In this paper, we introduce the notion of cubic BF -subalgebras of an BF algebra and give some of... more In this paper, we introduce the notion of cubic BF -subalgebras of an BF algebra and give some of its characterizations. The homomorphic image, inverse image and product of cubic BF -subalgebras are studied and some related properties are investigated. Acknowledgement The author would like to express his thanks to the referees for their comments and suggestions which improved the paper.
Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices
Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras ... more Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras are established. Some characterizations of bipolar fuzzy B-subalgebras of B-algebras are given. We have shown that the intersection of two bipolar fuzzy B-subalgebras is also a bipolar fuzzy B-subalgebra, but for the union it is not always true. We have also shown that if every bipolar fuzzy B-subalgebras has the finite image, then every descending chain of B-subalgebras terminates at finite step.
In this paper, the concepts of fuzzy translation to fuzzy subalgebras in BGalgebras are introduce... more In this paper, the concepts of fuzzy translation to fuzzy subalgebras in BGalgebras are introduced. The notion of fuzzy extens ions and fuzzy multiplications of fuzzy subalgebras are introduced and several relate d properties are investigated. In this paper, the relationships between fuzzy translations a d fuzzy extensions of fuzzy subalgebras are investigated.
In this paper, the concept of interval-valued intuitionistic fuzzy set to UP subalgebras and UP -... more In this paper, the concept of interval-valued intuitionistic fuzzy set to UP subalgebras and UP -ideals of UP -algebras are introduced. Relations among IVIF UP subalgebras with IVIF UP -ideals of UP -algebras are investigated. The homomorphic image and inverse image of IVIF UP -subalgebras and IVIF UP -ideals are studied and some related properties are investigated. Equivalence relations on IVIF UP -ideals are discussed. Also, the product of IVIF UP -algebras are investigated.
Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras ... more Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras are established. Some characterizations of bipolar fuzzy B-subalgebras of B-algebras are given. We have shown that the intersection of two bipolar fuzzy B-subalgebras is also a bipolar fuzzy B-subalgebra, but for the union it is not always true. We have also shown that if every bipolar fuzzy B-subalgebras has the finite image, then every descending chain of B-subalgebras terminates at finite step.
In this paper, we apply the concept of interval-valued fuzzy set to ideals and closed ideals in B... more In this paper, we apply the concept of interval-valued fuzzy set to ideals and closed ideals in B-algebras. The notion of an interval-valued fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated. Also, the product of interval-valued fuzzy B-algebra is investigated.
Capital budgeting requires dealing with high uncertainty from the unknown characteristics of cash... more Capital budgeting requires dealing with high uncertainty from the unknown characteristics of cash flow, interest rate, and study period forecasts for future periods. Many fuzzy extensions of capital budgeting techniques have been proposed and used in a wide range of applications to deal with uncertainty. In this paper, a new fuzzy extension of the most used capital budgeting techniques is proposed. In this content, first interval-valued Fermatean fuzzy sets (IVFFSs) are defined, and the algebraic and aggregation operations are determined for interval-valued Fermatean fuzzy (IVFF) numbers. The formulations of IVFF net present value, IVFF equivalent uniform annual value, and IVFF benefit-cost ratio (B/C) methods are generated. To validate the proposed methods, proposed formulations are illustrated with a hypothetical example, and the results are compared with classical fuzzy capital budgeting techniques.
In this paper, the notion of cubic subalgebras of BCH-algebras are introduced. Some characterizat... more In this paper, the notion of cubic subalgebras of BCH-algebras are introduced. Some characterization of cubic subalgebras of BCH-algebras are given. The homomorphic image and inverse image of cubic subalgebras are studied and investigated some related properties.
