Fuzzy-based linguistic patterns as a tool for the flexible assessment of a priority vector obtained by pairwise comparisons

Grobelny, Jerzy

doi:10.1016/j.fss.2015.05.012

Cited by 9 publications

(8 citation statements)

References 36 publications

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“…In addition to ⋅ * and ⋅ * , we set several other weight possibilities between them and obtain the corresponding interval weights by (8) replacing * into . Then, the membership functions of fuzzy weight vectors̃1 and̃2 by the upper approximation models are obtained by (2). They are illustrated as the dotted lines in Figures 2 and 3, respectively.…”

Section: Fuzzy Weight Vector By Upper Approximation Modelmentioning

confidence: 99%

“…For both comparison matrices, we set several other comparison possibilities ≥ * in approximation relation R by (13), and from each processed comparison matrix the interval weight vector is obtained by (16) replacing * into . Then, the membership functions fuzzy weight vectors̃1 and̃2 by the lower approximation model are obtained by (2) and illustrated as the bold lines in Figures 2 and 3, respectively.…”

Section: Fuzzy Weight Vector By Lower Approximation Modelmentioning

confidence: 99%

“…In order to represent our vague judgment, interval/fuzzy numbers may be more preferable and suitable than crisp numbers. Moreover, when linguistic patterns among the items are given, the comparison matrix is constructed based on transitivity so as to be robust for rank reverse [2]. In case of an interval/fuzzy comparison matrix, a crisp or interval/fuzzy weight vector could be obtained.…”

Section: Introductionmentioning

confidence: 99%

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Two Approximation Models of Fuzzy Weight Vector from a Comparison Matrix

Entani

2018

Advances in Fuzzy Systems

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In this study, our uncertain judgment on multiple items is denoted as a fuzzy weight vector. Its membership function is estimated from more than one interval weight vector. The interval weight vector is obtained from a crisp/interval comparison matrix by Interval Analytic Hierarchy Process (AHP). We redefine it as a closure of the crisp weight vectors which approximate the comparison matrix. The intuitively given comparison matrix is often imperfect so that there could be various approaches to approximate it. We propose two of them: upper and lower approximation models. The former is based on weight possibility and the weight vector with it includes the comparison matrix. The latter is based on comparison possibility and the comparison matrix with it includes the weight vector.

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Section: Fuzzy Weight Vector By Upper Approximation Modelmentioning

confidence: 99%

Section: Fuzzy Weight Vector By Lower Approximation Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Two Approximation Models of Fuzzy Weight Vector from a Comparison Matrix

Entani

2018

Advances in Fuzzy Systems

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“…When pattern (1) is true for all pairs of objects, we may assume that the solution is good. As it was demonstrated in a number of articles ([2], [3], [4], [5], [6]), it is possible to assess the truth level of formula (1) by means of the Łukasiewicz's implication formula (2):…”

Section: Overview Of Simulated Annealing Based On Linguistic Patternsmentioning

confidence: 99%

“…For instance, applications of fuzzy logic ( [14], [15]) allow the use of experts' knowledge and experience in this respect. One of the possible approaches to modeling in such a manner was proposed by Grobelny [2], [3], [4], and [5]. The idea of linguistic patterns presented in these works enables the designers to take advantage of expert's intuition by expressing it in a form similar to natural language.…”

Section: Introductionmentioning

confidence: 99%

Simulated Annealing Based on Linguistic Patterns: Experimental Examination of Properties for Various Types of Logistic Problems

Grobelny

Michalski

2017

Information Systems Architecture and Technology: Proceedings of 38th International Conference on Information Systems Architectu

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The paper presents simulation experiment results regarding properties of linguistic pattern based simulated annealing used for solving the facilities layout problems in logistics. In the article, we investigate four different arrangements (02 × 18, 03 × 12, 04 × 09, and 06 × 06) comprising of 36 items. The examined layouts also differ in the links matrix density (20%, 40%, and 60%) and in defining distance between objects' pairs for the distance membership function (absolute and relative). We formally examine how these factors influence corrected mean truth values and average classical goal function values based on Manhattan distance metric. The results generally revealed a significant influence of all of the studied effects on the analyzed dependent variables. Some of the findings, however, were surprising and confirmed previous outcomes showing that the linguistic pattern approach is not a simple extension of the classic simulated annealing.

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Scatter Plots Based on Fuzzy Logic in Supporting the Design of Graphical Interfaces

Grobelny

Michalski

2023

Lecture Notes in Computer Science

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Fuzzy-based linguistic patterns as a tool for the flexible assessment of a priority vector obtained by pairwise comparisons

Cited by 9 publications

References 36 publications

Two Approximation Models of Fuzzy Weight Vector from a Comparison Matrix

Two Approximation Models of Fuzzy Weight Vector from a Comparison Matrix

Simulated Annealing Based on Linguistic Patterns: Experimental Examination of Properties for Various Types of Logistic Problems

Scatter Plots Based on Fuzzy Logic in Supporting the Design of Graphical Interfaces

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