SOFTWARE SELECTION ON BASE OF SUGENO INTEGRAL

The article is devoted to the problem of  software selection. As a rule, this tasks are formalized as models of multi-criteria decision making (MCDM). The peculiarity of this problem is in the fact that the evaluation criteria , is generally defined by linguistic expert. This requires the use of special methods, in particularly, the theory of fuzzy sets. To solve the problem, an approach based on the  a fuzzy measure  was used . In general, a fuzzy measure allows one to take into account the effect of the mutual influence of criteria. The main difficulty lies in identifying this measure. The fuzzy Sugeno measure and  Sugeno integral were used. An example of solving the indicated problem is given.The article is devoted to the problem of software selection. As a rule, this tasks are formalized as models of multi-criteria decision making (MCDM). The peculiarity of this problem is in the fact that the evaluation criteria, is generally defined by linguistic expert. This requires the use of special methods, in particularly, the theory of fuzzy sets. To solve the problem, an approach based on the a fuzzy measure was used. In general, a fuzzy measure allows one to take into account the effect of the mutual influence of criteria. The main difficulty lies in identifying this measure. The fuzzy Sugeno measure and Sugeno integral were used. An example of solving the indicated problem is given

A NOVEL APPROACH TO CHARACTERIZING HESITATIONS IN INTUITIONISTIC FUZZY NUMBERS

Building upon the concept of D α operator introduced by Atanassov (1989), this article proposes an improved objective approach and a hybrid approach to operationalize D α so that the hesitation in an intuitionistic fuzzy number (IFN) can be further refined and characterized. Numerical experiments are carried out to demonstrate the features and novelty of the proposed approach compared to existing methods in the literature. The aim is to furnish an effective way to refine hesitations in intuitionistic fuzzy assessments for more reliable and confident decision aids

Kombinasi Metode F-AHP dan F-TOPSIS dengan Rasio Keuangan untuk Menentukan Peringkat Bank Perkreditan Rakyat di Kota Malang

Penentuan Peringkat Bank Perkreditan Rakyat dipandang penting untuk mempermudah masyarakat dalam memilih. Penentuan peringkat Bank Perkreditan Rakyat biasanya dilakukan sesuai dengan ketentuan Bank Indonesia peraturan Bank Indonesia (BI) No. 30/12/KEP/DIR Tanggal 30 April 1997 tentang Tata Cara Penilaian Kesehatan BPR. Banyak studi yang telah dilakukan untuk menentukan metode penentuan peringkat dengan pendekatan metode Fuzzy MCDM, BSC, F-AHP, F-TOPSIS, VIKOR, DANP pada bidang perbankan. Pada penelitian ini diusulkan sebuah model pendekatan evaluasi penilaian kinerja dengan kombinasi metode F-AHP dan F-TOPSIS dengan rasio keuangan sebagai kriteria penilaian (Capital, Assets, Equity dan Liquidity) untuk menentukan peringkat BPR di Kota Malang. Data yang digunakan adalah data laporan keuangan perbankan selama tiga tahun (2014-2016). Hasil penelitian menunjukkan bahwa kombinasi metode F-AHP dan F-TOPSIS dengan rasio keuangan dapat digunakan sebagai metode alternatif untuk menyusun peringkat Bank Perkreditan Rakyat di Kota Malang

Simple weighted average as an alternative method in aggregating students’ academic achievements

Purpose – It is a normal practice that students’ overall scores are computed by simple average (SA) method which considers all academic subjects as having the same weights or same degree of importance. This paper highlights the application of simple weighted average (SWA) as an alternative method in aggregating students’ academic achievements.The weights of the academic subjects must be determined prior to the use of SWA. Methodology – In a case study, a group of five teachers from one primary school was asked to rate five main subjects taught in primary schools according to their importance.These five teachers have taught the five subjects for more than six years. The obtained weights values were used to re-compute 2011 mid-semester final examination scores of 33 year-six pupils at the selected primary school.Findings – The teachers decided to give different weight to three subjects, but same weights to two subjects. Furthermore, the SWA scores give different ranking to the pupils as compared to the SA scores. Another sentence or two needed here to explain the findings. Significance – It is argued that the use of the SWA method is more suitable than the simple average method in finding the overall scores of students’ achievements.The SWA method considers the subjects to have different degrees of importance, as they do in the actual educational context