The motivation of this paper is to build up a new technique to manage multi-attribute decision-ma... more The motivation of this paper is to build up a new technique to manage multi-attribute decision-making (MADM) issues with interval-valued Pythagorean fuzzy (IVPF) set according to the concepts of Hamacher t-norm and t-conorm, and give its application in MADM problems. To begin with, we integrate the Hamacher operations on IVPF sets. Then, in view of these operations, we formulate a few IVPF aggregation operators, for example, IVPF Hamacher weighted average operator, IVPF Hamacher order weighted average operator, IVPF Hamacher hybrid average operator, IVPF Hamacher weighted geometric operator, IVPF Hamacher order weighted geometric operator, and IVPF Hamacher hybrid geometric operator. We investigate the distinguished features of these suggested operators. Moreover, we carry out the proposed aggregation operators to produce a method for solving MADM issues under IVPF data. We present an example of the emerging software system selection to elaborate on its practicality and effectivenes...
In this paper, the notion of left-right (respectively, right-left) derivation, f-derivation, gene... more In this paper, the notion of left-right (respectively, right-left) derivation, f-derivation, generalized derivation of KUS-algebras are introduced and their proper- ties are established in details.
In this paper, using t-norm T , the notion of (imaginable) T -fuzzy subalgebras of KU -algebras a... more In this paper, using t-norm T , the notion of (imaginable) T -fuzzy subalgebras of KU -algebras are introduced and investigated their related results. Images and preimages of KU -subalgebras under homomorphism are investigated. Using level subsets of KU -algebras, some characterization theorems are given. The direct product and T -product of T -fuzzy subalgebras of KU -algebras are discussed. 2010 AMS Classification: 06F35, 03G25, 94D05
Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures
The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzz... more The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.
Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures
In this chapter, the concepts of bipolar fuzzy H-ideals of BCI-algebras are introduced and their ... more In this chapter, the concepts of bipolar fuzzy H-ideals of BCI-algebras are introduced and their natures are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals, and bipolar fuzzy H-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy H-ideal are provided. Some characterization theorems of bipolar fuzzy H-ideals are established. A bipolar fuzzy H-ideal is established by using a finite collection of H-ideals. The authors have shown that if every bipolar fuzzy H-ideal has the finite image, then every descending chain of H-ideals terminates at finite step.
The dual probabilistic linguistic (DPL) term sets are considered superior to probabilistic lingui... more The dual probabilistic linguistic (DPL) term sets are considered superior to probabilistic linguistic term sets. Further, the generalized Dombi (GD) operators are pretty flexible with the general parameters during the aggregation process. Besides, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between criteria. In this study, we combine the merits of the GD operator, and BM operator for handling multicriteria group decision‐making issues under a DPL setting. The existing research on DPL term sets do not focus on both the subjective and objective weights of decision‐experts. As a result, the evaluation results are likely to be distorted. To tackle this situation, in this paper, we utilize the concepts of consistency and similarity between the decision‐experts to determine the decision‐experts subjective and objective weights, respectively. To calculate the weights of criteria, the grey correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. Since the existing aggregation operators fail to capture the interrelations between criteria under DPL setting, so for aggregating criteria values, we propose DPL generalized Dombi BM weighted averaging and geometric aggregation operators. We provide a case study regarding biomass feedstock selection to focus on the applicability of these proposed operators. Furthermore, we investigate the effects of the parameters upon ranking order. We also perform a sensitivity assessment of criteria weights to test the stability of our method. Lastly, we provide a comparison between our approach with various extant methods.
Journal of Ambient Intelligence and Humanized Computing
Multi-criteria decision-making (MCDM) approaches have acquired various expansions under uncertain... more Multi-criteria decision-making (MCDM) approaches have acquired various expansions under uncertain conditions in current years. The purpose of the current study is to broaden the implementation of the weighted aggregated sum product assessment (WASPAS) technique for decision-making (DM) in an uncertain environment. Thinking about the benefits of cubic intuitionistic sets (CIS) in dealing with the issue of uncertainty, the improvement of the cubic intuitionistic WASPAS (CI-WASPAS) technique for DM is taken into consideration within the paper. Experimental outcomes obtained for a real-world issue regarding bridge construction selection indicates that the suggested technique performs well compared to other established classification techniques.
