Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information

Archimedean Heronian mean operators based on complex intuitionistic fuzzy sets and their applications in decision-making problems

In this article, we derive the Archimedean aggregation operators for complex intuitionistic fuzzy sets, for this, first, we evaluate some Archimedean operational laws based on complex intuitionistic fuzzy values and then we discuss their special cases because the Archimedean norms are the general form of all existing norms, for instance, algebraic, Einstein, Hamacher, and Frank operational laws. Furthermore, we present the complex intuitionistic fuzzy Archimedean Heronian aggregation operator and complex intuitionistic fuzzy weighted Archimedean Heronian aggregation operator. Several special cases and the basic properties of the above-proposed operators are also diagnosed, because proposing the Heronian mean operators based on Archimedean norms are very challenging and complicated tasks, because of their features and structure. Additionally, a decision-making process is developed under the identified operators by using complex intuitionistic fuzzy information. Finally, we illustrate several examples to show the multi-attribute decision-making technique is more flexible than the prevailing works with the help of sensitive analysis between explored and certain prevailing works.

Multiple-Attribute Decision Making Based on Intuitionistic Hesitant Fuzzy Connection Set Environment

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach.

Economic modelling of electricity generation: long short-term memory and Q-rung orthopair fuzzy sets

The main goal of this study is to evaluate the impact of population mobility on electricity generation in Russian cities in the conditions of the spread of COVID-19, and identify hotspots. Furthermore, the evaluation is also conducted using hybrid fuzzy decision-making modelling. In this context, q-ROF DEMATEL and TOPSIS methods are taken into consideration. Additionally, a comparative evaluation is also performed with the help of Intuitionistic and Pythagorean fuzzy sets. The results are quite similar that allows to conclude that the findings are reliable and coherent. The study proves the hypothesis that human behavior changed during the COVID-19 pandemic, and electricity consumption is declining in major cities around the world. The biggest fall in energy generation was in Moscow and Yekaterinburg. In St. Petersburg and Nizhny Novgorod, the fall in energy generation is no so crucial because these cities have low building density. The study uses Long Short-Term Memory models with many different parameters. The Q-Rung Orthopair Fuzzy Sets model forecasts new COVID-19 using ten parameters. This study identifies factors influencing the spread of COVID-19 based on the theory of "broken windows" and outlines directions in limiting population mobility, which can form the basis of state policy. According to the analysis the air temperature is the variable that most affects this process.

(2,1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decision-making methods

Orthopair fuzzy sets are fuzzy sets in which every element is represented by a pair of values in the unit interval, one of which refers to membership and the other refers to non-membership. The different types of orthopair fuzzy sets given in the literature are distinguished according to the proposed constrain for membership and non-membership grades. The aim of writing this manuscript is to familiarize a new class of orthopair fuzzy sets called “(2,1)-Fuzzy sets” which are good enough to control some real-life situations. We compare (2,1)-Fuzzy sets with IFSs and some of their celebrated extensions. Then, we put forward the fundamental set of operations for (2,1)-Fuzzy sets and investigate main properties. Also, we define score and accuracy functions which we apply to rank (2,1)-Fuzzy sets. Moreover, we reformulate aggregation operators to be used with (2,1)-Fuzzy sets. Finally, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making (MCDM) problems in the environment of (2,1)-Fuzzy sets. To show the effectiveness and usability of the proposed technique in MCDM problems, an illustrative example is provided.

Entropy-Based Fuzzy TOPSIS Method for Investment Decision Optimization of Large-Scale Projects

Investment of large-scale projects must consider various factors, such as economic conditions and investment environment when making decisions. In large-scale project investment problems, almost 90% of them are completed in a multiobjective context. To this end, the authors of this paper have proposed an entropy-based fuzzy TOPSIS synthesis method to assist in the decision-making optimization of large-scale project investment. Firstly, in accordance with the background of the development of multiattribute decision-making method (MADM), closely related to large-scale project investment, the related research works were studied, and the relevant methods are sorted out. Then, the improved vague-entropy-weight based fuzzy TOPSIS (VEWF-TOPSIS) method, entropy and interval language intuitionistic fuzzy sets based TOPSIS (EILIF-TOPSIS) method, and information entropy attribute importance based intuitionistic fuzzy TOPSIS (IEAI-IF-TOPSIS) method were introduced, and a synthesis MADM method that comprehensively combines the above three methods was proposed. Finally, a numerical case was constructed to properly show the effectiveness of the method proposed in the present work, and the conclusions were put forward for providing ideas and methods for large-scale project investment decision-making. It is of great significance that the proposed framework would make large-scale project investment decisions more reasonable and practical, which enriches the research methods of MADM problems to a certain extent and can provide reference for the actual large-scale project investment decision-making problems.

