OWA-based aggregation operations in multi-expert MCDM model

This paper presents an analysis of multi-expert multi-criteria decision making (ME-MCDM) model based on the ordered weighted averaging (OWA) operators. Two methods of modeling the majority opinion are studied as to aggregate the experts' judgments, in which based on the induced OWA operators. Then, an overview of OWA with the inclusion of different degrees of importance is provided for aggregating the criteria. An alternative OWA operator with a new weighting method is proposed which termed as alternative OWAWA (AOWAWA) operator. Some extensions of ME-MCDM model with respect to two-stage aggregation processes are developed based on the classical and alternative schemes. A comparison of results of different decision schemes then is conducted. Moreover, with respect to the alternative scheme, a further comparison is given for different techniques in integrating the degrees of importance. A numerical example in the selection of investment strategy is used as to exemplify the model and for the analysis purpose

Weighted‐selective aggregated majority‐OWA operator and its application in linguistic group decision making

This paper focuses on the aggregation operations in the group decision-making model based on the concept of majority opinion. The weighted-selective aggregated majority-OWA (WSAM-OWA) operator is proposed as an extension of the SAM-OWA operator, where the reliability of information sources is considered in the formulation. The WSAM-OWA operator is generalized to the quanti- fied WSAM-OWA operator by including the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM-IOWA operator, with an ordering step, is introduced to the individual fusion strategy. The proposed aggregation operators are then implemented for the case of alternative scheme of heterogeneous group decision analysis. The heterogeneous group includes the consensus of experts with respect to each specific criterion. The exhaustive multicriteria group decision-making model under the linguistic domain, which consists of two-stage aggregation processes, is developed in order to fuse the experts' judgments and to aggregate the criteria. The model provides greater flexibility when analyzing the decision alternatives with a tolerance that considers the majority of experts and the attitudinal character of experts. A selection of investment problem is given to demonstrate the applicability of the developed model

The generalized circular intuitionistic fuzzy set and its operations

The circular intuitionistic fuzzy set (CIFS) is an extension of the intuitionistic fuzzy set (IFS), where each element is represented as a circle in the IFS interpretation triangle (IFIT) instead of a point. The center of the circle corresponds to the coordinate formed by membership ($\mathcal{M}$) and non-membership ($\mathcal{N}$) degrees, while the radius, $r$, represents the imprecise area around the coordinate. However, despite enhancing the representation of IFS, CIFS remains limited to the rigid $IFIT$ space, where the sum of $\mathcal{M}$ and $\mathcal{N}$ cannot exceed one. In contrast, the generalized IFS (GIFS) allows for a more flexible IFIT space based on the relationship between $\mathcal{M}$ and $\mathcal{N}$ degrees. To address this limitation, we propose a generalized circular intuitionistic fuzzy set (GCIFS) that enables the expansion or narrowing of the IFIT area while retaining the characteristics of CIFS. Specifically, we utilize the generalized form introduced by Jamkhaneh and Nadarajah. First, we provide the formal definitions of GCIFS along with its relations and operations. Second, we introduce arithmetic and geometric means as basic operators for GCIFS and then extend them to the generalized arithmetic and geometric means. We thoroughly analyze their properties, including idempotency, inclusion, commutativity, absorption and distributivity. Third, we define and investigate some modal operators of GCIFS and examine their properties. To demonstrate their practical applicability, we provide some examples. In conclusion, we primarily contribute to the expansion of CIFS theory by providing generality concerning the relationship of imprecise membership and non-membership degrees

Decision Analysis, Uncertainty Theories and Aggregation Operators in Financial Selection Problems

