Valuation Fuzzy Soft Sets: A Flexible Fuzzy Soft Set Based Decision Making Procedure for the Valuation of Assets

An integrated ELECTRE method for selection of rehabilitation center with m-polar fuzzy N-soft information

The primary goal of this research article is to apply ELECTRE I, a fundamental multi-criteria group decision-making technique, in an m-polar fuzzy N-soft environment. This new methodology helps us to pinpoint the best alternative(s) in the presence of multi-polar options with N-graded qualities. Its basic operational idea entails the comparison between any two alternatives by the assessment of score degrees. Concordance and discordance indices are then calculated to evaluate the alternatives' superiority and inferiority. We may disqualify the incompetent alternatives using concordance and discordance levels. An m-polar fuzzy N-soft dominance matrix can represent the combined effect of concordance and discordance dominance matrices. The steps of this new multi-criteria group decision making technique are summarized in a flowchart. In order to demonstrate its authenticity and applicability, we employ a case study involving the establishment of a rehabilitation facility for drug abusers. A comparison with the m-polar fuzzy PROMETHEE and m-polar fuzzy ELECTRE I methodologies establishes its validity. Finally, we conclude our study of the methodology proposed in this paper with a critical analysis of its benefits and drawbacks.

Extended fuzzy N-Soft PROMETHEE method and its application in robot butler selection

This paper extends the literature on fuzzy PROMETHEE, a well-known multi-criteria group decision-making technique. The PROMETHEE technique ranks alternatives by specifying an allowable preference function that measures their deviations from other alternatives in the presence of conflicting criteria. Its ambiguous variation helps to make an appropriate decision or choose the best option in the presence of some ambiguity. Here, we focus on the more general uncertainty in human decision-making, as we allow N-grading in fuzzy parametric descriptions. In this setting, we propose a suitable fuzzy N-soft PROMETHEE technique. We recommend using an Analytic Hierarchy Process to test the feasibility of standard weights before application. Then the fuzzy N-soft PROMETHEE method is explained. It ranks the alternatives after some steps summarized in a detailed flowchart. Furthermore, its practicality and feasibility are demonstrated through an application that selects the best robot housekeepers. The comparison between the fuzzy PROMETHEE method and the technique proposed in this work demonstrates the confidence and accuracy of the latter method.

Complex fermatean fuzzy N-soft sets: a new hybrid model with applications

Decision-making methods play an important role in the real-life of human beings and consist of choosing the best options from a set of possible choices. This paper proposes the notion of complex Fermatean fuzzy N-soft set (CFFNS f S) which, by means of ranking parameters, is capable of handling two-dimensional information related to the degree of satisfaction and dissatisfaction implicit in the nature of human decisions. We define the fundamental set-theoretic operations of CFFNS f S and elaborate the CFFS f S associated with threshold. The algebraic and Yager operations on CFFNS f numbers are also defined. Several algorithms are proposed to demonstrate the applicability of CFFNS f S to multi-attribute decision making. The advanced algorithms are described and accomplished by several numerical examples. Then, a comparative study manifests the validity, feasibility, and reliability of the proposed model. This method is compared with the Fermatean fuzzy Yager weighted geometric (FFY w G) and the Fermatean fuzzy Yager weighted average (FFY w A) operators. Further, we developed a remarkable CFFNS f -TOPSIS approach by applying innovative CFFNS f weighted average operator and distance measure. The presented technique is fantastically designed for the classification of the most favorable alternative by examining the closeness of all available choices from particular ideal solutions. Afterward, we demonstrate the amenability of the initiated approach by analyzing its tremendous potential to select the best city in the USA for farming. An integrated comparative analysis with existing Fermatean fuzzy TOPSIS technique is rendered to certify the terrific capability of the established approach. Further, we decisively investigate the rationality and reliability of the presented CFFNS f S and CFFNS f -TOPSIS approach by highlighting its advantages over the existent models and TOPSIS approaches. Finally, we holistically describe the conclusion of the whole work.