A Hybrid Intuitionistic Fuzzy-MEREC-RS-DNMA Method for Assessing the Alternative Fuel Vehicles with Sustainability Perspectives

Alternative fuel vehicles (AFVs) offer opportunities to lower fuel costs as well as to reduce greenhouse gas emissions, and, therefore, they are a feasible option for customers in the market. Due to technological advancements, decisions about suitable alternative fuel vehicles are a challenging problem for fleet operators. This paper aims to introduce a multi-attribute decision-analysis framework to rank and select the “alternative fuel vehicles (AFVs)” for a private home healthcare service provider in Chandigarh, India. The selection of AFVs can be treated as a decision-making problem, because of the presence of various qualitative and quantitative attributes. Thus, the current work introduces an integrated decision-making framework based on intuitionistic fuzzy-“method based on the removal effects of criteria (MEREC)”, “ranking sum (RS)”, and the “double normalization-based multi-aggregation (DNMA)” framework for assessing the AFVs. The combination of MEREC and RS is applied to assess the objective and subjective weighting values of various parameters for AFV assessment. The DNMA approach is utilized to prioritize the different AFVs over various significant parameters. According to the outcomes, the most significant parameters for AFV assessment are social benefits, fueling/charging infrastructure, and financial incentives, respectively. In this context, globally existing AFVs for the sustainable transportation sector are identified, and then prioritized against fifteen different criteria relevant to the environmental, economic, technological, social, and political aspects of sustainability. It is distinguished that electric vehicles (G2), hybrid electric vehicles (G1), and hydrogen vehicles (G3) achieve higher overall performance compared to the other technologies available in India. The assessment outcomes prove that electric vehicles can serve as a valuable alternative for decreasing carbon emissions and negative effects on the environment. This technology contributes to transportation sector development and job creation in less developed areas of the country. Moreover, a comparison with existing studies and a sensitivity investigation are conferred to reveal the robustness and stability of the developed framework.

To select suitable supplier for complex equipment military-civilian collaborative design based on fuzzy preference information that from matching perspective

Combine complex equipment collaborative development in military-civilian integration context not only fulfils actual development requirement, but also beneficial to the national economy. Design procedure as first stage of complex equipment military-civilian collaborative development process, select suitable design supplier is significant to whole development process of complex equipment. In order to select suitable design supplier for complex equipment, two aspects done in this paper. One is comprehensive analysis of evaluated influencing factors that affect complex equipment military-civilian collaborative design process, corresponding evaluation indicator constructed and a combination of grey correlation, entropy, DEMATEL (Decision-making Trial and Evaluation Laboratory) and VIKOR analysis theory to obtain grey entropy-DEMATEL-VIKOR, then the combined method is utilized to acquire matching attributes for followed research content. Meanwhile, satisfaction degree for matching side obtained with the help of information aggregation based on power generalized Heronian mean which on the basis of fuzzy preference information. Then, through constructed matching model, suitable design supplier obtained. Finally, a corresponding illustrative example given.

Research on the optimal aggregation method of fuzzy preference information based on spatial Steiner-Weber point

In view of the present situation that most aggregation methods of fuzzy preference information are extended or mixed by classical aggregation operators, which leads to the aggregation accuracy is not high. The purpose of this paper is to develop a novel method for spatial aggregation of fuzzy preference information. Thus we map the fuzzy preference information to a set of three-dimensional coordinate and construct the spatial aggregation model based on Steiner-Weber point. Then, the plant growth simulation algorithm (PGSA) algorithm is used to find the spatial aggregation point. According to the comparison and analysis of the numerical example, the aggregation matrix established by our method is closer to the group preference matrices. Therefore, the optimal aggregation point obtained by using the optimal aggregation method based on spatial Steiner-Weber point can best represent the comprehensive opinion of the decision makers.