[eng] The complexity of financial analysis, particularly on selection process or decision making problems, has increased rapidly over several decades. As a result, much attention has been focused on developing and implementing the efficient mathematical models for supporting this kind of problems. Multiple criteria decision analysis, an advanced field of operations research provides analysts or decision makers a broad range of methodologies, which are all suited to the complexity of financial decision analysis. In the financial modeling, uncertainty problems are inevitable, owing to the fact that the consequences of events are not precisely known. In addition, human judgments as part of analysis also contribute to it intricacy. Correspondingly, many studies have been concentrated on integrating uncertainty theories in modeling the real financial problems. One area of interest is on the inclusion of the element of human behavior or attitudinal character of decision makers. Aggregation operator in this case can offer a wide spectrum of analysis or flexibility in modeling the human behavior in financial decision analysis. In general, the main purpose of this work is on the study of financial selection problems from the perspective of decision analysis, uncertainty theories and aggregation operators. To be specific, the decision problems under a finite or discrete case and multidimensional factors are studied. The emphasis is given on the group decision making models, notably, the Dempster-Shafer theory (DST) of belief structure, the analytic hierarchy process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS). Moreover, the uncertainty theories based on fuzzy set theory and imprecise probability are employed, together with information fusion based on the ordered weighted average (OWA) operators. Quantitative and qualitative preferences, decision strategies based on the attitudinal character of decision makers, and majority concepts for group consensus are highlighted. The specific contributions of this work are summarized as the following: • The first contribution is on developing the multi-expert multi-criteria decision making (ME-MCDM) model with respect to two-stage aggregation processes. In specific, the aggregation of criteria is based on the integration of weighted arithmetic mean (WA) and OWA. The main attention is given on the proposed alternative OWAWA operator as an extension of immediate WA and OWAWA operators. Two approaches for modeling the majority opinion of experts are studied, in which based on the induced OWA (IOWA) operators. Some modifications to the support functions are suggested as to derive the order inducing variables. The analysis of ME-MCDM model based on these aggregation processes then is conducted. In this study the selection of investment strategy is used as to exemplify the model. • The weighted-selective aggregated majority-OWA operator may be considered as the second contribution. It is as an extension of the SAM-OWA operator, where the reliability of information sources is considered. The WSAM-OWA then is generalized to the quantified WSAM-OWA by incorporating the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM-IOWA with an ordering step is proposed for the individual fusion strategy. These aggregation operators are then implemented to the case of alternative scheme of heterogeneous group decision analysis, in particular for a selection of investment problem. • Third contribution is represented by the development of linguistic group decision making with Dempster-Shafer belief structure. Different type of linguistic aggregation operator such as the 2-tuple induced linguistic OWA operator is suggested. Specifically, it is based on order-inducing variables in which the ordering of the arguments and uncertain situations can be assessed with linguistic information. Then, by using the 2-TILOWA in the D-S framework, the belief structure-2-TILOWA operator can be formed. Some of its main properties are studied. This model is applied in a selection of financial strategies. • The extension of AHP for group decision making model is given as the fourth contribution, notably, based on the inclusion of IOWA operators. Two-stage aggregation processes used in the AHP-GDM model are extended. Firstly, a generalization of weighted maximal entropy OWA under the IOWA operator is proposed as to aggregate the criteria. Further, the majority concept based on the IOWA and Minkowski OWA-based similarity measure is suggested to determine a consensus among experts. This model provides a variant of decision strategies for analyzing the individual and the majority of experts. The application in investment selection problem is presented to test the reliability of the model. • The fifth contribution is on the integration of heavy ordered weighted geometric (HOWG) aggregation operators in AHP-GDM model. In the sense of heavy OWA operator (HOWA), the heavy weighted geometric (HWG) and HOWG are introduced as extensions of the normal weighted geometric mean (WG) and the OWG by relaxing the constraints on the associated weighting vector. These HWG and HOWG operators then are utilized in the aggregation process of AHP-GDM, specifically on the aggregation of individual judgments procedure. The main advantage of the model, besides the complete overlapping of information such in classical methods, is that it can also accommodate partial and non-overlapping information in the formulation. An investment selection problem is applied to demonstrate the model. • The extension of TOPSIS for group decision making model by the inclusion of majority concept may be considered as the sixth contribution. The