scholarly journals Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Jian Tang ◽  
Xiangyun Xie ◽  
Yanfeng Luo
Keyword(s):  
Fuzzy Set ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
New Type ◽  
Interval Valued

The concept of non-k-quasi-coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the non-k-quasi-coincidence of a fuzzy point with a fuzzy set. By using this new concept, we introduce the notion of interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and study their related properties. In addition, we also introduce the concepts of prime and completely semiprime interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals of ordered semigroups and characterize bi-regular ordered semigroups in terms of completely semiprime interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals. Furthermore, some new characterizations of regular and intra-regular ordered semigroups by the properties of interval valued(∈¯,∈¯∨qk~¯)-fuzzy quasi-ideals are given.

BI-IDEALS OF ORDERED SEMIGROUPS BASED ON THE INTERVAL-VALUED FUZZY POINT

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Hidayat Ullah Khan ◽  
Nor Haniza Sarmin ◽  
Asghar Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Fuzzy Set Theory ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
Interval Valued ◽  
Real World Problems

Interval-valued fuzzy set theory (advanced generalization of Zadeh's fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, we introduce the notion of generalized quasi-coincident with () relation of an interval-valued fuzzy point with an interval-valued fuzzy set. In fact, this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. Applying this newly defined idea, the notion of an interval-valued -fuzzy bi-ideal is introduced. Moreover, some characterizations of interval-valued -fuzzy bi-ideals are described. It is shown that an interval-valued -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. Finally, the concept of implication-based interval-valued fuzzy bi-ideals, characterizations of an interval-valued fuzzy bi-ideal and an interval-valued -fuzzy bi-ideal are considered. 

Regular (ϵ,ϵνqk) - Fuzzy Duo Ordered Semigroups

2013 ◽  
Vol 756-759 ◽  
pp. 3084-3088
Author(s):  
Qi Cheng ◽  
Feng Lian Yuan ◽  
Yun Qiang Yin ◽  
Qing Yan Chen
Keyword(s):  
Fuzzy Set ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
Fuzzy Ideal ◽  
Characterization Theorems ◽  
The Ideal

In this paper, the ideal of quasi-coincidence of a fuzzy point with a fuzzy set is generalized and the concept of an - fuzzy ideal (bi-ideal, quasi-ideal) of an ordered semigroup is introduced. The the notion of - fuzzy duo ordered semigroups is introduced and some characterization theorems are presented in terms of - fuzzy ideals.

scholarly journals New fuzzy generalized bi Γ-ideals of the type (∈,∈∨qk) in ordered Γ-semigroups

2017 ◽  
Vol 13 (4) ◽  
pp. 6666-670
Author(s):  
Ibrahim Gambo ◽  
Nor Haniza Sarmin ◽  
Hidayat Ullah Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Characteristic Function ◽  
Real Number ◽  
Fuzzy Set ◽  
Unit Interval ◽  
Membership Functions ◽  
Fuzzy Subset ◽  
Ordered Semigroups ◽  
The Past ◽  
Fuzzy Point

A fuzzy subset A defined on a set X is represented as A = {(x, A (x), where x ∈ X}. It is not always possible for membership functions of type λA : X → [0,1] to associate with each point x in a set X a real number in the closed unit interval [0,1] without the loss of some useful information. The importance of the ideas of “belongs to” (∈) and “quasi coincident with” (q) relations between a fuzzy point and fuzzy set is evident from the research conducted during the past two decades. Ordered Γ-semigroup (generalization of ordered semigroups) play an important role in the broad study of ordered semigroups. In this paper, we provide an extension of fuzzy generalized bi Γ-ideals and introduce (∈,∈∨qk)-fuzzy generalized bi Γ-ideals of ordered Γ-semigroup. The purpose of this paper is to link this new concept with ordinary generalized bi Γ-ideals by using level subset and characteristic function.

Multi-Criteria Decision Making Methods Based on Interval-Valued Intuitionistic Fuzzy Sets

2014 ◽  
Vol 22 (03) ◽  
pp. 469-488 ◽  
Author(s):  
Chunqiao Tan ◽  
Benjiang Ma ◽  
Desheng Dash Wu ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Evaluation Function ◽  
Score Functions ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Point ◽  
Decision Making Problem ◽  
Interval Valued

Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy set is used to capture fuzziness in multi-criteria decision making problems. The purpose of this paper is to develop a new method for solving multi-criteria decision making problem in interval-valued intuitionistic fuzzy environments. First, we introduce and discuss the concept of interval-valued intuitionistic fuzzy point operators. Using the interval-valued intuitionistic fuzzy point operators, we can reduce the degree of uncertainty of the elements in a universe corresponding to an interval-valued intuitionistic fuzzy set. Then, we define an evaluation function for the decision-making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision-maker's requirement. Furthermore, a series of new score functions are defined for multi-criteria decision making problem based on the interval-valued intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.

Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals

2016 ◽  
Vol 25 (2) ◽  
pp. 297-318
Author(s):  
Hidayat Ullah Khan ◽  
Nor Haniza Sarmin ◽  
Asghar Khan ◽  
Faiz Muhammad Khan
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Decision Making Process ◽  
Ordered Semigroup ◽  
New Approach ◽  
Ordered Semigroups ◽  
Applied Fields ◽  
Interval Valued

AbstractSeveral applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of (α,β)-fuzzy interior ideal. This new concept is called interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy ideals and interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals of an ordered semigroup is also an interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal.

scholarly journals Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 949
Author(s):  
Zhen Li ◽  
Xiaoyan Zhang
Keyword(s):  
Information Theory ◽  
Pattern Recognition ◽  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Fuzzy Set ◽  
Equivalence Relation ◽  
Target Concept ◽  
Actual Case ◽  
Interval Valued

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

scholarly journals Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 145
Author(s):  
Yun Jin ◽  
Zareena Kousar ◽  
Kifayat Ullah ◽  
Tahir Mahmood ◽  
Nimet Yapici Pehlivan ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Evaluation Process ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Membership Degree ◽  
Operational Laws ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

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