The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the... more The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the grade of membership and the grade of non-membership using a set of linguistic terms. In the present work, we first quote an example to point out that the existing complement operation of DHFLTS is on the wrong track. Meanwhile, we redefine this operation to fill the holes in the existing ones. Next, the notion of information energy under a dual hesitant fuzzy linguistic background is provided in order to build the criteria weight determination model. To further facilitate the theory of DHFLTS, we propose two vector similarity measures, i.e., Jaccard and Dice similarity measures, and their weighted forms for DHFLTS. In addition, we pioneer some generalized similarity measures of DHFLTSs and indicate that the Dice similarity measures are particular instances of the generalized similarity measures for some parameter values. Afterward, the similarity measures-based model with unknown weight...
The q-rung orthopair linguistic set (q-ROLS), a combined version of linguistic term sets and q-ru... more The q-rung orthopair linguistic set (q-ROLS), a combined version of linguistic term sets and q-rung orthopair fuzzy set, is an efficient mathematical tool to accomplish the imprecise information while solving the decision-making problems. Under this environment, we propose additional operations and relations to deal with the decision information, and some properties are well proved. Furthermore, we propound some cosine similarity measures and weighted cosine similarity measures for q-ROLSs based on the traditional cosine similarity measures with a brief study of related properties. In the proposed similarity measures, various linguistic scale functions are utilized in order to take into account the semantics of linguistic terms. Besides this, we employ the stated q-rung orthopair linguistic similarity measures to multi-criteria group decision making problems, in which the weights of DMs are delineated by the projection of individual decisions on the ideal decision results. At last, ...
The normal wiggly dual hesitant fuzzy set (NWDHFS) is a modern mathematical tool that can be used... more The normal wiggly dual hesitant fuzzy set (NWDHFS) is a modern mathematical tool that can be used to express the deep ideas of membership and non-membership information hidden in the thought-level of decision-makers (DMs). To enhance and expand the applicability of NWDHFSs, this study originates several types of distance and similarity measures between two NWDHFSs. The present paper first revises the basic operational laws of normal wiggly dual hesitant fuzzy elements (NWDHFEs) and then generalizes the rule of length extension for normal wiggly dual hesitant fuzzy setting. Meanwhile, we introduce a variety of distance and similarity measures under the background of NWDHFSs. After that, a family of weighted distance and similarity measures based on NWDHFS is presented and analyzed for discrete and continuous cases. The stated measures are the extension of several existing measures and have the capability to handle uncertain and vague information with a wider range of information. DMs...
The complex t-spherical fuzzy set (Ct-SFS) is a potent tool for representing fuzziness and uncert... more The complex t-spherical fuzzy set (Ct-SFS) is a potent tool for representing fuzziness and uncertainty compared to the picture fuzzy sets and spherical fuzzy sets. It plays a key role in modeling problems that require two-dimensional data. The present study purposes the aggregation technique of Ct-SFSs with the aid of Aczel–-Alsina (AA) operations. We first introduce certain novel AA operations of Ct-SFSs, such as the AA sum, AA product, AA scalar multiplication, and AA scalar power. Subsequently, we propound a series of complex t-spherical fuzzy averaging and geometric aggregation operators to efficiently aggregate complex t-spherical fuzzy data. In addition, we explore the different characteristics of these operators, discuss certain peculiar cases, and prove their fundamental results. Thereafter, we utilize these operators and propose entropy measures to frame a methodology for dealing with complex t-spherical fuzzy decision-making problems with unknown criteria weight data. Fina...
Making decisions are very common in the modern socio-economic environments. However, with the inc... more Making decisions are very common in the modern socio-economic environments. However, with the increasing complexity of the social, today’s decision makers (DMs) face such problems in which they hesitate and irresolute to provide their views. To cope with these uncertainties, many generalizations of fuzzy sets are designed, among them dual hesitant fuzzy set (DHFS) is quite resourceful and efficient in solving problems of a more vague nature. In this article, a novel concept called proportional dual hesitant fuzzy set (PDHFS) is proposed to further improve DHFS. The PDHFS is a flexible tool composed of some possible membership values and some possible non-membership values along with their associated proportions. In the theme of PDHFS, the proportions of membership values and non-membership values are considered to be independent. Some basic operations, properties, distance measure and comparison method are studied for the proposed set. Thereafter, a novel approach based on PDHFSs is...