majority concept is derived based on the induced generalized OWA (IGOWA) operators. Two fusion schemes in TOPSIS model are designed. First, an external fusion scheme to aggregate the experts’ judgments with respect to the concept of majority opinion on each criterion is suggested. Then, an internal fusion scheme of ideal and anti-ideal solutions that represents the majority of experts is proposed using the Minkowski OWA distance measures. The comparison of the proposed model with some other TOPSIS models with respect to distance measures is presented. Here, a general case of selection problem is presented, specifically on the human resource selection problem. • Finally, the group decision making model based on conflicting bifuzzy sets (CBFS) is proposed. Precisely, the subjective judgments of experts, mainly from positive and negative aspects are considered simultaneously in the analysis. Moreover, the weighting method for the attribute (or sub-attribute) is subject to the integration of subjective and objective weights. The synthesis of CBFS in the model is naturally done by extending the fuzzy evaluation in parallel with the intuitionistic fuzzy set. A new technique to compute the similarity measure is proposed, in which, being the degree of agreement between the experts. The model then is applied in the case study of flood control project selection problem. To sum up, the presented thesis dealt with the extension of multi-criteria decision analysis models for the financial selection problems (as a specific scope) and also the general selection problems with the inclusion of attitudinal character, majority concept and fuzzy set theory. In particular, the group decision making model, Dempster-Shafer belief structure, AHP and TOPSIS are proposed to overcome the shortcoming of the existing models, i.e., related to the financial decision analysis. The applicability and robustness of the developed models have been demonstrated and some sensitivity analyses are also provided. The main advantages of the proposed models are to provide a more general and flexible models for a wider analysis of the decision problems[spa] La tesis, a través del análisis y desarrollo del Análisis de decisiones, Teorías de incertidumbre y Operadores de agregación, busca contribuir al estado del arte y nuevas propuesta de las necesidades y demandas que los decisores, responsables o e inversores financieros se encuentran por la creciente complejidad de sus análisis y estrategias, sobre todo en los procesos de selección o en los problemas de decisión. Así, el objetivo principal de esta tesis es el estudio de los problemas de selección financiera desde la perspectiva del análisis de decisiones, las teorías de la incertidumbre y los operadores de agregación. En concreto, se estudian los problemas de decisión en virtud de un conjunto finito de alternativas (caso discreto) y de factores multidimensionales. En el trabajo se desarrolla una extensión de los modelos de análisis de decisiones multicriterio y multiexperto que se utilizan en la resolución de los problemas de selección financiera (como ámbito específico), pero también en los problemas de selección generales, con la inclusión del carácter actitudinal, el concepto de mayoría y la teoría de los conjuntos borrosos. En particular, el énfasis se sitúa en los modelos de toma de decisiones en grupo y en la estructura de creencias Dempster-Shafer (D-S), el proceso analítico jerárquico (AHP) i la técnica de orden de preferencia por similitud con la solución ideal (TOPSIS). Además, se aplican las teorías de incertidumbre basadas en conjuntos borrosos y de probabilidades imprecisas juntamente con la fusión de la información basada en operadores OWA. También se destaca las preferencias cuantitativas y cualitativas, las estrategias de decisión basadas en el carácter actitudinal de los decisores, y el concepto de mayoría en el consenso grupal, de forma que se propone el desarrollo de operadores OWA, la generalización de los modelos AHP y TOPSIS, juntamente con el modelo de toma de decisiones grupal y la estructura de creencias Dempster-Shafer, con el fin de superar las deficiencias de los modelos existentes en relación con el análisis de decisiones financieras. En particular, la investigación realizada se puede sintetizar en siete aportaciones específicas al state-of-the-art del Análisis de decisiones y los operadores de agregación, con aplicaciones en diferentes problemas de decisión financiera: 1. Operadores de agregación basados en los OWA en los modelos de decisión Multiexpertos y Multicriterio. 2. Operadores ponderados SAM-OWA y su aplicación en modelos GDM con operadores lingüísticos. 3. Modelos GDM con operadores lingüísticos adaptados a la teoría de Dempster-Shafer con la aplicación de operadores de agregación inducidos lingüísticos. 4. Generalización del modelo AHP para decisiones grupales usando operadores OWA inducidos. 5. Introducción de operadores OWA geométricos y pesados en los modelos GDM y AHP. 6. Ampliación de los modelos TOPSIS con operadores de agregación basados en los OWA. 7. Desarrollo y aplicación del Conflicting bifuzzy a modelos de decisión MAGDM En la tesis se demuestra la aplicabilidad y la robustez de los modelos desarrollados, tanto con un esquema de agregación de expertos clásicos como con un esquema alternativo que separa por criterios de decisión. Las principales ventajas de los modelos propuestos son que se tratan modelos más generales y flexibles para un análisis más amplio de los problemas de decisión, en particular de los de selección financiera, que incorporen diversos criterios, expertos y componentes de incertidumbre y lingüísticos

