Logic Connectives for Soft Sets and Fuzzy Soft Sets

Ali, Muhammad Irfan; Shabir, Muhammad

doi:10.1109/tfuzz.2013.2294182

Cited by 36 publications

(12 citation statements)

References 41 publications

(43 reference statements)

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“…Feng and Li 21 ascertained the relationships among five different types of soft subsets, and revealed some nonclassical algebraic properties of soft sets. Ali and Shabir 22 investigated logic connectives for both soft sets and fuzzy soft sets. It should be noted that fuzzy sets, rough sets, and soft sets are closely related soft computing models 23‐25 .…”

Section: Introductionmentioning

confidence: 99%

Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

et al. 2020

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The notion of intuitionistic fuzzy soft sets (IFSSs) provides an effective tool for solving multiple attribute decision making with intuitionistic fuzzy information. The most crucial issue in decision making based on IFSSs is how to derive the ranking of alternatives from the information quantified in terms of intuitionistic fuzzy values. In this study, we propose a new extension of the preference ranking organization method for enrichment evaluation (PROMETHEE), by taking advantage of IFSSs. In addition to presenting a myriad of new notions, such as intuitionistic fuzzy membership (or nonmembership) deviation matrices, intuitionistic fuzzy membership (or nonmembership) preference matrices, and aggregated intuitionistic fuzzy preference matrices, we put more emphasis on the construction of three distinct preference structures and related utility functions on the corresponding weakly ordered sets by considering the positive, negative, and net flows of the alternatives based on the aggregated intuitionistic fuzzy preference matrix. We present a new algorithm for solving multiple attribute decision-making problems with the extended PROMETHEE method based on IFSSs. Moreover, a benchmark problem concerning risk investment is investigated to give a comparative analysis and show the feasibility of our approach. K E Y W O R D S decision making, intuitionistic fuzzy set, outranking, PROMETHEE, soft set | INTRODUCTIONDecision making is a ubiquitous activity in daily life, which can be seen as a process of ranking a collection of alternatives or selecting the optimal one(s) from them based on the provided decision information. Multiple attribute decision making (MADM) refers to the decisionmaking process in which alternatives are evaluated by virtue of several attributes, reflecting the performance of alternatives from independent perspectives. In the MADM process, it is of vital importance to reconcile the contradictory goals, make decisions with many criteria, and strive for compromise solutions. 1 Up to now, researchers around the world have paid much attention to MADM problems and have attained fruitful results in diverse aspects. 2 For instance, Liu et al 3 proposed a model for evaluating and selecting a transport service provider based on singlevalued neutrosophic numbers. Using linguistic neutrosophic numbers, Pamučar et al 4 presented an enhanced combinative distance-based assessment (CODAS) decision-making approach and a pairwise model for determining the weights of criteria. Pamučar et al 5 defined the normalized weighted geometric Bonferroni mean operator of interval rough numbers and developed a hybrid decision-making method involving interval rough decision-making trial and evaluation laboratory (DEMATEL) and complex proportional assessment (COPRAS) models. With the integrated use of the full consistency method (FUCOM) and fuzzy multiattributive border approximation area comparison (MABAC) method, Božanić et al 6 developed a decision-making model for selecting the most favorable location in single-span Baile...

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Section: Introductionmentioning

confidence: 99%

Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

et al. 2020

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“…They further combined soft sets with intuitionistic fuzzy sets, and brought forth the notion of intuitionistic fuzzy soft sets in [18]. In addition, soft sets and their extensions have been successfully applied to algebra [19][20][21][22], data analysis [11,23], decision making [24][25][26][27][28][29][30], graph theory [31] and mathematical logic [32].…”

Section: Introductionmentioning

confidence: 99%

Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

et al. 2019

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Intuitionistic fuzzy multiple attribute decision making deals with the issue of ranking alternatives based on the decision information quantified in terms of intuitionistic fuzzy values. Lexicographic orders can serve as efficient and indispensable tools for comparing intuitionistic fuzzy values. This paper introduces a number of lexicographic orders by means of several measures such as the membership, non-membership, score, accuracy and expectation score functions. Some equivalent characterizations and illustrative examples are provided, from which the relationships among these lexicographic orders are ascertained. We also propose three different compatible properties of preorders with respect to the algebraic sum and scalar product operations of intuitionistic fuzzy values, and apply them to the investigation of compatible properties of various lexicographic orders. In addition, a benchmark problem regarding risk investment is further explored to give a comparative analysis of different lexicographic orders and highlight the practical value of the obtained results for solving real-world decision-making problems.

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“…The soft set theory is combined with fuzzy and IFS theories to develop fuzzy soft set, 16 intuitionistic fuzzy soft set. 17,18 In references 19,20 the operations on fuzzy soft sets are developed. The soft set and fuzzy soft set in an incomplete environment are proposed in Zou et al 21 Both fuzzy and intuitionistic fuzzy soft sets have seen wide applications in MCDM.…”

Section: Introductionmentioning

confidence: 99%

Soft information set for multicriteria decision making

Aggarwal

2019

Int J Intell Syst

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An information source value is perceived differently by different agents. In this paper, we present a new knowledge representation structure, termed as soft information set (SIS), to provide a parameterized representation of the information values, as perceived by an agent. The properties of SIS are investigated and the notion of relations in SIS is devised. The significance of the proposed SIS in aiding multi criteria decision making is illustrated through real case‐studies.

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Logic Connectives for Soft Sets and Fuzzy Soft Sets

Cited by 36 publications

References 41 publications

Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

Soft information set for multicriteria decision making

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