on their experiences and the experiments about the existing system or other similar systems because there is no general procedure and mathematical model could replace human creativity in generating alternatives (Opricovic and Tzeng 2004)....
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...Up to now, the VIKOR method has been applied widely in many fields, such as mountain destination choosing (Opricovic and Tzeng 2004), alternative hydropower systems evaluating (Opricovic and Tzeng 2004), forestation and forest preservation (Kaya and Kahraman 2011), post-earthquake sustainable…...
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...After comparing the TOPSIS method and the VIKOR method in terms of aggregation function and normalization effects, Opricovic and Tzeng (2004) pointed out that although both of the TOPSIS method and the VIKOR method are on the basis of the distance of an object (or alternative) to the ideal…...
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Journal Article•DOI•

Hesitant fuzzy sets

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Vicenç Torra¹•Institutions (1)

Autonomous University of Barcelona¹

01 Jun 2010-Journal of intelligent systems

TL;DR: It is proved that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set, and it is proved also that the operations proposed are consistent with the ones of intuitionist fuzzy sets when applied to the envelope.

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Abstract: Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.

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2,232 citations

"A VIKOR-based method for hesitant f..." refers background in this paper

...Torra and Narukawa (2009), Torra (2010) firstly introduced this new extension of fuzzy set and gave some basic operations on it....
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...In what follows, we review some basic concepts related to HFSs: Definition 1 (Torra and Narukawa 2009; Torra 2010)....
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...All these extensions are based on the same rationale that it is not clear to assign the membership degree of an element to a fixed set (Torra and Narukawa 2009; Torra 2010)....
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...Torra (2010) firstly gave the concept of HFS, defined some of its basic operations....
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...Recently, on the basis of the above extensional forms of fuzzy set, Torra and Narukawa (2009), Torra (2010) proposed a new generalized type of fuzzy set called hesitant fuzzy set (HFS), which opens new perspectives for further research on decision making under hesitant environments....
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