A Border Approximation Area Approach Considering Bipolar Neutrosophic Linguistic Variable for Sustainable Energy Selection

In the last few decades, the computational methods under Multi-Criteria Decision-Making (MCDM) have experienced significant growth in research interests from various scientific communities. Multi-Attributive Border Approximation area Comparison (MABAC) is one of the MCDM methods where its computation procedures are based on distances and areas, and able to express a complex decision systematically. Previous literature have suggested the combination of MABAC with fuzzy sets, in which this combination is used to solve problems that are characterized by uncertain and incomplete information. Differently from the fuzzy MABAC, which directly used single membership, this paper proposes bipolar neutrosophic MABAC of which the positive and negative of truth, indeterminate and false memberships of bipolar neutrosophic set are introduced to enhance decision in sustainable energy selection. Fourteen criteria and seven alternatives of sustainable energy are the main MCDM structures that need to be solved using the proposed method. A group of experts were invited to provide rating of performance values of criteria and alternatives of sustainable energy problem using a bipolar neutrosophic linguistic scale. The distances of alternatives from the Border Approximation Area of bipolar neutrosophic MABAC are the main output of the proposed method prior to making the final decision. The computational results show that ‘Biomass’ is the optimal alternative to sustainable energy selection. Comparable results are also presented to check the consistency of the proposed method

Owa-based aggregation operations in multi-expert MCDM model

This paper presents an analysis of multi-expert multi-criteria decision making (ME-MCDM) model based on the ordered weighted averaging (OWA) operators. Two methods of modeling the majority opinion are studied as to aggregate the experts' judgments, in which based on the induced OWA operators. Then, an overview of OWA with the inclusion of different degrees of importance is provided for aggregating the criteria. An alternative OWA operator with a new weighting method is proposed which termed as alternative OWAWA (AOWAWA) operator. Some extensions of ME-MCDM model with respect to two-stage aggregation processes are developed based on the classical and alternative schemes. A comparison of results of different decision schemes then is conducted. Moreover, with respect to the alternative scheme, a further comparison is given for different techniques in integrating the degrees of importance. A numerical example in the selection of investment strategy is used as to exemplify) the model and for the analysis purpose.Ministry of Higher Education Malaysia / University of Malaysia Terengganu (UMT

Novel Concept of Energy in Bipolar Single-Valued Neutrosophic Graphs with Applications

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signless Laplacian energy with single-valued neutrosophic graphs (SVNGs). This integration is used to solve problems that are characterized by indeterminate and inconsistent information. However, when the information is endowed with both positive and negative uncertainty, then bipolar single-valued neutrosophic sets (BSVNs) constitute an appropriate knowledge representation of this framework. A BSVNs is a generalized bipolar fuzzy structure that deals with positive and negative uncertainty in real-life problems with a larger domain. In contrast to the previous study, which directly used truth and indeterminate and false membership, this paper proposes integrating energy, Laplacian energy, and signless Laplacian energy with BSVNs to graph structure considering the positive and negative membership degree to greatly improve decisions in certain problems. Moreover, this paper intends to elaborate on characteristics of eigenvalues, upper and lower bound of energy, Laplacian energy, and signless Laplacian energy. We introduced the concept of a bipolar single-valued neutrosophic graph (BSVNG) for an energy graph and discussed its relevant ideas with the help of examples. Furthermore, the significance of using bipolar concepts over non-bipolar concepts is compared numerically. Finally, the application of energy, Laplacian energy, and signless Laplacian energy in BSVNG are demonstrated in selecting renewable energy sources, while optimal selection is suggested to illustrate the proposed method. This indicates the usefulness and practicality of this proposed approach in real life