Defining Bonferroni means over lattices

In the face of mass amounts of information and the need for transparent and fair decision processes, aggregation functions are essential for summarizing data and providing overall evaluations. Although families such as weighted means and medians have been well studied, there are still applications for which no existing aggregation functions can capture the decision makers\u27 preferences. Furthermore, extensions of aggregation functions to lattices are often needed to model operations on L-fuzzy sets, interval-valued and intuitionistic fuzzy sets. In such cases, the aggregation properties need to be considered in light of the lattice structure, as otherwise counterintuitive or unreliable behavior may result. The Bonferroni mean has recently received attention in the fuzzy sets and decision making community as it is able to model useful notions such as mandatory requirements. Here, we consider its associated penalty function to extend the generalized Bonferroni mean to lattices. We show that different notions of dissimilarity on lattices can lead to alternative expressions.<br /

Developing an integrated AHP and Intuitionistic FuzzyTOPSIS methodology

U ovom se istraživanju daje pregled analitičkog hijerarhijskog postupka (AHP) i intuicijskih FuzzyTOPSIS (IFT) metoda. Rad se bavi procjenom metodologije zasnovane na AHP-IFT gdje se nesigurnosti opisuju lingvističkim vrijednostima. Najprije se problem izbora dobavljača formulira primjenom AHP, a zatim se koristi za određivanje težina kriterija. Kasnije se IFT koristi za postizanje rangiranja među alternativama temeljenim na mišljenju donositelja odluka (DMs). Ovaj model omogućuje točnu i laku klasifikaciju svojstava dobavljača prema tome kako su rangirani u hibridnom modelu. Daje se numerički primjer kako bi se objasnio glavni dobiveni rezultat u radu.This research gives an overview of the Analytic Hierarchy Process (AHP) and Intuitionistic FuzzyTOPSIS (IFT) methods. This study deals with an evaluation methodology based on the AHP-IFT where the uncertainties are handled with linguistic values. First, the supplier selection problem is formulated using AHP and, then, it is used to determine the weights of the criteria. Later, IFT is used to obtain full- ranking among alternatives based on opinion of the Decision Makers (DMs). The present model provides an accurate and easy classification in supplier attributes by those that have been prioritized in the hybrid model. A numerical example is given to clarify the main developed result in this paper

Developing an integrated AHP and Intuitionistic FuzzyTOPSIS methodology

U ovom se istraživanju daje pregled analitičkog hijerarhijskog postupka (AHP) i intuicijskih FuzzyTOPSIS (IFT) metoda. Rad se bavi procjenom metodologije zasnovane na AHP-IFT gdje se nesigurnosti opisuju lingvističkim vrijednostima. Najprije se problem izbora dobavljača formulira primjenom AHP, a zatim se koristi za određivanje težina kriterija. Kasnije se IFT koristi za postizanje rangiranja među alternativama temeljenim na mišljenju donositelja odluka (DMs). Ovaj model omogućuje točnu i laku klasifikaciju svojstava dobavljača prema tome kako su rangirani u hibridnom modelu. Daje se numerički primjer kako bi se objasnio glavni dobiveni rezultat u radu.This research gives an overview of the Analytic Hierarchy Process (AHP) and Intuitionistic FuzzyTOPSIS (IFT) methods. This study deals with an evaluation methodology based on the AHP-IFT where the uncertainties are handled with linguistic values. First, the supplier selection problem is formulated using AHP and, then, it is used to determine the weights of the criteria. Later, IFT is used to obtain full- ranking among alternatives based on opinion of the Decision Makers (DMs). The present model provides an accurate and easy classification in supplier attributes by those that have been prioritized in the hybrid model. A numerical example is given to clarify the main developed result in this paper

The interval-valued intuitionistic fuzzy geometric choquet aggregation operator based on the generalized banzhaf index and 2-additive measure

Based on the operational laws on interval-valued intuitionistic fuzzy sets, the generalized Banzhaf interval-valued intuitionistic fuzzy geometric Choquet (GBIVIFGC) operator is proposed, which is also an interval-valued intuitionistic fuzzy value. It is worth pointing out that the GBIVIFGC operator can be seen as an extension of some geometric mean operators. Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex. In order to overall reflect the interaction among elements and reduce the complexity of solving a fuzzy measure, we further introduce the GBIVIFGC operator w.r.t. 2-additive measures. Furthermore, if the information about weights of experts and attributes is incompletely known, the models of obtaining the optimal 2-additive measures on criteria set and expert set are given by using the introduced cross entropy measure and the Banzhaf index. Finally, an approach to pattern recognition and multi-criteria group decision making under interval-valued intuitionistic fuzzy environment is developed, respectively

On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.<br /