Intuitionistic fuzzy set of Γ‐submodules and its application in modeling spread of viral diseases, mutated COVID‐ n , via flights

In this study, we generalize fuzzy Γ‐module, as intuitionistic fuzzy Γ‐submodule of Γ‐module (IFΓM), and utilize it for modeling the spread of coronavirus in air travels. Certain fundamental features of intuitionistic fuzzy Γ‐submodule are provided, and it is proved that IFΓM can be considered as a complete lattice. Some elucidatory examples are demonstrated to explain the properties of IFΓM. The relevance between the upper and lower α‐level cut and intuitionistic fuzzy Γ‐submodules are presented and the characteristics of upper and lower under image and inverse image of IFΓM are acquired. It is verified that the image and inverse image of intuitionistic fuzzy Γ‐submodule are preserved under the module homomorphism. The obtained IFΓM is used to model the aerial transition of viral diseases, that is, COVID‐n, via flights.

A Novel MADM Framework under q-Rung Orthopair Fuzzy Bipolar Soft Sets

In many real-life problems, decision-making is reckoned as a powerful tool to manipulate the data involving imprecise and vague information. To fix the mathematical problems containing more generalized datasets, an emerging model called q-rung orthopair fuzzy soft sets offers a comprehensive framework for a number of multi-attribute decision-making (MADM) situations but this model is not capable to deal effectively with situations having bipolar soft data. In this research study, a novel hybrid model under the name of q-rung orthopair fuzzy bipolar soft set (q-ROFBSS, henceforth), an efficient bipolar soft generalization of q-rung orthopair fuzzy set model, is introduced and illustrated by an example. The proposed model is successfully tested for several significant operations like subset, complement, extended union and intersection, restricted union and intersection, the ‘AND’ operation and the ‘OR’ operation. The De Morgan’s laws are also verified for q-ROFBSSs regarding above-mentioned operations. Ultimately, two applications are investigated by using the proposed framework. In first real-life application, the selection of land for cropping the carrots and the lettuces is studied, while in second practical application, the selection of an eligible student for a scholarship is discussed. At last, a comparison of the initiated model with certain existing models, including Pythagorean and Fermatean fuzzy bipolar soft set models is provided.

An algorithm to compute the strength of competing interactions in the Bering Sea based on pythagorean fuzzy hypergraphs

The networks of various problems have competing constituents, and there is a concern to compute the strength of competition among these entities. Competition hypergraphs capture all groups of predators that are competing in a community through their hyperedges. This paper reintroduces competition hypergraphs in the context of Pythagorean fuzzy set theory, thereby producing Pythagorean fuzzy competition hypergraphs. The data of real-world ecological systems posses uncertainty, and the proposed hypergraphs can efficiently deal with such information to model wide range of competing interactions. We suggest several extensions of Pythagorean fuzzy competition hypergraphs, including Pythagorean fuzzy economic competition hypergraphs, Pythagorean fuzzy row as well as column hypergraphs, Pythagorean fuzzy k-competition hypergraphs, m-step Pythagorean fuzzy competition hypergraphs and Pythagorean fuzzy neighborhood hypergraphs. The proposed graphical structures are good tools to measure the strength of direct and indirect competing and non-competing interactions. Their aptness is illustrated through examples, and results support their intrinsic interest. We propose algorithms that help to compose some of the presented graphical structures. We consider predator-prey interactions among organisms of the Bering Sea as an application: Pythagorean fuzzy competition hypergraphs encapsulate the competing relationships among its inhabitants. Specifically, the algorithm which constructs the Pythagorean fuzzy competition hypergraphs can also compute the strength of competing and non-competing relations of this scenario.