Abstract The uncertain probabilistic linguistic term set (UPLTS) one of the modern development in... more Abstract The uncertain probabilistic linguistic term set (UPLTS) one of the modern development in fuzzy set theory, can express not only the decision makers (DMs) linguistic assessment information but also the uncertain probability/weight/importance degree of each linguistic assessment value, so it is an efficient tool for addressing the ignorance problems. The current study mainly focuses on developing a more effective way to cope with multiple criteria group decision making (MCGDM) problems in which the assessment information are in the form of UPLTSs, and the weight information is also entirely unknown. Firstly, some weaknesses of the existing operational laws and score function of UPLTSs are pointed out through some critical examples and then redefined them to overcome existing flaws in order to acquire more accurate results in practical decision making problems. Also, we establish various properties of the revised operational laws along with proofs. To design a novel comparison method, the concept of deviation degree is introduced in order to accommodate the situation in which two different UPLTSs have the same score values. After that, based on the proposed operational laws, several existing aggregation operators are modified, and a novel aggregation operator, namely uncertain probabilistic linguistic simple weighted geometry (UPLSWG) operator is designed. Meanwhile, some interesting properties of these proposed operators are carefully analysed. Furthermore, an entropy technique under uncertain probabilistic linguistic information is structured for computing the completely unknown weights of criteria. Following this, a new extension of weighted aggregated sum product assessment (WASPAS) method called uncertain probabilistic linguistic-WASPAS (UPL-WASPAS) methodology based on the proposed aggregation operators is studied under the UPLTS context for ranking objects in MCGDM problems. To show the applicability and potentiality of the developed method, an example of supplier selection is addressed, and a detailed performance comparison analysis is conducted. Furthermore, sensitivity analysis is also made to determine the impact of the parameter on the ranking of alternatives.
The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the... more The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the grade of membership and the grade of non-membership using a set of linguistic terms. In the present work, we first quote an example to point out that the existing complement operation of DHFLTS is on the wrong track. Meanwhile, we redefine this operation to fill the holes in the existing ones. Next, the notion of information energy under a dual hesitant fuzzy linguistic background is provided in order to build the criteria weight determination model. To further facilitate the theory of DHFLTS, we propose two vector similarity measures, i.e., Jaccard and Dice similarity measures, and their weighted forms for DHFLTS. In addition, we pioneer some generalized similarity measures of DHFLTSs and indicate that the Dice similarity measures are particular instances of the generalized similarity measures for some parameter values. Afterward, the similarity measures-based model with unknown weight...
The q-rung orthopair linguistic set (q-ROLS), a combined version of linguistic term sets and q-ru... more The q-rung orthopair linguistic set (q-ROLS), a combined version of linguistic term sets and q-rung orthopair fuzzy set, is an efficient mathematical tool to accomplish the imprecise information while solving the decision-making problems. Under this environment, we propose additional operations and relations to deal with the decision information, and some properties are well proved. Furthermore, we propound some cosine similarity measures and weighted cosine similarity measures for q-ROLSs based on the traditional cosine similarity measures with a brief study of related properties. In the proposed similarity measures, various linguistic scale functions are utilized in order to take into account the semantics of linguistic terms. Besides this, we employ the stated q-rung orthopair linguistic similarity measures to multi-criteria group decision making problems, in which the weights of DMs are delineated by the projection of individual decisions on the ideal decision results. At last, ...