In this article, we present the idea of a hesitant multi-fuzzy set. We join the characteristics o... more In this article, we present the idea of a hesitant multi-fuzzy set. We join the characteristics of a hesitant multi-fuzzy set with the parametrization of the soft set and constructs the hesitant multi-fuzzy soft set. We center around the fundamental operations for the instance of the hesitant multi-fuzzy soft subsets. Also, we look at the root mean square sum level soft set or RMSS-level soft set to deal with uncertainties. We also provide the utilization of hesitant multi-fuzzy soft set into the decision-making issues. Finally, we deliver a standard algorithm to resolve decision-making issues and test the effectiveness of it by a socialistic decision-making problem.
The notions of $$(\in ,\in \vee q)$$-cubic p- (a- and q-) ideals of BCI-algebras are introduced a... more The notions of $$(\in ,\in \vee q)$$-cubic p- (a- and q-) ideals of BCI-algebras are introduced and some related properties are investigated. Several characterization for these generalized $$(\in ,\in \vee q)$$-cubic ideals are defined and relationship between $$(\in ,\in \vee q)$$-cubic p-ideals, $$(\in ,\in \vee q)$$-cubic q-deals and $$(\in ,\in \vee q)$$-cubic a-ideals of BCI-algebras are discussed.
In this paper, the notions of cubic intuitionistic KU-subalgebras and KU-ideals of a KU-algebras ... more In this paper, the notions of cubic intuitionistic KU-subalgebras and KU-ideals of a KU-algebras are introduced, and several properties are investigated. Characterizations of cubic intuitionistic KU-subalgebras and KU-ideals of KU-algebras are considered. Relations between a cubic intuitionistic KU-subalgebra and a cubic intuitionistic KU-ideal are given.
Analele Universitatii "Ovidius" Constanta - Seria Matematica
In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals an... more In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.
In this paper, we introduce the notion of cubic BF -subalgebras of an BF algebra and give some of... more In this paper, we introduce the notion of cubic BF -subalgebras of an BF algebra and give some of its characterizations. The homomorphic image, inverse image and product of cubic BF -subalgebras are studied and some related properties are investigated. Acknowledgement The author would like to express his thanks to the referees for their comments and suggestions which improved the paper.
Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices
Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras ... more Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras are established. Some characterizations of bipolar fuzzy B-subalgebras of B-algebras are given. We have shown that the intersection of two bipolar fuzzy B-subalgebras is also a bipolar fuzzy B-subalgebra, but for the union it is not always true. We have also shown that if every bipolar fuzzy B-subalgebras has the finite image, then every descending chain of B-subalgebras terminates at finite step.
In this paper, the concepts of fuzzy translation to fuzzy subalgebras in BGalgebras are introduce... more In this paper, the concepts of fuzzy translation to fuzzy subalgebras in BGalgebras are introduced. The notion of fuzzy extens ions and fuzzy multiplications of fuzzy subalgebras are introduced and several relate d properties are investigated. In this paper, the relationships between fuzzy translations a d fuzzy extensions of fuzzy subalgebras are investigated.
In this paper, the concept of interval-valued intuitionistic fuzzy set to UP subalgebras and UP -... more In this paper, the concept of interval-valued intuitionistic fuzzy set to UP subalgebras and UP -ideals of UP -algebras are introduced. Relations among IVIF UP subalgebras with IVIF UP -ideals of UP -algebras are investigated. The homomorphic image and inverse image of IVIF UP -subalgebras and IVIF UP -ideals are studied and some related properties are investigated. Equivalence relations on IVIF UP -ideals are discussed. Also, the product of IVIF UP -algebras are investigated.
Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras ... more Based on the concept of bipolar fuzzy set, a theoretical approach of B-subalgebras of B-algebras are established. Some characterizations of bipolar fuzzy B-subalgebras of B-algebras are given. We have shown that the intersection of two bipolar fuzzy B-subalgebras is also a bipolar fuzzy B-subalgebra, but for the union it is not always true. We have also shown that if every bipolar fuzzy B-subalgebras has the finite image, then every descending chain of B-subalgebras terminates at finite step.