A Novel Algebraic Structure of (α,β)-Complex Fuzzy Subgroups

A complex fuzzy set is a vigorous framework to characterize novel machine learning algorithms. This set is more suitable and flexible compared to fuzzy sets, intuitionistic fuzzy sets, and bipolar fuzzy sets. On the aspects of complex fuzzy sets, we initiate the abstraction of (α,β)-complex fuzzy sets and then define α,β-complex fuzzy subgroups. Furthermore, we prove that every complex fuzzy subgroup is an (α,β)-complex fuzzy subgroup and define (α,β)-complex fuzzy normal subgroups of given group. We extend this ideology to define (α,β)-complex fuzzy cosets and analyze some of their algebraic characteristics. Furthermore, we prove that (α,β)-complex fuzzy normal subgroup is constant in the conjugate classes of group. We present an alternative conceptualization of (α,β)-complex fuzzy normal subgroup in the sense of the commutator of groups. We establish the (α,β)-complex fuzzy subgroup of the classical quotient group and show that the set of all (α,β)-complex fuzzy cosets of this specific complex fuzzy normal subgroup form a group. Additionally, we expound the index of α,β-complex fuzzy subgroups and investigate the (α,β)-complex fuzzification of Lagrange’s theorem analog to Lagrange’ theorem of classical group theory.

Parameter reduction analysis under interval-valued m-polar fuzzy soft information

This paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.

Three-Way Decisions Based on Q-Rung Orthopair Fuzzy 2-Tuple Linguistic Sets with Generalized Maclaurin Symmetric Mean Operators

As a typical model of three-way decisions (3WD), decision-theoretic rough sets (DTRS), have gained attention from scholars in decision-making problems. The q-rung orthopair fuzzy 2-tuple linguistic variable (QROF2-TLV) is a mixture of two different notions, q-rung orthopair fuzzy sets (QROFS) and 2-tuple linguistic variables (2-TLV), and is an extensive and proficient technique for coping with awkward and complicated information in realistic decision-making. In this paper, we first propose a DTRS model for 3WD based on QROF2-TLV that gives a new method for evaluating loss functions (LF) of DTRS. We further present the q-rung orthopair fuzzy 2-tuple linguistic generalized Maclaurin symmetric mean (QROF2-TLGMSM) and weighted QROF2-TLGMSM operators and then provide the LFs of DTRS based on QROF2-TLV with the values aggregated by the QROF2-TLGMSM operator. Thus, we propose the q-rung orthopair fuzzy 2-tuple linguistic variable DTRS (QROF2-TLV-DTRS) model. Subsequently, a technique for concluding another DTRS model, which can give the related semantic translation of the decision consequences of every other option, is presented. The model is applied to expound the proposed technique in detail, and the impacts of various conditional probabilities on decision outcomes are discussed. A comparative analysis of the proposed approach is also conducted to examine the proficiency of the proposed method.

Decision making under measure-based granular uncertainty with intuitionistic fuzzy sets

Yager has proposed the decision making under measure-based granular uncertainty, which can make decision with the aid of Choquet integral, measure and representative payoffs. The decision making under measure-based granular uncertainty is an effective tool to deal with uncertain issues. The intuitionistic fuzzy environment is the more real environment. Since the decision making under measure-based granular uncertainty is not based on intuitionistic fuzzy environment, it cannot effectively solve the decision issues in the intuitionistic fuzzy environment. Then, when the issues of decision making are under intuitionistic fuzzy environment, what is the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets is still an open issue. To deal with this kind of issues, this paper proposes the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. The decision making under measure-based granular uncertainty with intuitionistic fuzzy sets can effectively solve the decision making issues in the intuitionistic fuzzy environment, in other words, it can extend the decision making under measure-based granular uncertainty to the intuitionistic fuzzy environment. Numerical examples are applied to verify the validity of the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets. The experimental results demonstrate that the decision making under measure-based granular uncertainty with intuitionistic fuzzy sets can represent the objects successfully and make decision effectively. In addition, a practical application of applied intelligence is used to compare the performance between the proposed model and the decision making under measure-based granular uncertainty. The experimental results show that the proposed model can solve some decision problems that the decision making under measure-based granular uncertainty cannot solve.