The normal wiggly dual hesitant fuzzy set (NWDHFS) is a modern mathematical tool that can be used... more The normal wiggly dual hesitant fuzzy set (NWDHFS) is a modern mathematical tool that can be used to express the deep ideas of membership and non-membership information hidden in the thought-level of decision-makers (DMs). To enhance and expand the applicability of NWDHFSs, this study originates several types of distance and similarity measures between two NWDHFSs. The present paper first revises the basic operational laws of normal wiggly dual hesitant fuzzy elements (NWDHFEs) and then generalizes the rule of length extension for normal wiggly dual hesitant fuzzy setting. Meanwhile, we introduce a variety of distance and similarity measures under the background of NWDHFSs. After that, a family of weighted distance and similarity measures based on NWDHFS is presented and analyzed for discrete and continuous cases. The stated measures are the extension of several existing measures and have the capability to handle uncertain and vague information with a wider range of information. DMs...
The complex t-spherical fuzzy set (Ct-SFS) is a potent tool for representing fuzziness and uncert... more The complex t-spherical fuzzy set (Ct-SFS) is a potent tool for representing fuzziness and uncertainty compared to the picture fuzzy sets and spherical fuzzy sets. It plays a key role in modeling problems that require two-dimensional data. The present study purposes the aggregation technique of Ct-SFSs with the aid of Aczel–-Alsina (AA) operations. We first introduce certain novel AA operations of Ct-SFSs, such as the AA sum, AA product, AA scalar multiplication, and AA scalar power. Subsequently, we propound a series of complex t-spherical fuzzy averaging and geometric aggregation operators to efficiently aggregate complex t-spherical fuzzy data. In addition, we explore the different characteristics of these operators, discuss certain peculiar cases, and prove their fundamental results. Thereafter, we utilize these operators and propose entropy measures to frame a methodology for dealing with complex t-spherical fuzzy decision-making problems with unknown criteria weight data. Fina...
Making decisions are very common in the modern socio-economic environments. However, with the inc... more Making decisions are very common in the modern socio-economic environments. However, with the increasing complexity of the social, today’s decision makers (DMs) face such problems in which they hesitate and irresolute to provide their views. To cope with these uncertainties, many generalizations of fuzzy sets are designed, among them dual hesitant fuzzy set (DHFS) is quite resourceful and efficient in solving problems of a more vague nature. In this article, a novel concept called proportional dual hesitant fuzzy set (PDHFS) is proposed to further improve DHFS. The PDHFS is a flexible tool composed of some possible membership values and some possible non-membership values along with their associated proportions. In the theme of PDHFS, the proportions of membership values and non-membership values are considered to be independent. Some basic operations, properties, distance measure and comparison method are studied for the proposed set. Thereafter, a novel approach based on PDHFSs is...
Abstract The uncertain probabilistic linguistic term set (UPLTS) one of the modern development in... more Abstract The uncertain probabilistic linguistic term set (UPLTS) one of the modern development in fuzzy set theory, can express not only the decision makers (DMs) linguistic assessment information but also the uncertain probability/weight/importance degree of each linguistic assessment value, so it is an efficient tool for addressing the ignorance problems. The current study mainly focuses on developing a more effective way to cope with multiple criteria group decision making (MCGDM) problems in which the assessment information are in the form of UPLTSs, and the weight information is also entirely unknown. Firstly, some weaknesses of the existing operational laws and score function of UPLTSs are pointed out through some critical examples and then redefined them to overcome existing flaws in order to acquire more accurate results in practical decision making problems. Also, we establish various properties of the revised operational laws along with proofs. To design a novel comparison method, the concept of deviation degree is introduced in order to accommodate the situation in which two different UPLTSs have the same score values. After that, based on the proposed operational laws, several existing aggregation operators are modified, and a novel aggregation operator, namely uncertain probabilistic linguistic simple weighted geometry (UPLSWG) operator is designed. Meanwhile, some interesting properties of these proposed operators are carefully analysed. Furthermore, an entropy technique under uncertain probabilistic linguistic information is structured for computing the completely unknown weights of criteria. Following this, a new extension of weighted aggregated sum product assessment (WASPAS) method called uncertain probabilistic linguistic-WASPAS (UPL-WASPAS) methodology based on the proposed aggregation operators is studied under the UPLTS context for ranking objects in MCGDM problems. To show the applicability and potentiality of the developed method, an example of supplier selection is addressed, and a detailed performance comparison analysis is conducted. Furthermore, sensitivity analysis is also made to determine the impact of the parameter on the ranking of alternatives.
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