In this paper, we apply the concept of interval-valued fuzzy set to ideals and closed ideals in B... more In this paper, we apply the concept of interval-valued fuzzy set to ideals and closed ideals in B-algebras. The notion of an interval-valued fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated. Also, the product of interval-valued fuzzy B-algebra is investigated.
Capital budgeting requires dealing with high uncertainty from the unknown characteristics of cash... more Capital budgeting requires dealing with high uncertainty from the unknown characteristics of cash flow, interest rate, and study period forecasts for future periods. Many fuzzy extensions of capital budgeting techniques have been proposed and used in a wide range of applications to deal with uncertainty. In this paper, a new fuzzy extension of the most used capital budgeting techniques is proposed. In this content, first interval-valued Fermatean fuzzy sets (IVFFSs) are defined, and the algebraic and aggregation operations are determined for interval-valued Fermatean fuzzy (IVFF) numbers. The formulations of IVFF net present value, IVFF equivalent uniform annual value, and IVFF benefit-cost ratio (B/C) methods are generated. To validate the proposed methods, proposed formulations are illustrated with a hypothetical example, and the results are compared with classical fuzzy capital budgeting techniques.
In this paper, the notion of cubic subalgebras of BCH-algebras are introduced. Some characterizat... more In this paper, the notion of cubic subalgebras of BCH-algebras are introduced. Some characterization of cubic subalgebras of BCH-algebras are given. The homomorphic image and inverse image of cubic subalgebras are studied and investigated some related properties.
The motivation of this paper is to build up a new technique to manage multi-attribute decision-ma... more The motivation of this paper is to build up a new technique to manage multi-attribute decision-making (MADM) issues with interval-valued Pythagorean fuzzy (IVPF) set according to the concepts of Hamacher t-norm and t-conorm, and give its application in MADM problems. To begin with, we integrate the Hamacher operations on IVPF sets. Then, in view of these operations, we formulate a few IVPF aggregation operators, for example, IVPF Hamacher weighted average operator, IVPF Hamacher order weighted average operator, IVPF Hamacher hybrid average operator, IVPF Hamacher weighted geometric operator, IVPF Hamacher order weighted geometric operator, and IVPF Hamacher hybrid geometric operator. We investigate the distinguished features of these suggested operators. Moreover, we carry out the proposed aggregation operators to produce a method for solving MADM issues under IVPF data. We present an example of the emerging software system selection to elaborate on its practicality and effectivenes...
In this paper, the notion of left-right (respectively, right-left) derivation, f-derivation, gene... more In this paper, the notion of left-right (respectively, right-left) derivation, f-derivation, generalized derivation of KUS-algebras are introduced and their proper- ties are established in details.
In this paper, using t-norm T , the notion of (imaginable) T -fuzzy subalgebras of KU -algebras a... more In this paper, using t-norm T , the notion of (imaginable) T -fuzzy subalgebras of KU -algebras are introduced and investigated their related results. Images and preimages of KU -subalgebras under homomorphism are investigated. Using level subsets of KU -algebras, some characterization theorems are given. The direct product and T -product of T -fuzzy subalgebras of KU -algebras are discussed. 2010 AMS Classification: 06F35, 03G25, 94D05
Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures
The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzz... more The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.
Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures
In this chapter, the concepts of bipolar fuzzy H-ideals of BCI-algebras are introduced and their ... more In this chapter, the concepts of bipolar fuzzy H-ideals of BCI-algebras are introduced and their natures are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals, and bipolar fuzzy H-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy H-ideal are provided. Some characterization theorems of bipolar fuzzy H-ideals are established. A bipolar fuzzy H-ideal is established by using a finite collection of H-ideals. The authors have shown that if every bipolar fuzzy H-ideal has the finite image, then every descending chain of H-ideals terminates at finite step.