An extended TODIM approach for group emergency decision making based on bidirectional projection with hesitant triangular fuzzy sets

With the recent Covid-19 outbreak, group emergency decision-making (GEDM), as a new management model to pursue both social stability and decrease the negative impact of emergencies, has become highly popular. Evaluating and choosing the best emergency response is the core of the GEDM and selecting the choices can be regarded as a multi-attribute group decision-making (MAGDM) problem. Due to the increasing complexity and fuzziness of emergency decision-making environment, decision-makers (DMs) often cannot express completely rational preference information in many real EDM situations. At the same time, the existing methods seldom consider the DM's psychological mindset at the point of decision making. In this paper, an extended TODIM (an acronym for interactive and multi-criteria decision-making in Portugese) method based on bidirectional projection is proposed to solve the GEDM problem in the context of hesitant triangular fuzzy sets (HTFSs) and the novel method is applied to a case study and compared with other existing methods. The validity and applicability of the proposed method are discussed.

Aggregation of L-Probabilistic Quasi-Uniformities

The problem of aggregating fuzzy structures, mainly fuzzy binary relations, has deserved a lot of attention in the last years due to its application in several fields. Here, we face the problem of studying which properties must satisfy a function in order to merge an arbitrary family of (bases of) L-probabilistic quasi-uniformities into a single one. These fuzzy structures are special filters of fuzzy binary relations. Hence we first make a complete study of functions between partially-ordered sets that preserve some special sets, such as filters. Afterwards, a complete characterization of those functions aggregating bases of L-probabilistic quasi-uniformities is obtained. In particular, attention is paid to the case L={0,1}, which allows one to obtain results for functions which aggregate crisp quasi-uniformities. Moreover, we provide some examples of our results including one showing that Lowen’s functor ι which transforms a probabilistic quasi-uniformity into a crisp quasi-uniformity can be constructed using this aggregation procedure.

Diagnosing and routing electronic service quality improvement of academic libraries with the FMEA approach in an intuitionistic fuzzy environment

Purpose

In this way, the aim of this study is to expand and evelop the application of this technique in FMEA to rank failure modes of ESQ of academic libraries in an intuitionistic fuzzy environment. Assessment of electronic service quality (ESQ) of libraries is significantly important according to their major roles. It should be noted that the ESQ has a significant impact on customer satisfaction, which improves organizational performance. Accordingly, low ESQ means waste of organizational resources and poor user satisfaction. So, there is a dire need to reflect reasons inducing failure modes in academic library ESQ. Thus, investigation of failure modes affecting academic library ESQ is highly important. One solution in this area is utilization of the intuitionistic fuzzy (IF) failure mode and effects analysis (FMEA) as one of the widely used methods for prediction and identification of failure modes.

Design/methodology/approach

The present study in terms of objective is applied and in terms of the type of method is descriptive-analytical. The research sample included four experts of Yazd academic Libraries (Iran). To collect data, three types of questionnaires were distributed among experts. The purpose of the first questionnaire was to identify and reach an agreement on e-library failure modes. Type II questionnaire was used to determine the importance of identified risk factors and Type III questionnaire was used to prioritize the factors.

Findings

Results indicate that the difficulty of using websites, lack of provided information feedback to users and lack of links on the website to users' are the main priorities for improving ESQ in the studied academic libraries.

Originality/value

In this approach, the Intuitionistic fuzzy Elimination Et Choix Traduisant la REalité and technique for order of preference by similarity to ideal solution method were used to rank failure modes in academic library ESQ within the FMEA framework.]

Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values

In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets. In order to address intuitionistic fuzzy decision-making problems in a more efficient way, many scholars have produced increasingly better procedures for ranking intuitionistic fuzzy values. In this study, we further investigate the problem of ranking intuitionistic fuzzy values from a geometric point of view, and we produce related applications to decision-making. We present Minkowski score functions of intuitionistic fuzzy values, which are natural generalizations of the expectation score function and other useful score functions in the literature. The rationale for Minkowski score functions lies in the geometric intuition that a better score should be assigned to an intuitionistic fuzzy value farther from the negative ideal intuitionistic fuzzy value. To capture the subjective attitude of decision makers, we further propose the Minkowski weighted score function that incorporates an attitudinal parameter. The Minkowski score function is a special case corresponding to a neutral attitude. Some fundamental properties of Minkowski (weighted) score functions are examined in detail. With the aid of the Minkowski weighted score function and the maximizing deviation method, we design a new algorithm for solving decision-making problems based on intuitionistic fuzzy soft sets. Moreover, two numerical examples regarding risk investment and supplier selection are employed to conduct comparative analyses and to demonstrate the feasibility of the approach proposed in this article.

