A family of fuzzy distance measures of fuzzy numbers

Aguilar-Pena, Concepcion; Hierro, Antonio-Francisco Roldán-López De; Hierro, Concepción Roldán-López De; Martínez-Moreno, Juan

doi:10.1007/s00500-014-1497-0

Cited by 11 publications

(4 citation statements)

References 24 publications

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“…Distance measures have been widely used to measure the amount of deviation and degree of proximity between arguments (Aguilar-Peña et al 2016). In recent years, the Hamming distance measure (Liao et al 2014), Euclidean distance measure (Biswas et al 2016), Hausdorff distance (Zhou et al 2019), cosine distance (Liao and Xu 2015), and logarithmic functionbased distance (Zhou et al 2016) have been developed.…”

Section: Distance-based Methods For Deriving Dms' Weights and Criteria Weightsmentioning

confidence: 99%

Single-valued neutrosophic ELECTRE II for multi-criteria group decision-making with unknown weight information

et al. 2020

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This paper develops a novel multi-criteria group decision-making method for resolving single-valued neutrosophic group decision-making problems with unknown weight information. Firstly, considering the different knowledge backgrounds of decision-makers (DMs), two distance-based methods are developed to obtain the weights of DMs and criteria. One of these methods focuses on the closeness between the decision matrix given by an individual DM and that of the group judgment, and the proximity between the decision matrix given by an individual DM and the matrices given by all the other DMs to determine the weights of DMs with respect to each criterion. The other method extends the maximizing deviation method to objectively obtain the weights of criteria. Secondly, an extended ELECTRE (ELimination Et Choix Traduisant la REalité) II is investigated to effectively circumvent the issue that criteria cannot compensate for each other. In this method, three levels of concordance and discordance sets are constructed to fully denote the underlying preference information and specify the outranking degrees of alternatives. Finally, two illustrative examples are presented to demonstrate the feasibility of the proposed approach, followed by a sensitivity analysis and a comparative analysis to test its robustness and effectiveness.

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Section: Distance-based Methods For Deriving Dms' Weights and Criteria Weightsmentioning

confidence: 99%

Single-valued neutrosophic ELECTRE II for multi-criteria group decision-making with unknown weight information

et al. 2020

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“…The main purpose of the consensus reaching method is to ensure that both value forms of grey numbers are transformed into common value form for easier computation. Furthermore, type-1 fuzzy numbers are well established in decision making application [23][24][25][26][27][28][29][30][31][32]. This consensus reaching method is basically an extension of [10] research work on replacing the characteristic function on grey set with fuzzy membership function.…”

Section: Layer 1: Consensus Reaching Methodsmentioning

confidence: 99%

Grey Number Based Methodology for Non-homogeneous Preference Elicitation in Fuzzy Risk Analysis Management

Bakar

Khalif

Yaakob

et al. 2019

Applying Fuzzy Logic for the Digital Economy and Society

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The incomplete and vagueness of real-world information has triggered the emergence of grey system in human decision making environment. The grey system serves as an alternative methodology that plays the role in complementing the uncertainty in systems with partial information [1][2][3][4]. Similarly as fuzzy sets [5] and rough sets [6][7][8], grey sets characterised the uncertainties in the form of grey

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“…Distance measures are fundamentally important tools in various scientific fields, such as decision‐making, pattern recognition, and cluster analysis (Aguilar‐Peña, Roldán‐López De Hierro, Roldán‐López De Hierro, & Martínez‐Moreno, ; Garg & Kumar, ). However, the traditional distance measures for HFLTSs require β ‐normalization, which may result in information distortion.…”

Section: Unbalanced Hfltss and Their Signed Distancesmentioning

confidence: 99%

Signed distance‐based ORESTE for multicriteria group decision‐making with multigranular unbalanced hesitant fuzzy linguistic information

et al. 2018

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The objective of this study is to develop an integrated approach for solving multicriteria group decision‐making problems with multigranular unbalanced hesitant fuzzy linguistic term sets (HFLTSs). Firstly, a signed distance‐based transformation function is proposed to unify multigranular unbalanced hesitant fuzzy linguistic (HFL) assessments. Secondly, a mathematical programming model based on the maximum consensus is constructed to allocate decision‐makers (DMs)' weights objectively. Thirdly, a new signed distance‐based preference score function is defined to aggregate HFL assessments and determine the weak ranking of alternatives, and a novel preference, indifference, and incomparability test framework is constructed to identify the subtle relations among alternatives. On these bases, a signed distance‐based ORESTE (Organísation, rangement et Synthèse de données relarionnelles, in French) method, in which knowledge regarding criterion values and weights are expressed as multigranular unbalanced HFLTSs, is developed to obtain the ranking of alternatives. Finally, an illustrative example, followed by sensitivity and comparative analyses, is presented to verify the feasibility and effectiveness of the proposed approach.

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A family of fuzzy distance measures of fuzzy numbers

Cited by 11 publications

References 24 publications

Single-valued neutrosophic ELECTRE II for multi-criteria group decision-making with unknown weight information

Single-valued neutrosophic ELECTRE II for multi-criteria group decision-making with unknown weight information

Grey Number Based Methodology for Non-homogeneous Preference Elicitation in Fuzzy Risk Analysis Management

Signed distance‐based ORESTE for multicriteria group decision‐making with multigranular unbalanced hesitant fuzzy linguistic information

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