Pythagorean fuzzy sets and their variants
Shahid Ahmad Bhat; Akanksha Singh
Abstract
The analytic hierarchy process (AHP), is one of the well-known and most widely used technique to determine the priority weights of alternatives from pairwise comparison matrices. Several fuzzy and intuitionistic fuzzy extensions of AHP have been proposed in the literature. However, these extensions are ...
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The analytic hierarchy process (AHP), is one of the well-known and most widely used technique to determine the priority weights of alternatives from pairwise comparison matrices. Several fuzzy and intuitionistic fuzzy extensions of AHP have been proposed in the literature. However, these extensions are not appropriate to present some real-life situations. For this reason, Ilbahara et al. extend the AHP to Pythagorean fuzzy analytic hierarchy process (PFAHP). In this method, an interval valued Pythagorean fuzzy pairwise comparison matrix is transformed into a crisp matrix and then crisp AHP is applied to obtain the normalized priority weights from the transformed crisp matrix. However, it is observed that the transformed crisp matrix, obtained on applying the step of Ilbahara et al.’s method, violates the reciprocal propriety of pairwise comparison matrices and the obtained normalized priority weights are the weights of non-pairwise comparison matrices. Therefore, in this paper, the shortcomings of the existing method are discussed and a modified method is proposed to overcome these shortcomings. Finally, based on a real-life decision-making problem, the superiority of the proposed method over the existing method is shown.
Fuzzy sets and their variants
Gia Sirbiladze
Abstract
The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article two variants of probabilistic extensions the OWA operator - POWA and FPOWA (introduced by J.M. Merigo [27, 28]) are considered ...
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The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article two variants of probabilistic extensions the OWA operator - POWA and FPOWA (introduced by J.M. Merigo [27, 28]) are considered as a basis of our generalizations in the environment of fuzzy uncertainty (parts II and III of this work), where different monotone measures (fuzzy measure) are used as uncertainty measures instead of the probability measure. For the identification of “classic” OWA and new operators (presented in parts II and III) of aggregations, the Information Structure is introduced where the incomplete available information in the general decision-making system is presented as a condensation of uncertainty measure, imprecision variable and objective function of weights.
Other
Mazdak Khodadadi-Karimvand; Hadi Shirouyehzad
Abstract
One of the most important issues that organizations have to deal with is the timely identification and detection of risk factors aimed at preventing incidents. Managers’ and engineers’ tendency towards minimizing risk factors in a service, process or design system has obliged them to analyze ...
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One of the most important issues that organizations have to deal with is the timely identification and detection of risk factors aimed at preventing incidents. Managers’ and engineers’ tendency towards minimizing risk factors in a service, process or design system has obliged them to analyze the reliability of such systems in order to minimize the risks and identify the probable errors. Concerning what was just mentioned, a more accurate Failure Mode and Effects Analysis (FMEA) is adopted based on fuzzy logic and fuzzy numbers. Fuzzy TOPSIS is also used to identify, rank, and prioritize error and risk factors. This paper uses FMEA as a risk identification tool. Then, Fuzzy Risk Priority Number (FRPN) is calculated and triangular fuzzy numbers are prioritized through Fuzzy TOPSIS. In order to have a better understanding toward the mentioned concepts, a case study is presented.
Fuzzy sets and their variants
Gia Sirbiladze
Abstract
The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article several variants of the generalizations of the fuzzy-probabilistic OWA operator - POWA (introduced by J.M. Merigo [27,28]) ...
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The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [58] to provide a method for aggregating inputs that lie between the max and min operators. In this article several variants of the generalizations of the fuzzy-probabilistic OWA operator - POWA (introduced by J.M. Merigo [27,28]) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as an uncertainty measure. The considered monotone measures are: possibility measure, Sugeno additive measure, monotone measure associated with Belief Structure and capacity of order two. New aggregation operators are introduced: AsPOWA and SA-AsPOWA. Some properties of new aggregation operators are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno integral) and the Associated Probability Class (APC) of a monotone measure. For the new operators the information measures – Orness, Entropy, Divergence and Balance are introduced as some extensions of the definitions presented in [28].
Fuzzy sets and their variants
Gia Sirbiladze
Abstract
The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [34] to provide a method for aggregating inputs that lie between the max and min operators. In this article we continue to present some extensions of OWA-type aggregation operators. Several variants of the generalizations of the ...
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The Ordered Weighted Averaging (OWA) operator was introduced by R.R. Yager [34] to provide a method for aggregating inputs that lie between the max and min operators. In this article we continue to present some extensions of OWA-type aggregation operators. Several variants of the generalizations of the fuzzy-probabilistic OWA operator - FPOWA (introduced by J.M. Merigo [13,14]) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as uncertainty measures. The considered monotone measures are: possibility measure, Sugeno additive measure, monotone measure associated with Belief Structure and Choquet capacity of order two. New aggregation operators are introduced: AsFPOWA and SA-AsFPOWA. Some properties of new aggregation operators and their information measures are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno integral) and the Associated Probability Class (APC) of a monotone measure. New aggregation operators belong to the Information Structure I6 (see Part I, section 3). For the illustration of new constructions of AsFPOWA and SA-AsFPOWA operators an example of a fuzzy decision-making problem regarding the political management with possibility uncertainty is considered. Several aggregation operators (“classic” and new operators) are used for the comparing of the results of decision making.
Intuitionistic fuzzy sets and their variants
Imo Eyo; Jeremiah Eyoh; Uduak Umoh
Abstract
This paper presents a time series analysis of a novel coronavirus, COVID-19, discovered in China in December, 2019 using intuitionistic fuzzy logic system with neural network learning capability. Fuzzy logic systems are known to be universal approximation tools that can estimate a nonlinear function ...
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This paper presents a time series analysis of a novel coronavirus, COVID-19, discovered in China in December, 2019 using intuitionistic fuzzy logic system with neural network learning capability. Fuzzy logic systems are known to be universal approximation tools that can estimate a nonlinear function as closely as possible to the actual values. The main idea in this study is to use intuitionistic fuzzy logic system that enables hesitation and has membership and non-membership functions that are optimized to predict COVID-19 outbreak cases. Intuitionistic fuzzy logic systems are known to provide good results with improved prediction accuracy and are excellent tools for uncertainty modelling. The hesitation-enabled fuzzy logic system is evaluated using COVID-19 pandemic cases for Nigeria, being part of the COVID-19 data for African countries obtained from Kaggle data repository. The hesitation enabled fuzzy logic model is compared with the classical fuzzy logic system and artificial neural network and shown to offer improved performance in terms of root mean squared error, mean absolute error and mean absolute percentage error. Intuitionistic fuzzy logic system however incurs a setback in terms of the high computing time compared to the classical fuzzy logic system.
Ordered structures and their variants
George Georgescu
Abstract
The mp-quantales were introduced in a previous paper as an abstraction of the lattices of ideals in mp-rings and the lattices of ideals in conormal lattices. Several properties of m-rings and conormal lattices were generalized to mp-quantales. In this paper we shall prove new characterization theorems ...
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The mp-quantales were introduced in a previous paper as an abstraction of the lattices of ideals in mp-rings and the lattices of ideals in conormal lattices. Several properties of m-rings and conormal lattices were generalized to mp-quantales. In this paper we shall prove new characterization theorems for mp-quantales and for semiprime mp-quantales (these last structures coincide with the PF-quantales). Some proofs reflect the way in which the reticulation functor (from coherent quantales to bounded distributive lattices) allows us to export some properties from conormal lattices to mp-quantales.