An m-Polar Fuzzy PROMETHEE Approach for AHP-Assisted Group Decision-Making

The Analytical Hierarchy Process (AHP) is arguably the most popular and factual approach for computing the weights of attributes in the multi-attribute decision-making environment. The Preference Ranking Organization Method for Enrichment of Evaluations (PROMETHEE) is an outranking family of multi-criteria decision-making techniques for evaluating a finite set of alternatives, that relies on multiple and inconsistent criteria. One of its main advantages is the variety of admissible preference functions that can measure the differences between alternatives, in response to the type and nature of the criteria. This research article studies a version of the PROMETHEE technique that encompasses multipolar assessments of the performance of each alternative (relative to the relevant criteria). As is standard practice, first we resort to the AHP technique in order to quantify the normalized weights of the attributes by the pairwise comparison of criteria. Afterwards the m-polar fuzzy PROMETHEE approach is used to rank the alternatives on the basis of conflicting criteria. Six types of generalized criteria preference functions are used to measure the differences or deviations of every pair of alternatives. A partial ranking of alternatives arises by computing the positive and negative outranking flows of alternatives, which is known as PROMETHEE I. Furthermore, a complete ranking of alternatives is achieved by the inspection of the net flow of alternatives, and this is known as PROMETHEE II. Two comparative analysis are performed. A first study checks the impact of different types of preference functions. It considers the usual criterion preference function for all criteria. In addition, we compare the technique that we develop with existing multi-attribute decision-making methods.

Multi-Granulation Picture Hesitant Fuzzy Rough Sets

We lay the theoretical foundations of a novel model, termed picture hesitant fuzzy rough sets, based on picture hesitant fuzzy relations. We also combine this notion with the ideas of multi-granulation rough sets. As a consequence, a new multi-granulation rough set model on two universes, termed a multi-granulation picture hesitant fuzzy rough set, is developed. When the universes coincide or play a symmetric role, the concept assumes the standard format. In this context, we put forward two new classes of multi-granulation picture hesitant fuzzy rough sets, namely, the optimistic and pessimistic multi-granulation picture hesitant fuzzy rough sets. Further, we also investigate the relationships among these two concepts and picture hesitant fuzzy rough sets.

Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators

In fuzzy set theory, t-norms and t-conorms are fundamental binary operators. Yager proposed respective parametric families of both t-norms and t-conorms. In this paper, we apply these operators for the analysis of Pythagorean fuzzy sets. For this purpose, we introduce six families of aggregation operators named Pythagorean fuzzy Yager weighted averaging aggregation, Pythagorean fuzzy Yager ordered weighted averaging aggregation, Pythagorean fuzzy Yager hybrid weighted averaging aggregation, Pythagorean fuzzy Yager weighted geometric aggregation, Pythagorean fuzzy Yager ordered weighted geometric aggregation and Pythagorean fuzzy Yager hybrid weighted geometric aggregation. These tools inherit the operational advantages of the Yager parametric families. They enable us to study two multi-attribute decision-making problems. Ultimately we can choose the best option by comparison of the aggregate outputs through score values. We show this procedure with two practical fully developed examples.

Multi-Attribute Decision-Making Based on m-Polar Fuzzy Hamacher Aggregation Operators

In this paper, we introduce certain aggregation operators, namely, the m-polar fuzzy (mF) Hamacher weighted average operator, mF Hamacher ordered weighted average (mFHOWA) operator, mF Hamacher hybrid average (mFHHA) operator, mF Hamacher weighted geometric (mFHWG) operator, mF Hamacher weighted ordered geometric operator, and mF Hamacher hybrid geometric (mFHHG) operator. We discuss some properties of these operators, inclusive of their ability to implement both symmetric and asymmetric treatments of the items. We develop an algorithmic model to solve multi-attribute decision-making (MADM) problems in mF environment using mF Hamacher weighted average operator (mFHWA) and mFHWG operators. They can compensate for the possible asymmetric roles of the attributes that describe the problem. In the end, to prove the validity and feasibility of the proposed work, we give applications for selecting the most affected country regarding human trafficking, selecting health care waste treatment methods and selecting the best company for investment. We also solve practical MADM problems by using ELECTRE-I method, and give a comparative analysis.