The dual probabilistic linguistic (DPL) term sets are considered superior to probabilistic lingui... more The dual probabilistic linguistic (DPL) term sets are considered superior to probabilistic linguistic term sets. Further, the generalized Dombi (GD) operators are pretty flexible with the general parameters during the aggregation process. Besides, the Bonferroni mean (BM) operator has the advantage of considering interrelationships between criteria. In this study, we combine the merits of the GD operator, and BM operator for handling multicriteria group decision‐making issues under a DPL setting. The existing research on DPL term sets do not focus on both the subjective and objective weights of decision‐experts. As a result, the evaluation results are likely to be distorted. To tackle this situation, in this paper, we utilize the concepts of consistency and similarity between the decision‐experts to determine the decision‐experts subjective and objective weights, respectively. To calculate the weights of criteria, the grey correlation coefficient of the assessment value of criteria is used to reflect the similarity between the criteria and its reference value. Since the existing aggregation operators fail to capture the interrelations between criteria under DPL setting, so for aggregating criteria values, we propose DPL generalized Dombi BM weighted averaging and geometric aggregation operators. We provide a case study regarding biomass feedstock selection to focus on the applicability of these proposed operators. Furthermore, we investigate the effects of the parameters upon ranking order. We also perform a sensitivity assessment of criteria weights to test the stability of our method. Lastly, we provide a comparison between our approach with various extant methods.
Journal of Ambient Intelligence and Humanized Computing
Multi-criteria decision-making (MCDM) approaches have acquired various expansions under uncertain... more Multi-criteria decision-making (MCDM) approaches have acquired various expansions under uncertain conditions in current years. The purpose of the current study is to broaden the implementation of the weighted aggregated sum product assessment (WASPAS) technique for decision-making (DM) in an uncertain environment. Thinking about the benefits of cubic intuitionistic sets (CIS) in dealing with the issue of uncertainty, the improvement of the cubic intuitionistic WASPAS (CI-WASPAS) technique for DM is taken into consideration within the paper. Experimental outcomes obtained for a real-world issue regarding bridge construction selection indicates that the suggested technique performs well compared to other established classification techniques.
In this article, we present the idea of a hesitant multi-fuzzy set. We join the characteristics o... more In this article, we present the idea of a hesitant multi-fuzzy set. We join the characteristics of a hesitant multi-fuzzy set with the parametrization of the soft set and constructs the hesitant multi-fuzzy soft set. We center around the fundamental operations for the instance of the hesitant multi-fuzzy soft subsets. Also, we look at the root mean square sum level soft set or RMSS-level soft set to deal with uncertainties. We also provide the utilization of hesitant multi-fuzzy soft set into the decision-making issues. Finally, we deliver a standard algorithm to resolve decision-making issues and test the effectiveness of it by a socialistic decision-making problem.
The notions of $$(\in ,\in \vee q)$$-cubic p- (a- and q-) ideals of BCI-algebras are introduced a... more The notions of $$(\in ,\in \vee q)$$-cubic p- (a- and q-) ideals of BCI-algebras are introduced and some related properties are investigated. Several characterization for these generalized $$(\in ,\in \vee q)$$-cubic ideals are defined and relationship between $$(\in ,\in \vee q)$$-cubic p-ideals, $$(\in ,\in \vee q)$$-cubic q-deals and $$(\in ,\in \vee q)$$-cubic a-ideals of BCI-algebras are discussed.
In this paper, the notions of cubic intuitionistic KU-subalgebras and KU-ideals of a KU-algebras ... more In this paper, the notions of cubic intuitionistic KU-subalgebras and KU-ideals of a KU-algebras are introduced, and several properties are investigated. Characterizations of cubic intuitionistic KU-subalgebras and KU-ideals of KU-algebras are considered. Relations between a cubic intuitionistic KU-subalgebra and a cubic intuitionistic KU-ideal are given.
Analele Universitatii "Ovidius" Constanta - Seria Matematica
In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals an... more In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.
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