Group decision-making with Fermatean fuzzy soft expert knowledge

With the rapid growth of population, the global impact of solar technology is increasing by the day due to its advantages over other power production technologies. Demand for solar panel systems is soaring, thus provoking the arrival of many new manufacturers. Sale dealers or suppliers face an uncertain problem to choose the most adequate technological solution. To effectively address such kind of issues, in this paper we propose the Fermatean fuzzy soft expert set model by combining Fermatean fuzzy sets and soft expert sets. We describe this hybrid model with numerical examples. From a theoretical standpoint, we demonstrate some essential properties and define operations for this setting. They comprise the definitions of complement, union and intersection, the OR operation and the AND operation. Concerning practice in this new environment, we provide an algorithm for multi-criteria group decision making whose productiveness and authenticity is dutifully tested. We explore a practical application of this approach (that is, the selection of a suitable brand of solar panel system). Lastly, we give a comparison of our model with certain related mathematical tools, including fuzzy and intuitionistic fuzzy soft expert set models.

Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information

The main objective of this article is to lay the foundations of a novel multi-criteria optimization technique, namely, the complex Pythagorean fuzzy N-soft VIKOR (CPFNS-VIKOR) method that is highly proficient to express a great deal of linguistic imprecision and vagueness inherent in human assessments. This strategy provides a versatile decision-making tool for the ranking-based fuzzy modeling of two-dimensional parameterized data. The CPFNS-VIKOR method integrates the ground-breaking specialities of the VIKOR method with the outstanding parametric structure of the complex Pythagorean fuzzy N-soft model. It is exclusively designed for the specification of a compromise optimal solution having maximum group utility and minimum individual regret of the opponent by analyzing their weighted proximity from ideal solutions. The developed strategy factually permits specific linguistic terms to demystify the individual perspectives of the decision-making experts regarding the efficacy of the alternatives and the priorities of the applicable criteria. We comprehensively assemble these independent appraisals of all the experts using the complex Pythagorean fuzzy N-soft weighted averaging operator. Moreover, we calibrate the ranking measure by utilizing group utility measure and regret measure in order to specify the hierarchical outranking of the feasible alternatives. We demonstrate the systematic methodology and framework of the proposed method with the assistance of an explicative flow chart. We skilfully investigate an empirical analysis related to selection of constructive industrial robots for the modernization of a manufacturing industry which really justifies the remarkable accountability of the proposed strategy. Furthermore, we validate this technique by a comparative study with the existing complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method, complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method and Pythagorean fuzzy TOPSIS (PF-TOPSIS) method. The comparative study is exemplified with an illustrative bar chart that visually endorses the rationality of the proposed methodology by interpreting highly compatible and accurate final outcomes. Finally, we holistically analyze the functionality of the developed strategy to enlighten its merits and prominence over other available competent approaches.

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.

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-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.

Mass Appraisal Models of Real Estate in the 21st Century: A Systematic Literature Review

With the increasing volume and active transaction of real estate properties, mass appraisal has been widely adopted in many countries for different purposes, including assessment of property tax. In this paper, 104 papers are selected for the systematic literature review of mass appraisal models and methods from 2000 to 2018. The review focuses on the application trend and classification of mass appraisal and highlights a 3I-trend, namely AI-Based model, GIS-Based model and MIX-Based model. The characteristics of different mass appraisal models are analyzed and compared. Finally, the future trend of mass appraisal based on model perspective is defined as “mass appraisal 2.0”: mass appraisal is the appraisal procedure of model establishment, analysis and test of group of properties as of a given date, combined with artificial intelligence, geo-information systems, and mixed methods, to better model the real estate value of non-spatial and spatial data.

Diagnostic methods and risk analysis based on fuzzy soft information

In our daily life problem we face uncertainties in making right decisions. In this study, we propose two different decision-making problems in medical field. The first problem is fever diagnosing and second problem is mouth cancer risk analysis. In the first problem, we use fuzzy soft similarity measures and fuzzy soft matrix operations to diagnose the type of fever. We consider a hypothetical case study and manipulate similarity measures on it. Our work diagnoses different patients having similar symptoms. We also develop a small application using JAVA. In the second problem, we perform risk analysis of mouth cancer. The proposed fuzzy soft expert system takes two biochemical parameters as inputs that is, serum total malondialdehyde (MDA), and serum proton donors capacity (donors_protons) and determines the risk of mouth cancer. Our study facilitates doctors by diagnosing mouth cancer at its earlier stages. There are four main components of our fuzzy soft expert system. The first component is named as fuzzification which converts crisp input into linguistic variables and formulates fuzzy sets. The second component transforms fuzzy sets into their respective fuzzy soft sets. The third component determines indispensable parameters and performs parameter reduction. The fourth component performs risk analysis by using algorithm. We use exemplary dataset and run all the components of fuzzy soft expert system to compute cancer risk.